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HORIZONS User Manual
Version 3.75 (April 4, 2013)

Table of Contents


INTRODUCTION

PURPOSE:

The JPL Horizons On-Line Ephemeris System provides easy access to key solar system data and flexible production of highly accurate ephemerides for solar system objects. This includes 611,000+ asteroids, 3200 comets, 176 natural satellites, all planets, the Sun, 60+ spacecraft, and several dynamical points such as Earth-Sun L1, L2, L4, L5, and system barycenters. Users may also define their own objects, then use the system to integrate the trajectory, or conduct parameter searches of the comet/asteroid database, searching on combinations of up to 42 different parameters. Rise, transit and set may be identified to the nearest minute. Close-approaches by asteroids and comets to planetary bodies (and Ceres, Pallas, and Vesta) can be rapidly identified along with the encounter uncertainties and impact probabilities. Orbit uncertainties can be computed for asteroids and comets.

More than 100 different observational and physical aspect quantities can be requested at intervals for both topocentric and geocentric situations in one of 9 coordinate systems and 4 time scales (CT, TT, UT, Civil). Over 1500 Earth station locations are on file, along with several on other major bodies, in addition to spacecraft "observer sites". Users may search for or define topocentric site coordinates on any planet or natural satellite (with known rotational model), if the desired site is not predefined. Output is suitable for observers, mission planners and other researchers, although this determination is ultimately the users' responsibility.

Five types of customizable output can be requested:

  1. Observables (RA/DEC, Az/El, physical aspect, angles, etc.)
  2. Osculating elements
  3. Cartesian state vectors
  4. Close approaches to planets (and Ceres, Pallas, and Vesta)
  5. SPK binaries (asteroids and comets only)

The first four are ASCII tables. Output is returned to the user via e-mail, FTP or Kermit protocols. Table output can be requested in a format suitable for spreadsheet import. SPK file output allows user programs to reproduce the integrated target state at any instant. The SPK files can be used by existing visualization, animation and mission-design software.

The underlying planet/satellite ephemerides and small-body osculating elements are the same ones used at JPL for radar astronomy, mission planning and spacecraft navigation.

OVERVIEW OF USAGE:

There are three different ways to access the program:
  • Telnet (full access, active interactive prompt-based interface):
    1. Telnet directly to the system (telnet ssd.jpl.nasa.gov 6775). No account or password is required.
    2. Specify an object to get a summary data screen.
    3. Follow prompts. At any prompt, type ? or ?! for short and long explanations.
    4. Transmit results to your system by e-mail, FTP or Kermit


  • E-mail (full access, except for SPK file production, batch interface):
    1. Send e-mail to "horizons@ssd.jpl.nasa.gov" with subject "BATCH-LONG".
    2. An example command file will be mailed back to you.
    3. Edit this text file, then mail it back with the subject header "JOB".
    4. Results of your request are mailed back to you.


  • Web (partial access, passive interactive GUI interface):
    1. Point your browser to http://ssd.jpl.nasa.gov/horizons.cgi

The Horizons system was intended to be easy to use and should have a step-function learning curve. The remainder of this documentation summarizes system capabilities, but is not necessary for successful use.

While using the telnet system, type "?" or "?!" at any prompt for an explanation of options. See ACKNOWLEDGEMENTS section for contact information.


CONNECTING TO THE SYSTEM

TELNET:

The Horizons on-line ephemeris and data system is available as a telnet service. This is suitable for people who want full access to all program features in an interactive prompt-based way. From a telnet-capable machine, running a "VT100" type terminal emulation, telnet to "ssd.jpl.nasa.gov 6775":

From Unix command line:

telnet ssd.jpl.nasa.gov 6775
... where 6775 is a port number. Alternatively, from within a web-browser, enter the URL:
telnet://ssd.jpl.nasa.gov:6775

The system will start a terminal session automatically. No user-ID or password is required. If your connection is refused, there are two possible causes:

  1. The port number wasn't specified or passed along. A few PC-type telnet programs do not to fully implement the telnet protocol and may not pass the port number to the network, or may need to be reconfigured to function properly or may have a different syntax for specifying port numbers. Consult your user's guide for information.
  2. Firewall/security restriction at your end. Please contact your local computer system administrator in this case. Since no password or security information is exchanged, you may be able to request a firewall exception from your institution.

Once you connect, the system will attempt to determine your window size. If it cannot, it will default to a 24 row by 79 column screen display. If this is inappropriate, and your display paging is choppy, manually set your screen size by using the command "TTY {rows} {columns}", where {rows} and {columns} are replaced by appropriate integers.

Window sizes less than 79 columns aren't recommended since data-screen displays are formatted with that minimum size in mind and will be difficult to read on something smaller.

Access may be automated. Example scripts may be found in the anonymous FTP directory ftp://ssd.jpl.nasa.gov/pub/ssd, and include:

   Automate SPK file production:
    ftp://ssd.jpl.nasa.gov/pub/ssd/smb_spk

   Automate observer table production:
    ftp://ssd.jpl.nasa.gov/pub/ssd/obs_tbl
    ftp://ssd.jpl.nasa.gov/pub/ssd/obs_tbl.inp (sample input file for 'obs_tbl')

   Automate osculating element table production:
    ftp://ssd.jpl.nasa.gov/pub/ssd/osc_tbl
    ftp://ssd.jpl.nasa.gov/pub/ssd/osc_tbl.inp (sample input file for 'osc_tbl')

WEB:

Point your browser to http://ssd.jpl.nasa.gov/horizons.cgi. This graphical interface is intended for the more casual user or general public and now offers access to most (but not all) program features using pull-down menus, fill-in boxes and buttons to click. Verify default settings for time and coordinate systems are as intended for the run.

E-MAIL:

The program can also be controlled by sending e-mail messages to the address "horizons@ssd.jpl.nasa.gov". Response is determined by the subject of the message. This option is for those who want access to most program features without the overhead of answering prompts or manipulating graphical interfaces; generally those already familiar with what the program does and who know what they want. It has the additional capability of allowing users to specify up to 10000 discrete times (to aid astrometric reduction) and up to 200 objects at once. It does not allow SPK file production available via telnet.

To get started, send e-mail to the above address with the subject "BATCH-LONG". The latest, fully-commented example run-stream will be mailed back. Edit this file to produce the results you want, then mail back with the subject "JOB". Recognized e-mail subject commands are:

    SUBJECT HEADER  MEANING
    --------------  -----------------------------------------------------------
    JOB             Horizons run-stream
    DOC-TEXT        Request ASCII (plain-text) version of current documentation
    DOC-PS          Request PostScript version of current documentation
    BATCH-LONG      Request latest fully commented example batch file
    BATCH-BRIEF     Request latest example batch file without comments
    QUESTION        Message forwarded to cognizant engineer

GENERAL DEFINITIONS

The remainder of this document uses these abbreviations and terms. Understanding their meaning will help you properly interpret program documentation and output.

RA
Right ascension; the angular distance on the celestial sphere eastward along the celestial equator from the reference equinox to the meridian of the object. RA is analogous to longitude, with the plane containing the equinox defining zero RA much as the Greenwich meridian defines zero longitude. Expressed in units of hours, minutes and seconds or degrees, as requested.

DEC
Declination; the angular distance on the celestial sphere north (positive) or south (negative) of the celestial equator. It is analogous to latitude. Usually expressed in degrees.

AZ
Azimuth; the angle measured eastward along the "horizon" (the plane perpendicular to the local zenith) from the North to the point where the meridian passing through local zenith and the object intersects the horizon plane.

EL
Elevation; the angular distance above or below the plane perpendicular to the local zenith. Note this plane is not necessarily the visible horizon, due to station elevation ("horizon dip" effect).

Geometric coordinates
Referred to the mean equator and equinox of a particular reference frame (ICRF/J2000 or FK4/B1950.0). Geometric coordinates are the true, or instantaneous states of a body at a particular ephemeris time.

Astrometric coordinates
Accounts for the finite but varying amount of time it takes light to travel from the target to the observer and is expressed with respect to the mean equator and equinox of a particular reference frame (ICRF or FK4/B1950.0).

Apparent coordinates
Takes into account factors which appear to change target position with respect to the background stars and inertial coordinate system: light-time, stellar aberration, the relativistic deflection of light. Usually, a final rotation to some "of-date" coordinate system is performed, such as precession-nutation to the Earth's true-equator and equinox-of-date.

Refracted coordinates
Apparent coordinates approximately corrected for atmospheric refraction. Available only for Earth-based sites.

Small body
Refers to a comet or asteroid for which the trajectory is integrated from orbital elements. Typically no cartographic coordinate system is available, with the exceptions, so far, being Gaspra and Ida.

Major body
Refers to a planet, natural satellite, spacecraft or the Sun. Only major bodies can be coordinate centers (observing sites). In special cases, a comet or asteroid can be redefined as a "major body", such as a spacecraft encounter, where it is desirable to generate an ephemeris of the approaching spacecraft as seen from the target. State vectors are interpolated from previously defined ephemerides, such as DE-405, which are stored as Chebyshev coefficients. Interpolation recovers the state to mm level.

Target body
Refers to the object of interest, selected by the user. It can be a major-body or small-body.

Primary body
Refers to closest body about which a target body orbits. For natural satellites, this would be a planet, although they orbit the Sun as well. For planets and small-bodies, the primary body is the Sun.

OBJECT SELECTION

After connecting by telnet, the primary thing one has to learn to to use Horizons effectively is how to select objects. You will be prompted for everything else.

There are two categories of objects to select:

1. MAJOR BODIES
defined as planets, natural satellites, spacecraft, and "special cases"
2. SMALL BODIES
comets and asteroids.

This division is a result of the objects being stored differently as far as the system is concerned. Major bodies are represented in pre-computed trajectory files which are interpolated very accurately to retrieve position and velocity at any instant. Small-bodies have their position and velocity at one instant compactly stored in a database and are then numerically integrated "on-the-fly" by Horizons to other times of interest (also very accurately), using all known physics.

When an object is specified, the request is first examined for "keywords" that tell the system more about what is wanted. If there aren't any keywords, the system will then try to match against the major body list. If no match is found among the major bodies, it will then match against the small-body database.

For example, if you simply input "Io", it will return a list of matches from among the major bodies, including the moon of Jupiter, and then stop, waiting for a unique specification that matches just one object. To uniquely specify Io, enter it's IAU number, "501", which was displayed on the previous list of multiple matches.

To instead select the small-body named Io, provide more information by specifying it one of these ways:

   Horizons> Io;        (semi-colon tells Horizons its a small-body look-up)
   Horizons> 85         (no match on major body [at least right now], so
                         search "falls through" to small-body number look-up)
   Horizons> 85;        (semi-colon tells Horizons its a small-body look-up)
   Horizons> NAME= Io   (Keyword "NAME" tells Horizons its an asteroid or
                         comet small-body look-up)
   Horizons> ASTNAM= Io (Keyword "ASTNAM" tells Horizons its an asteroid name)

Further details, discussion, and examples follow.

MAJOR BODIES

Type 'MB' to get a list of all major-body strings that can be used to search on. To select a major body, enter one of the following:

  1. A string to search on ("Mars" or "Trit"). Case insensitive.
  2. A JPL ID integer code or fragment
  3. An IAU code

Examples (at the main prompt):

     Horizons> mars bary (uniquely select Mars center; '4' does the same)
     Horizons> mars  (list all major bodies with 'mars' in an ID field)
     Horizons> 501   (uniquely select Io)
     Horizons> N*    (list all major bodies with 'n' in an ID field)

Major planets may have two integer ID's assigned. Those >100, ending in 99 (such as 199, 299, 399, etc.) refer to planet CENTERS. To select planet SYSTEM BARYCENTERS, use the codes less than 10 (1, 2, 3). For example, "399" is the Earth's center, '3' is the Earth-Moon Barycenter and "301" is the center of the Moon. For Mercury, Venus and Mars, there is no significant difference between planet-center and system barycenter (1=199, 2=299, 4=499, as far as Horizons selection is concerned).

If a planet name is entered, it may not be considered unique if a distinct system barycenter is present. For example, if "Saturn" is entered, a list containing "Saturn" and the "Saturn Barycenter" will be returned. To specify Saturn (the planet-center), you must use its unique ID code, "699".

System barycenters are available over longer time-spans than planet-centers because planet-centers are defined by satellite solutions. These satellite solutions are based on shorter data arcs than the entire system and can therefore be extrapolated only over shorter time-spans. For example, the planet Jupiter (599) might be available over the interval 1600-2500, while the Jupiter system barycenter (5) is available over 3000 B.C. to A.D. 3000.

Horizons can also compute ephemerides for surface points on extended, rotating target bodies: Moon, Sun, planets, natural satellites, and body with a defined rotational model.

Surface Targets:

To specify an arbitrary target point on the surface of a major body having a defined shape and rotation model, the most general target specification form allows two types of coordinate-type inputs, both in units of degrees and km:

  Geodetic/planetographic coordinatess:

           {g: E.Long, latitude, h@}BODY  

  Or, in cylindrical coordinates: 

           {c: E.Long,     DXY, DZ@}BODY

... where the brackets {} indicate optional components of the general specification.

For example, while "301" specifies the target to be the center of the Moon, and "Apollo 11 @ 301" specifies the Apollo 11 landing site as target, the following ....

            g: 348.8, -43.3, 0 @ 301

... specifies the crater Tycho on the Moon (body 301), at geodetic (planetographic) coordinates 348.8 degrees east longitude, -43.3 degrees latitude (south), and zero km altitude with respect to the IAU reference triaxial ellipsoid surface.

To alternatively input cylindrical coordinates, DXY is distance from the spin axis in the body equator plane in km, DZ is distance above (+) or below (-) that plane, also in km.

When a surface target is specified, two new markers are placed in observer table output. They indicate if the point on the target surface is lit (by the Sun) and if it is on the near or far-side of the target body relative to the observer.

Altered descriptions are printed at the end of the tables as necessary to describe the output.

SMALL BODIES

To select an asteroid or comet, enter a list of parameters to search on SEPARATED BY A SEMI-COLON (;). TYPE 'SB' FOR LIST OF 42 FIELD KEYWORDS THAT CAN BE MATCHED, or see list later in this document. Match symbols are from the set { >, <, <>, = }.

For example, "A < 2.5; IN > 7.8; STYP = S, GM <> 0; " searches for all S-type small-bodies with semi-major axis less than 2.5 au and inclination greater than 7.8 degrees with a known (non-zero) GM. Spaces in the command are not considered, nor are upper/lower-case distinctions.

Exceptions are object names and designations. Name searches consider spaces. Designation searches consider spaces AND upper/lower-case. If you want to match a fragment of a name or designation, end it with a '*' (e.g. DES = 1993*;). Otherwise, it is assumed a complete name or designation is specified and the search must match exactly and completely.

For example:

     NAME = CERES;   (matches only if object name is "Ceres")
     NAME = CER*;     (match "Ceres", "Lucerna", "Cicero", etc.)

The same keyword can be used more than once in a search command. For example, "IN >10; IN < 20;" will list those objects possessing an inclination between 10 and 20 degrees. If the directive "LIST;" is in the search request, the matched parameters will be displayed. For example, "IN > 150; LIST" will display the inclination of each object with inclination greater than 150 degrees.

Once a small-body is uniquely identified, a screen of data will be displayed. If more than one small-body matches given parameters, a list of matching objects is displayed. Individual objects from the matched list can then be requested by giving the displayed "record number", followed by a semi-colon.

The semi-colon is used to indicate a small-body request and resolve number ambiguities. For example, entering '1' will select Mercury Barycenter. Enter '1;' to retrieve the small-body in record #1 (Ceres).

Osculating elements for more than one comet apparition may be listed ("apparition" refers to a particular perihelion passage), since out-gassing near perihelion can alter the orbit for each passage. Select an apparition from the list with the closest epoch prior to the date of interest for the ephemeris, or add the "CAP" directive to the search to automatically select the closest apparition of interest:

     CAP;         (return last apparition before current date)
     CAP < JD#;   (return last apparition before specified Julian Day Number)
     CAP < YEAR;  (return last apparition before given integer year)

If the number after a '<' is less than 10000, it is assumed to be a year integer. Otherwise, the number is taken to be a Julian Day Number. If "CAP;" is specified, the search is automatically recognized as being a comets-only search.

The record (or file) number of unnumbered asteroids and comet apparitions should NOT be considered constants; they WILL change as the database is updated.

To enter your own heliocentric ecliptic elements, type ";". This capability is described in more detail in a later section.

Example queries follow. Where more than one example is given, the first is most likely to complete as intended. For example, "ASTNAM = Vesta;" will always return the asteroid while, if you use the convenient form "Vesta", it's possible that a future natural satellite name will someday include that string and there will no longer be a unique match. A good habit might be to include at least one semi-colon in all small-body searches to be clear when you are looking for a comet or asteroid.

 Search for objects matching a set of parameters:
   Horizons> A < 2.5; IN > 7.8; STYP = S; GM <> 0;       (asteroid & comets)
   Horizons> A < 2.5; IN > 7.8; STYP = S; GM <> 0; AST;  (asteroids only)
   Horizons> A < 2.5; IN > 7.8; STYP = S; GM <> 0; COM;  (comets only)

 Match by name:
   Horizons> ASTNAM= Vesta;
   Horizons> Vesta;
   Horizons> Vesta

 Match by name fragment:
   Horizons> NAME= all*;
   Horizons> all*;

 "Wildcard" match designation:
   Horizons> DES = 1993*; (Objects with designations containing 1993)
   Horizons> 1993*;
   Horizons> 1993*

  NOTE: The '*' must be at the end. It toggles searches on sub-strings of
        characters and is not a true positional wildcard. For example,
        '19*3;' is not a recognized search.

 Match exact designation:
   Horizons> DES= 1990 MU;
   Horizons> 1990 MU;
   Horizons> 1990 MU

 Select numbered asteroid:
   Horizons> 1;                    (Object in database record #1 ["1 Ceres"])

 Define an arbitrary object not in database
   Horizons> ;

 Comet searches:
   Horizons> COMNAM= HER*;         (Comet names (only) containing "her")
   Horizons> DES= 73P;             (Request comet 73P apparitions, including
                                    fragments, if any)
   Horizons> DES= 73P; NOFRAG      (Request apparitions of comet 73P,
                                    excluding fragments)
   Horizons> DES= 73P; CAP         (Request comet 73P apparition solution
                                    closest to present date, including any
                                    fragments)
   Horizons> DES= 73P; NOFRAG; CAP (Request comet 73P apparition solution
                                    closest to present date, excluding any
                                    fragments)
   Horizons> COM; NOFRAG; CAP      (List the apparition solutions closest to
                                    to the present date for all comets,
                                    excluding fragments)
   Horizons> NAME=Halley;CAP<1690; (Request last Halley apparition prior to
                                     the year 1690)

SPACECRAFT TRAJECTORIES IN HORIZONS

Horizons was generally intended to make the natural-body dynamics work of the JPL Solar System Dynamics Group accessible to astronomers and mission planners. However, it is often convenient to make spacecraft trajectory information available through the same mechanism, especially for space-based telescopes.

Sources of the spacecraft trajectory data in Horizons include navigation teams at JPL, flight projects at other NASA centers, ESA, as well as TLE-based orbits from the Joint Space Operations Center (JSOC).

While Horizons will always have the latest comet/asteroid/natural satellite solutions, keeping current with the externally produced spacecraft trajectories is problematic; there is no mandate or funding or staff for this, and maneuvers and mission planning changes can occur without notification.

Some flight projects do set up a regular delivery schedule to keep Horizons current (some mission science teams use Horizons for planning). More typically, a spacecraft is added if its inclusion is requested by a researcher with a specific need. The flight project might provide on request an initial planning trajectory prior to launch and a final historical trajectory after end of mission.

This is often sufficient for spaceraft in interplanetary phases, since the spacecraft are maneuvered to such reference trajectories, which are often designed years in advance.

However, spacecraft trajectories can get 'orphaned' in Horizons if updates stop happening. Always check the revision date in the upper left corner of the Horizons spacecraft datasheet to determine the last time the spacecraft's trajectory was updated, and read the data-sheet comments for mission status information.

Spacecraft in low Earth orbit in particular (such as ISS, HST, Swift, GALEX) need frequent updates to maintain high accuracy. Predicts more than a few days into the future can have 10s or 100's of km of error. If more accurate predicts are needed, and the last update was more than a few days ago, an update to Horizons can be done on request.

For interplanetary missions, users having high-precision applications (such as mission data reduction) should contact JPL Solar System Dynamics to verify the status of the specific trajectory in Horizons if there is doubt as to the available trajectory's revision status:

       Donald.K.Yeomans@jpl.nasa.gov (Supervisor, 818-354-2127) 
       Jon.D.Giorgini@jpl.nasa.gov   (SSDG analyst)

Some archival mission trajectories are available. These spacecraft trajectories are often expressed relative to older, target-body trajectories such that multi-km offsets can appear if output is instead requested relative to a modern target-body trajectory. This is because the modern solutions are derived from different measurement datasets and dynamical models (planetary ephemerides), introducing inconsistencies.

To avoid this, Horizons usually includes the original mission-target ephemeris to permit consistent reconstruction with the archived spacecraft trajectory.

For example, the NEAR spacecraft trajectory during the Eros mapping phase was expressed relative to the asteroid Eros within the dynamical system of the DE200 planetary ephemeris, and has not been updated, while Eros' trajectory is now expressed in Horizons relative to the Sun in the system of the DE405 planetary ephemeris.

To obtain the historically accurate position of NEAR with respect to Eros as it was during the mission, select the archived Eros trajectory along with the archived NEAR trajectory. How to do this is explained in the Horizons data-sheet for NEAR, but amounts to specifying the SPK ID of the archived target body instead of integrating it from the database of orbital elements.

For example, to obtain ....

         1) NEAR wrt historical Eros orbit solution (#177): 
             Specify target as "NEAR" with observing center "@2000433"

         2) NEAR wrt current Eros orbit solution:
             Not available

         3) Eros historical orbit solution (#177) wrt to NEAR:
             Specify target as "2000433" with observing center "@NEAR"

         4) Eros current orbit solution wrt NEAR (offset wrt to historical):
             Specify target as "Eros;" or "2000433;", observing center "@NEAR"

COORDINATE CENTER (OBSERVING SITE) SELECTION

While osculating element tables may be generated with respect to a major body center only, vector and observer tables may produce output with respect to an arbitrary observing site, defined with respect to a major body center.

EARTH SITES

For the Earth, a list of 750+ sites is predefined. The list generally matches that of the Minor Planet Center, expanding on radar sites (which have negative ID numbers on this system) as necessary. Station "500" is the geocenter.

NON-EARTH SITES

For the Earth, a list of 1500+ sites is predefined. The list generally matches that of the Minor Planet Center while expanding on radar sites (which have negative ID numbers on this system) as necessary. Station "500" is the geocenter.

USING A PREDEFINED SITE

There are several equivalent ways of specifying an observing location. The most general form is ...

                                 site @ body

... where "site" is a numeric code or name fragment to match, and "body" is a numeric major body code or name fragment to match. A list of such major body codes follows later in this document.

Here are four equivalent ways of searching for the same Earth location:

     Code         Meaning
     -----------  -------------------------------------------------------------
     675@399      Site #675 on Earth (Palomar Mountain)
     palomar@399         "
     675@                "
     Palomar             "           (observer table only)

OBSERVER & VECTOR TABLES:

If an observer or vector table has been requested, the "@" symbol may be dropped; the Earth will be assumed if an integer like "675" or a name fragment like "Palom" is input. However, if you are trying to specify an observing site not on Earth, you MUST use the "@" symbol for correct interpretation. For example, if an observer table as seen from the Sun is desired, it must be specified as "@10" or "@sun". Specifying "10" only will select the Caussols site.

ELEMENT TABLES:

For an osculating element table, the DIFFERENT assumption is made that a coordinate center request lacking a "@" symbol is a major body. For example, '10' would mean the Caussols site for an observer or vector table, but "Sun" for a vector table. '10@' or '10@399' would mean the Caussols site for both table types.

The different assumptions are meant to be efficient for the particular types of output requested, expediting "typical" usage. However, the full form "site @ body" can always be used to avoid having to remember "quirks".

If your specification returns more than one possible match, the list of matched sites is returned. Refine your site request to be more specific, by using the numeric codes listed, for example, and try again.

While one can spell out the names of the bodies and sites, it is possible unique matches won't be returned. Thus, use the unique ID numbers when known. For example, "675@Earth" will first look for the body, match both the Earth & Earth-Moon barycenter, thus have to quit before finding specific Palomar site coordinates. "675@399" is unique and avoids this problem. Spaces & upper/lower case are ignored.

Here are examples for sites on bodies other than the Earth:

     Code         Meaning
     ------------ -------------------------------------------------------------
     Viking@499   List all defined Viking lander sites on Mars
     Viking 1@499 Select Viking 1 landing site on Mars
     1 @301       Site #1 on the Moon
     500 @ 501    Io body center
     3 @ 499      Site #3 on Mars 

    The asterisk ('*') can be used to generate lists:

     Code         Meaning
     ------------ -------------------------------------------------------------
       *@301      List all predefined sites on the Moon
       *@Phobos   List all predefined sites on the Martian moon Phobos
       *@399      List all predefined sites on Earth
       *@         List all predefined sites on Earth (observer/vector table)
       *          List all predefined sites on Earth (observer/vector table)
       *          List all major bodies (element table only)
     
    There are a several ways to request a body-centered site for a major body. 
 
     Code         Meaning
     ------------ -------------------------------------------------------------
     500@601      Mimas body center 
     geo@601            " 
       g@601            " 
       g@Mimas          "
     500@Deimos   Deimos body center
     geo          Earth Geocenter
       g@399      Earth Geocenter     

INPUT OF TOPOCENTRIC SITE COORDINATES

Many small or recently discovered natural satellites do not have defined rotation models, thus do not support topocentric site definition. Only body-centered observers can be defined.

However, for sites with IAU rotation models, topocentric sites may be input by the user as follows:

     Code         Meaning
     ------------ -------------------------------------------------------------
      c @ Europa  Request prompting for user location on satellite Europa
     coord @ 502  (same thing) 

After coordinate input is requested, the site location may be entered as either geodetic or cylindrical coordinate triplets, separated by commas:

              GEODETIC (generally this means map coordinates)
                  E-long - Geodetic east longitude (DEGREES)
                  lat    - Geodetic latitude  (DEGREES)
                  h      - Altitude above reference ellipsoid (km)

              CYLINDRICAL
                  E-long - Angle eastward from XZ plane      (DEGREES)
                  DXY    - Distance from Z axis              (KM)
                  DZ     - Height above XY equator plane     (KM)

This system always uses planetographic/geodetic coordinates. This is typically the one used on maps, such as those by the USGS, unless the map says otherwise. In these coordinates, the rotational pole of the body that lies on the positive (north) side of the invariable plane of the solar system (the plane perpendicular to the solar system's angular momentum vector) is called the "north pole".

Northern latitudes are positive, southern are negative. The planetographic latitude takes into account body oblateness and, for a point on the surface, is the angle between the body equatorial plane and the normal to the reference surface at that point. For a point not on the reference surface, the geodetic latitude is the latitude of the point on the reference surface where the normal passes through the point at some altitude (h) above the reference surface.

Prograde (or direct) rotation of a body is rotation eastward, or counter- clockwise, as seen from the north pole. For such bodies, east longitude is measured negatively to the east (0 to -360 degrees) from the prime meridian. Retrograde rotation is rotation clockwise (westward) as seen from the north pole. East longitude is measured positively to the east (0 to 360 degrees) from the prime meridian.

Exceptions are the Earth, Moon and Sun where longitude has historically been measured both east and west of the prime meridian 0 to 180 degrees. Though these bodies are direct rotators, longitude is nonetheless measured positively to the east on this system, 0 to 360 degrees, due to historical precedence. If the positive west longitude of a site on these 3 bodies is given, it should be input here as positive east longitude, which would be (360 - West Longitude). If the negative east longitude is given instead, for these exceptions only, one can input the negative east longitude. It will be converted to a positive east longitude on output, however.

The following major bodies are either retrograde or exceptions and require site input with positive east longitude:

       Retrograde (+ east longitude):
       ------------------------------
          Venus (299), Arial (701), Umbriel (702), Titania (703),
          Oberon (704), Miranda (705), Cordelia (706), Ophelia (707),
          Bianca (708), Cressida (709), Desdemona (710), Juliet (711),
          Portia (712), Rosalind (713), Belinda (714), Puck (715),
          Uranus (799), Pluto (999), Charon (901)

       Also + east longitude (prograde exceptions): 
       --------------------------------------------
          Sun (10), Earth (399), Moon (301)

All others are prograde and must be input with negative longitude east of the adopted prime meridian. Since such sites are usually expressed in terms of positive west longitude on maps, negative east longitude would be ...

                           ( West longitude - 360 )

INTERPRETING NON-EARTH OBSERVER TABLES

When placing a site on a body other than the Earth, some definitions become useful:

Visually interfering body:

The largest other body in the system. Such a body may visually complicate observations at the site due to its brightness or by covering up the target. On the Earth, the "interfering body" is the Moon. On Io, it would be Jupiter. On Mars, it would be Phobos (largest body, though unlikely to genuinely interfere). Mercury and Venus have no interfering bodies.

Observer tables provide some optional quantities that can be used to characterize the effect of the interfering body (or IB): how far is the target from the IB in the plane-of-sky, is it obscured by the IB, what fraction of the IB is lit by the Sun as seen from the observing site, and so on.

Deflecting body:

This is the Sun PLUS the most massive object in the planet/satellite system. These two masses are used to compute the relativistic deflection of light that can change the apparent position of the target body.

Other changes:

   REFRACTION

     There are no refraction effects modeled for non-Earth sites. Any request
     for refraction is ignored and the refraction angle will be zero. This 
     affects rise-set determination on non-Earth bodies as well.

   AIRMASS

     There is no airmass model or airmass cut-off available for non-Earth 
     sites. Any request for airmass computation is ignored.

   APPARENT RA & DEC

     The origin of Right Ascension for apparent coordinates on NON-EARTH sites
     with rotational models is the meridian containing the Earth equinox of 
     J2000.0. Apparent declination is with respect to the particular body's 
     true equator-of-date.  This allows an observer to align axes with the pole
     and use the local apparent sidereal time output by this system to set the 
     RA origin and acquire the target.

     For objects lacking a pole & prime meridian rotational model (spacecraft
     and certain asteroids that may have been redefined as "major bodies"),
     the reference frame (ICRF or FK4/B1950.0) coordinate system is used to
     compute apparent places. That is, apparent RA and DEC are defined with
     respect to the Earth mean-equator and equinox of the frame epoch.

   TIME
 
     The print-time output by this system for observer tables (UT or TT) is
     the instantaneous time on Earth and refers to the same instant throughout
     the universe, regardless of where the observer is located. For non-Earth
     sites, UT and TT is not linked to the rotation of the particular body. 
     Local apparent solar time at the observing site can be requested, as can
     the instantaneous light time from Earth to the non-Earth site.

LIMITATIONS OF NON-EARTH/MOON ROTATION MODELS

For bodies outside the Earth-Moon system, precession and nutation effects are usually not known to high accuracy. Thus, the NON-Earth/Moon IAU rotation models, used by this system to determine topocentric site motion relative to the inertial frame as a function of time, are good to about 0.1 degree in the present era.

For the gas giants Jupiter, Saturn, Uranus and Neptune, IAU longitude is based on the "Set III" prime meridian rotation angle of the magnetic field. By contrast, pole direction (thus latitude) is relative to the body dynamical equator. There can be an offset between the magnetic pole and the dynamical pole of rotation.

For many satellites, the official IAU pole direction was simply assumed perpendicular to the body's mean orbit plane, lacking better information. For many satellites in the IAU model, the rotation rate was assumed equal to the mean orbital period.

Some small satellite rotational models are strictly valid only at the time of the Voyager spacecraft flyby; extrapolation to other times is hazardous. Topocentric results for such bodies (610-614, for example) should be used cautiously if at all. Results in these cases reflect only the best available model, which is a suspect one.

As rotation models are refined through observation of surface features by visiting spacecraft (Cassini, etc.), Horizons will be updated to use the best officially sanctioned models available.


OTHER COMMANDS

  Program information:
    MB .............. Show planet/natural-satellite (major-body) ID fields.
    SB .............. Show small-body search-field names & meanings.
    NEWS ............ Display program news (new capabilities, updates, etc.).
    ?! .............. Extended help ('?' for brief help).

  Program controls:
    LIST ............ Toggle display of small-body match-parameter values.
    PAGE ............ Toggle screen paging (scrolling) on or off.
    EMAIL {X} ....... Set your email address to {X} for output delivery.
    TTY {R} {C}...... Check or reset screen size; "tty" or "tty 24 79" to set.
    X ............... Exit JPL on-line system (also "QUIT" or "EXIT").
    - ............... Return to the previous prompt (back-up!).


Short-cuts:

        * Move backward through the prompts by typing "-".
        * Quit from ANY prompt by entering 'q'.
        * To use a default (or previously entered value), press return.
        * After selecting an object, enter "e+" to produce an ephemeris
          format like the last one, without additional prompting.

SAVING PROGRAM SETTINGS

Telnet (interactive) users may go through program options once, then save all settings for recall during future sessions. This can save time, if you find yourself always changing certain defaults or routinely defining the same output format each time you connect. Others in your organization may load and use the same pre-defined format settings by name.

To save program settings, go through the prompts and define the settings as you require. Then return to the main "Horizons>" prompt.

     #1)  Type "SAVE {NAME}", where {NAME} contains 1-12 characters.  
     #2)  Input a password that allows you to later DELETE or REPLACE the macro
     #3)  Next time you telnet to Horizons, type "LOAD {NAME}".

   Your output preferences will then be loaded in as the new defaults.

If you make a mistake or want to change a setting later, two commands are relevant: DELETE and SAVE

DELETE a macro with command "DELETE {NAME}". Alternatively, change specific settings manually, then replace the stored macro with a SAVE to an existing name. Delete and replace operations require input of a confirming password. LOAD does not. Thus, anyone can use your settings if they know the macro name. Only those who know the password can change or delete a macro.

Start/stop dates are also saved in the macro, as is observing location. You need only load the macro and select the target. Remaining defaults will be as defined in the format macro. If the macro is for an individual (personal use), you may want to set the e-mail address prior to saving. Otherwise don't, so users of the macro will be prompted for it in the future.

A macro may be loaded, then specific settings overruled by responding to the program prompts. For example, if your last table prior to saving the macro was a "vector" table, that table type will be saved as the default.

Settings for the other table types are saved as well so, to access them, manually respond to the prompt requesting table type, over-riding the macro's "vector" default on that issue. Start and stop times are also macro settings that may commonly be overruled as necessary.

Ideally, macro names would be something clean and logical:

            "OBS670-1" for macro #1 for Observatory Code 670, etc. 

   ... but the name is up to you. 

The use of macros may make it less likely to stumble upon new capabilities as they are added, though they will described here and in the system news, as appropriate.


INTEGRATOR DISPLAY

Comet and asteroid ephemerides are integrated from initial conditions called "osculating elements". These describe the 3-dimensional position and velocity of the body at a specific time. The integrator starts with this state and takes small time steps, summing the perturbing forces at each step before taking another step. A variable order, variable step-size integrator is used to control error growth. In this way, the gravitational attraction of other major solar system bodies on the target body trajectory is taken into account.

The integrator starts at the epoch, or time, of the osculating elements. It then integrates forward or backward, as necessary, to the start of the requested table. Once it reaches the table start time, it may have to reverse direction and go forward in time to generate the table.

Every 50th step will be displayed so the user can get some sense of the progress of the ephemeris. Direction reversals are also displayed. If output is requested at small time intervals, the integrator may proceed rapidly to the start of the table. There may then be long (apparent) pauses, as numerous interpolations within a given integration step are performed to compute states at closely spaced print times.

The last number on the integrator display line is the most recent step size in days.


SPECIFICATION OF TIME

ACCEPTED FORMATS:

Time may be specified many ways in addition to the primary form "YYYY-MMM-DD HH:MM". Of particular note are Julian day number and day-of-year forms. Examples are shown below. Input start times may be specified to 1/1000th of a second if the default output setting is changed from "minutes".

Generally, if the input start time has more digits of precision specified than the selected output format, start time will be truncated to the appropriate level. For example, if a start time of 23:45:12.4 is specified, but the output format is only set to minutes, start time will automatically be changed to 23:45(:00.000).

                    YOUR INPUT             PROGRAM INTERPRETATION
                 ------------------------  ----------------------
Recommended:     1997-May-5 12:30:23.3348   ( 5 MAY 1997 12:30:23.334 )

Acceptable:      1965-Jan-27.47083333       (27 JAN 1965 11:18 )
                 1/9/96 3 12 59.2           ( 9 JAN 1996 03:13 )
                 1 9 96 3,12,59.2           ( 9 JAN 1996 03:13 )
                 2 jan 91 3:00 12.2         ( 2 JAN 1991 03:00 )
                 91 MAR 10 12:00:00         (10 MAR 1991 12:00 )
                 29 February 1975 3:00      ( 1 MAR 1975 03:00 )
                 10 October 29 3:58         (29 OCT 2010 03:58 )
                 dec 31 86 12               (31 DEC 1986 12:00 )
                 86-365 // 12               (31 DEC 1986 12:00 )
                 JUL 98                     ( 1 JUL 1998 00:00 )
                 JD 2451545.                ( 1 JAN 2000 12:00 )
                 JD2451545.                 ( 1 JAN 2000 12:00 )
                 278bc-jan-12 12:34         (B.C. 12 JAN  278 12:34)
                 AD 99-Aug-12 12:34         (A.D. 12 JAN   99 12:34)
                 bc 278-Jan-12 12:34        (B.C. 12 JAN  278 12:34)

The program will interpret other forms as well, but if you get too casual, you may end up with a surprise interpretation.

The program's time-span prompts indicate the earliest & latest dates that may be used for the selected target/center combination, as well as the type of time assumed being input (UT, CT, or TT).

For cartesian coordinates or osculating elements tables, only CT may be used. For "observer tables", output may be either UT or TT. TO CHANGE THE UT DEFAULT for observer tables, append a "TT" when entering START time. To switch back, append a "UT" to the start time.

The three time systems are described as follows:

CT
("Coordinate Time"); typically for cartesian and osculating element tables. The uniform time scale and independent variable of the ephemerides. CT is the same as the IAU's current TDB time-scale ("Barycentric Dynamical Time").

TT
("Terrestrial (Dynamic) Time"), called TDT prior to 1991, used for observer quantity tables. This is proper time as measured by an Earth-bound observer and is directly related to atomic time, TAI. TT periodically differs from CT by, at most, 0.002 seconds.

UT
is Universal Time This can mean one of two non-uniform time-scales based on the rotation of the Earth. For this program, prior to 1962, UT means UT1. After 1962, UT means UTC or "Coordinated Universal Time". Future UTC leap-seconds are not known yet, so the closest known leap-second correction is used over future time-spans.

TIME ZONE CORRECTIONS:

Output time-tags may also be in local civil time. When specifying start time, enter your time-zone correction in the format:

                     YYYY-Mon-Dy HH:MM UT{s}HH{:MM}
 ... where
 
    {s} ...  optional sign (+ or -). If unspecified, it is assumed "+".
    HH  ...  integer hours time-zone difference from UT
  {:MM} ...  optional minutes offset (usually 0)

North American standard time (winter) zone corrections are as follows:

          Atlantic Standard Time (AST) =  UT-4 hours
          Eastern Standard Time  (EST) =  UT-5 hours
          Central Standard Time  (CST) =  UT-6 hours
          Mountain Standard Time (MST) =  UT-7 hours
          Pacific Standard Time  (PST) =  UT-8 hours

If daylight savings is in effect (summer), add one hour to above offsets.

For example, "1999-Jun-2 12:30 UT-8" produces a table in Pacific Standard Time. A "-7" would provide Pacific Daylight Time (or MST, if it is winter).

GREGORIAN AND JULIAN CALENDAR DATES:

Input calendar dates 1582-Oct-15 and after are taken to be expressed in the extended Gregorian calendar system. Prior dates are assumed to be in the Julian proleptic calendar.

Historically, not all regions switched calendars at the same time (or even in the same century). Thus, the user must be aware of which calendar was in effect for a particular historical record. It should NOT be assumed this system's calendar automatically correlates with a date from an arbitrary historical document.

Here is the progression near the calendar switch point:

       Calendar Type    Calendar Date   Julian Day Number
       -------------    -------------   -----------------
        Julian           1582-Oct-03        2299158.5
        Julian           1582-Oct-04        2299159.5 --->
         (skipped)      "1582-Oct-05"       2299160.5    |
         (skipped)      "1582-Oct-06"       2299151.5    |
         (skipped)      "1582-Oct-07"       2299152.5    |
         (skipped)      "1582-Oct-08"       2299153.5    |
         (skipped)      "1582-Oct-09"       2299154.5    |
         (skipped)      "1582-Oct-10"       2299155.5    |
         (skipped)      "1582-Oct-11"       2299156.5    |
         (skipped)      "1582-Oct-12"       2299157.5    |
         (skipped)      "1582-Oct-13"       2299158.5    |
         (skipped)      "1582-Oct-14"       2299159.5    |
        Gregorian        1582-Oct-15        2299160.5 <---
        Gregorian        1582-Oct-16        2299161.5
        Gregorian        1582-Oct-17        2299162.5

Note that Julian (calendar) dates are different than (and unrelated to) Julian day numbers.

Examination of this table shows that the date labels from Oct 5, 1582 through Oct 14, 1582 don't exist. Of course, the days themselves do, as is shown in the continuous Julian day number column; it's just a matter of what one calls them. If you specify a non-existent calendar date label that was "skipped", this program will automatically use a day number, as shown above, that maps into the previous Julian calendar system. For example, requesting a date of 1582-Oct-14 (skipped) is the same as requesting the Julian calendar date 1582-Oct-04.

ANCIENT DATES:

Objects 0-10, 199, 299, 301, 399 and 499 (planet barycenters, their equivalents and the Sun & Moon) are available over a 3000 B.C. to A.D. 3000 interval. When specifying ancient calendar dates, this system requires input in the "BC/AD" scheme. If no "BC" marker is input with a calendar date, it is assumed to be "AD". Exceptions are AD years less than 100 which must have an AD symbol in the date in order to be recognized as a valid year. For example, "66ad-jan-27" will be accepted, but "66-Jan-27" cannot be parsed.

In this system, there are no negative years. The progression is as follows:

               Julian Day Number       Labeling-convention
                 (Jan 1 00:00)       BC/AD      Arithmetical 
               -----------------     -----      ------------
                   1720327.5          3bc           -2
                   1720692.5          2bc           -1
                   1721057.5          1bc            0
                   1721423.5          1ad            1
                   1721788.5          2ad            2

From this, one can see that no days (in the arithmetical year "0", for example) are skipped in the BC/AD scheme, but they do have a different label than in the corresponding arithmetical system.

Output observer-table lines begin with a 'b' in column 1, to indicate B.C. dates, and a space (" ") to indicate A.D. dates.

OUTPUT STEPPING:

Fixed time steps:

Output time steps are specified as integers with some associated units from the set {days, hours, minutes}. Example responses to the prompt include "30 days", "1 day", "10 min", and so on. To get half day steps, specify "12 hour".

It is possible to obtain output at less than 1 minute intervals. After specifying a start and stop time, give a positive integer as the "time-step", without giving units, such as "10". This will divide the time span into 10 parts. For example, if start and stop times are one hour (3600 seconds) apart, specifying a step of "240" will produce output every 15 seconds (3600/15 = 240 intervals). "3600" will produce output every second.

Rise/set and satellite eclipse circumstances may not be accurate to less than a minute since factors such as the primary's oblateness and atmosphere are not currently modelled.

Calendar steps:

If a step-size in units of "years" or "months" is specified, output steps will follow the calendar based on the starting date.

For example, if the start is 2008-Feb-29, and output is requested at "1 year" steps, output will be returned only for Feb 29 calendar days in those leap years having 29 days in Februrary.

If output is requested at "1 month" intervals, output will occur for every successive month on the 29th of that month. If a start date on the 31st is requested, output will only occur for months having 31 days.

Time-varying steps:

Output is typically at fixed time intervals. However, observer tables may additionally be requested at time-varying steps based on an angular shift specification. That is, "output only if the object has moved at least X arcseconds in the plane-of-sky".

When specifying step-size, with the telnet or e-mail interfaces, respond with something like "VAR ####", where '####' is an integer from 60 to 3600 arcseconds. This will trigger output whenever the object's position is predicted to be '####' arcseconds different from the current output step in the observer's plane-of-sky.

To preserve system performance, the time-varying output mode uses a simple linear extrapolation to predict the time when the object should have moved the requested distance. Due to non-linearities in the object's actual motion in the plane-of-sky, this projection can be off by .1 to 5 (or more) arcsecs. Thus the angular-motion print criteria you give should be considered approximate.

Computed quantities will be exact for the given time in the output, but the particular output time may not be exactly that required for the requested angular change.


REFERENCE FRAMES

It is necessary to adopt a commonly agreed-upon coordinate system for describing the position and velocity of an object in three-dimensional space. This program has two basic frames available:

"J2000" refers to the frame of the current planetary ephemeris. This is closely aligned with the International Celestial Reference Frame (ICRF). The planetary ephemeris coordinates differ from ICRF by at most 0.001 arcseconds, while the ICRF is thought to differ from the FK5 optical catalog system by at most 0.01 arcseconds.

The planetary ephemeris (and ICRF) coordinate directions are defined purely with respect to external radio sources (quasars), but can be thought of as closely corresponding to these basis directions:

  • +Z coordinate is normal to Mean Earth Equator of Epoch J2000.0
  • +X coordinate is parallel to Mean Earth Dynamical Equinox of Epoch J2000.0
  • +Y coordinate completes the right-handed system

"B1950" selects an inertial reference frame based on Earth Mean-Equator and FK4 optical catalog Equinox of Epoch B1950.0 (FK4/B1950.0), where the Epoch of B1950.0 is the Julian date at the start of the Besselian year B1950.0 (2433282.42345905). The Fricke equinox correction at Epoch is applied.


COORDINATE SYSTEMS

CARTESIAN VECTORS and OSCULATING ELEMENTS may be requested in one of three available coordinates systems derived from the selected basic reference frame. These systems can be described with respect to the reference frames (above) as follows:

  Earth mean equator and equinox of reference epoch

    Reference epoch: J2000.0 or B1950.0
    xy-plane: plane of the Earth's mean equator at the reference epoch
    x-axis  : out along ascending node of the instantaneous plane of the
              Earth's orbit and the Earth's mean equator at the reference epoch
    z-axis  : along the Earth mean north pole at the reference epoch

  Ecliptic and mean equinox of reference epoch

    Reference epoch: J2000.0 or B1950.0
    xy-plane: plane of the Earth's orbit at the reference epoch
    x-axis  : out along ascending node of instantaneous plane of the Earth's
              orbit and the Earth's mean equator at the reference epoch
    z-axis  : perpendicular to the xy-plane in the directional (+ or -) sense
              of Earth's north pole at the reference epoch.

  Body mean equator and node of date

    Reference epoch: "of date"
    Reference plane: ICRF or FK4/B1950.0
    xy-plane: central-body mean equator plane at reference epoch
    x-axis  : out along the ascending node of the central-body mean equator
              plane on the reference plane at the reference epoch
    z-axis  : along the central-body mean north pole at the reference epoch

OBSERVER TABLE COORDINATES, such as RA and DEC, may be with respect to two
possible coordinate systems:

Earth mean equator and equinox of reference epoch (astrometric coordinates):

    Reference epoch: J2000.0 or B1950.0
    xy-plane: plane of the Earth's mean equator at the reference epoch
    x-axis  : out along ascending node of the instantaneous plane of the
              Earth's orbit and the Earth's mean equator at the reference epoch
    z-axis  : along the Earth mean north pole at the reference epoch

Body true equator and Earth equinox of date (apparent coordinates)
    Reference epoch: "of date"
    xy-plane: plane of the body's true equator at the reference epoch
    x-axis  : out along ascending node of instantaneous plane of the Earth's
              orbit and the Earth's true equator plane at the reference epoch
    z-axis  : along the body's true north pole at the reference epoch

SEARCHING FOR SMALL-BODIES

Search for small-bodies with following keywords (Type R=real, I=integer, C=char). Use comparisons from the set { <, >, <>, = }. Separate each field with a semi-colon. Example search formulation:

     A < 2.5; IN > 7.8; STYP = S; GM <> 0;

The first group of keywords are common to asteroids AND comets:

 Type     Keyword     Description
 ----     -------     -----------
  C       NAME ...... Asteroid OR comet name fragment
  C       DES ....... Object designation
  R       EPOCH ..... Julian Date of osculating elements
  R       CALEPO .... Calendar date of osc. elements; YYYYMMDD.ffff
  R       A ......... Semi-major axis (au)
  R       EC ........ Eccentricity
  R       IN ........ Inclination of orbit plane (DEG) wrt ecliptic
  R       OM ........ Longitude of Ascending Node (DEG) wrt ecliptic/equinox
  R       W ......... Argument of Perihelion (DEG) wrt ecliptic/equinox
  R       TP ........ Perihelion Julian Date
  R       CALTP ..... Perihelion calendar date; YYYYMMDD.ffff
  R       MA ........ Mean anomaly (DEG) 
  R       PER ....... Orbital period (YRS)
  R       RAD ....... Object radius (KM)
  R       GM ........ Object GM (KM^3/S^2), only a few are known
  R       QR ........ Perihelion distance (au)
  R       ADIST ..... Aphelion distance (au)
  R       ANGMOM .... Specific angular momentum (au^2/DAY)
  R       N ......... Mean motion (DEG/DAY)
  R       DAN ....... Heliocentric dist. (au) of ascending node
  R       DDN ....... Heliocentric dist. (au) of descending node
  R       L ......... Ecliptic longitude of perihelion (DEG)
  R       B ......... Ecliptic latitude of perihelion (DEG)
  I       NOBS ...... Number of astrometric determinations in solution
  C       SOLN ...... Solution ID

The next parameters are ASTEROID SPECIFIC. If one or more is used, the search will conclude faster by examining asteroids only. For example, including something like 'H > -10;' will limit the search to asteroids only:

  C       ASTNAM .... Asteroid name fragment (designation if unnamed)
  R       B-V ....... B-V color (asteroid)
  R       H ......... Absolute magnitude parameter (asteroid)
  R       G ......... Magnitude slope parameter; can be < 0 (asteroid)
  R       ROTPER .... Rotational period, hrs (asteroid)
  R       ALBEDO .... Geometric albedo (asteroid)
  C       STYP ...... Spectral type, Tholen scheme (asteroid)

The next parameters are COMET SPECIFIC. If one or more is used, the search will conclude faster by examining comets only. For example, including something like "M1 > -10;" will limit the search to comets only:

  C       COMNAM .... Comet name fragment (designation if unnamed)
  I       COMNUM .... Comet number
  R       M1 ........ Total absolute magnitude (comet)
  R       M2 ........ Nuclear absolute magnitude (comet)
  R       K1 ........ Total magnitude scaling factor (comet)
  R       K2 ........ Nuclear magnitude scaling factor (comet)
  R       PHCOF ..... Phase coefficient for k2=5 (comet)
  R       A1 ........ Radial non-grav accel (comet), 10^-8 au/DAY^2
  R       A2 ........ Transverse non-grav accel (comet), 10^-8 au/DAY^2
  R       A3 ........ Normal non-grav accel (comet), au/DAY^2
  R       DT ........ Non-grav lag/delay parameter (comet), days

Only 1 of the 4 keywords 'ASTNAM', 'COMNAM', 'NAME' or 'DES' can be specified on a given search.

Directives:

There are 5 special directives that may be used to limit or control searches:

     Directive  Description
     ---------  -----------
     COM .....  Limit search to comets only

     AST .....  Limit search to asteroids only

     LIST ....  Display parameter values for matched objects. (This may be
                set as a default for all subsequent searches by typing "LIST"
                at the main system prompt, "Horizons>".)

                For example,
                 "A < 2.5; IN > 10; AST;"        (match parameters against
                                                  asteroids ONLY)
                 "A < 2.5; IN > 10; AST; LIST;"  (match AND display values
                                                  of the parameters)

     NOFRAG ..  Exclude/skip comet fragments

     CAP .....  A filter that guarantees only one comet apparition will be
                 returned for each comet. It may be used three ways:

                 CAP;        (returns last apparition before the current date)
                 CAP < JD#;  (returns last apparition before the specified
                               Julian Day Number)
                 CAP < YEAR; (returns last apparition before the given integer
                               year)

If the number after a '<' is less than 10000, it is assumed to be a year integer. Otherwise, the number is taken to be a Julian Day Number. If "CAP;" is specified, the search is automatically recognized as being a comets-only search.

Contents of Small-body Database & Update Frequency:

Excluded from the database are single opposition asteroids with observational data arcs less than 30 days, unless they are NEO's, "PHA's" or radar targets (which ARE included). Everything else is in.

Except for "PHA's" and NEOs, which are usually included within a couple hours of announcement, there can be a delay of a few days to a couple weeks before newly discovered objects (that meet the filter criteria) are added. Users can input their own objects, as described in the next section. The database is updated hourly with new objects and orbit solutions.


USER-SPECIFIED SMALL-BODIES

It is possible to define an object not in the database by inputting its HELIOCENTRIC ECLIPTIC elements and some other parameters. Type ';' at the main prompt. It is also possible to display a DASTCOM3 object, then "cut-and-paste" elements back into the program, varying parameters (such as magnitude), as needed. Cut-and-paste is a function of your local terminal capability.

PRESS <return> ON A BLANK LINE WHEN DONE. Input format is:

          LABEL= VALUE LABEL= VALUE ...
          LABEL= VALUE ...
            .
            .

... where acceptable label strings are defined as follows:

     EPOCH ....  Julian ephemeris date (CT) of osculating elements
     EC .......  Eccentricity
     QR .......  Perihelion distance in (au)
     TP .......  Perihelion Julian date
     OM .......  Longitude of ascending node (DEGREES) wrt ecliptic
     W ........  Argument of perihelion (DEGREES) wrt ecliptic
     IN .......  Inclination (DEGREES) wrt ecliptic

Instead of {TP, QR}, {MA, A} or {MA,N} may be specified (not both):

     MA .......  Mean anomaly (DEGREES)
     A ........  Semi-major axis (au)
     N ........  Mean motion (DEG/DAY)

Note that if you specify elements with MA, {TP, QR} will be computed from them. The program always uses TP and QR internally.

OPTIONAL INPUTS

       RAD ......  Object radius (KM)
       AMRAT ....  Area-to-mass ratio (m^2/kg). Setting to a non-zero value
                    activates calculation of solar radiation pressure
                    acceleration. Total absorption is assumed, so scale the
                    value to account for reflectivity. For example, if 15%
                    of light is reflected, specify a value for AMRAT for
                    which the actual value is multiplied by 1.15.

For asteroids, additional OPTIONAL parameters can be given:

       H ........  Absolute magnitude parameter (asteroid)
       G ........  Magnitude slope parameter; can be < 0 (asteroid)

For comets, additional OPTIONAL parameters can be given:

       M1 ........ Total absolute magnitude (comet)
       M2 ........ Nuclear absolute magnitude (comet)
       K1 ........ Total magnitude scaling factor (comet)
       K2 ........ Nuclear magnitude scaling factor (comet)
       PHCOF ..... Phase coefficient for k2=5 (comet)
       A1 ........ Radial non-grav accel (comet), au/DAY^2
       A2 ........ Transverse non-grav accel (comet),  au/DAY^2
       A3 ........ Normal non-grav accel (comet), au/DAY^2
       DT ........ Non-grav lag/delay parameter (comet), days.

You may enter each value on a separate line or several on one line. If you make a mistake, re-entering the label on another line will over-ride the previously specified value. To erase a value, enter something like "H=", where no value is given. To cancel all input, enter "-" as the first character on a line. To log-out, enter a "q" or "x" as first character on a line.

When done, after having pressed <return> on a blank line, you will be asked whether the reference frame of the elements is FK5/J2000.0 or FK4/B1950.0. You will also be asked the object name.

Example input:

     EPOCH= 2450200.5
      EC= .8241907231263196 QR= .532013766859137 TP= 2450077.480966184235
      OM= 89.14262290335057 W = 326.0591239257098 IN= 4.247821264821585
      A1= -5.113711376907895D-10 A2= -6.288085687976327D-10

CUSTOMIZING REQUESTED EPHEMERIDES

Keys are embedded in output ephemerides to assist with automated reading of the output by user's own software. The keys are defined as follows:

       $$SOE    Start of ephemeris
       $$EOE    End of ephemeris

Ephemerides may be customized by changing output default flags. The '*' symbols below denote login defaults. All tables may be optionally output in a "comma-separated-value" format for import into spreadsheets.

1. Cartesian state vector table

Any object with respect to any major body.

       Reference frame:
    *      J2000 (ICRF/J2000.0) 
           B1950 (FK4/B1950.0)    

       Coordinate system:
           Earth mean equator and equinox of frame Epoch (J2000.0 or B1950.0)
    *      Ecliptic and mean equinox of frame Epoch (J2000.0 or B1950.0)
           Central body mean equator and node of date

       Aberration corrections:
    *      NONE  (geometric state vectors)
           LT    (light-time)
           LT+S  (light-time & stellar aberration)     

       Units:
           KM and seconds
           KM and days
           AU and days

       Quantities Output:

        Format   Output
        ------   ------
             1   Position components {x,y,z} only 
             2   State vector {x,y,z,vx,vy,vz}
    *        3   State vector + 1-way light-time + range + range-rate 
             4   Position     + 1-way light-time + range + range-rate 
             5   Velocity components {vx, vy, vz} only             
             6   1-way light-time + range + range-rate

2. Osculating elements table

Any object with respect to any planet or barycenter

       Reference frame:
  *        J2000 (ICRF/J2000.0) 
           B1950 (FK4/B1950.0  )    
 
       Coordinate system:
           Earth mean equator and equinox of frame Epoch (J2000.0 or B1950.0)
  *        Ecliptic and mean equinox of frame Epoch (J2000.0 or B1950.0)
           Central body mean equator and node of date

       Units:
           KM and seconds
           KM and days
           AU and days

  *    Output quantities (fixed):
           JDCT     Epoch Julian Date, Coordinate Time
            EC      Eccentricity   
            QR      Periapsis distance
            IN      Inclination w.r.t. xy-plane (degrees)            
            OM      Longitude of Ascending Node (degrees)                 
            W       Argument of Perifocus (degrees)                    
            Tp      Periapsis time (user specifies absolute or relative date) 
             N      Mean motion (degrees/DU)
            MA      Mean anomaly (degrees)                               
            TA      True anomaly (degrees)
             A      Semi-major axis 
            AD      Apoapsis distance
            PER     Orbital Period

3. Observer table

Any object with respect to geocentric or topocentric observer, including spacecraft and sites on other planets or natural satellites.

        Default quantities. Always output:
           Time
           Solar-presence
           Lunar-presence

Selectable quantities. Output in order requested. No initial default exists. You will be prompted at least once. A detailed definition of these values follows, with the '*' symbols marking those quantities affected by user selection of airless or refraction-corrected apparent quantities. Quantities preceded by a '>' are statistical uncertainties that can be computed for asteroids and comets if a covariance is available, either in the database or supplied by the user. Number assignments could change if new quantities are added:

  1. Astrometric RA & DEC  15. Sun sub-long & sub-lat  29. Constellation ID
 *2. Apparent RA & DEC     16. Sub Sun Pos. Ang & Dis  30. Delta-T (CT - UT)
  3.   Rates; RA & DEC     17. N. Pole Pos. Ang & Dis *31. Obs eclip. lon & lat
 *4. Apparent AZ & EL      18. Helio eclip. lon & lat  32. North pole RA & DEC
  5.   Rates; AZ & EL      19. Helio range & rng rate  33. Galactic latitude
  6. Sat. X & Y, pos. ang  20. Obsrv range & rng rate  34. Local app. SOLAR time
  7. Local app. sid. time  21. One-Way Light-Time      35. Earth->Site lt-time
  8. Airmass               22. Speed wrt Sun & obsrvr >36. RA & DEC uncertainty
  9. Vis mag. & Surf Brt   23. Sun-Obs-Targ ELONG ang >37. POS error ellipse
 10. Illuminated fraction  24. Sun-Targ-Obs PHASE ang >38. POS uncertainty (RSS)
 11. Defect of illumin.    25. Targ-Obsrv-Moon/Illum% >39. Range & Rng-rate sig.
 12. Sat. angle separ/vis  26. Obs-Primary-Targ angl  >40. Doppler/delay sigmas
 13. Target angular diam.  27. Pos. Ang;radius & -vel  41. True anomaly angle
 14. Obs sub-lng & sub-lat 28. Orbit plane angle       42. Local app. hour angle

  ... or select a pre-defined format below:
  A = All quantities      B = Geocentric only        C = Small-body geocentric
  D = Small-body topo.    E = Spacecraft geocentric  F = Spacecraft topocentric
 
  The alphabetic assignments specifically mean:
  A = 1-42                       B = 1-3,6,9-33,41     C = 1-3,9-11,13,18-29,
                                                           33,36-41
  D = 1-5,8-10,11,13,18-29,      E = 1-3,8,10,18-25,   F = 1-5,8,10,18-25,29,42
      33-34,36-42                    29,41

... with the small-body cases primarily skipping cartographic dependent quantities. Note that Ida and Gaspra are exceptions, having IAU-defined mapping grids, so that C & D options won't provide all available data for such objects. In the list below, '*' indicates initial program default settings.

        Reference coordinate frame:
  *       J2000 (ICRF/J2000.0) 
          B1950 (FK4/B1950.0 )    
          Body true-equator and Earth equinox of-date

        Time scale:
  *       UT  (Universal Time) 
          TT  (Terrestrial Time)

        Time zone correction (used for UT-based tables only)

        Time format
  *       Calendar
          JD (Julian date)
          Both

        Time output precision (calendar format only)
  *       MINUTES (HH:MM)
          SECONDS (HH:MM:SS)
          FRACSEC (HH:MM:SS.fff)

        Right-ascension format
  *       Hours, minutes, seconds of arc (DEC degrees, minutes, seconds)
          Decimal degrees 

        High-precision RA/DEC output
  *       No  (~ 10^-2 arcsec; HH MM SS.ff DD MM SS.f)
          Yes (~ 10^-4 arcsec; HH MM SS.ffff DD MM SS.fff)

        Apparent coordinate corrections
  *       Airless apparent 
          Refracted apparent

        Minimum elevation (integer value)
  *       -90 degrees

        Maximum airmass (real value)
  *       38.0 (refracted elevation = -0 deg)

        Rise/Transit/Set print ONLY
  *       No
          TVH -- True visual horizon. Includes dip and refraction (Earth only).
          GEO -- Geometric horizon. Includes refraction (Earth only).
          RAD -- Radar horizon. Geometric horizon, no refraction.

        Skip Daylight
  *       No
          Yes 

DEFINITION OF OBSERVER TABLE QUANTITIES

The menu of observer table output quantities was shown above. The format of the table is as follows. "Labels" refers to column headings at the start of the table:

TIME
One output line for each step. The line begins with a 'b' if the date is BC, a blank (" ") if AD. This is followed by the date and time, which is either UT or TT, in calendar or JD format (or both), depending on user defaults.

SOLAR PRESENCE
Time tag is followed by a blank, then a solar-presence symbol:
        '*'  Daylight (refracted solar upper-limb on or above apparent horizon)
        'C'  Civil twilight/dawn
        'N'  Nautical twilight/dawn
        'A'  Astronomical twilight/dawn
        ' '  Night OR geocentric ephemeris 
INTERFERING BODYLUNAR PRESENCE
The solar presence symbol is immediately followed by another marker symbol:
        'm'  Refracted upper-limb of Moon/IB on or above apparent horizon
        ' '  Refracted upper-limb of Moon/IB below apparent horizon OR 
              geocentric ephemeris
        'r'  Rise    (target body on or above cut-off RTS elevation)
        't'  Transit (target body at or past local maximum RTS elevation)
        's'  Set     (target body on or below cut-off RTS elevation)
The 'rts' codes will be displayed under two conditions only: if the print interval is less than or equal to 30 minutes or the RTS-only print option has been selected.

For non-Earth observing sites, no twilight/dawn codes (C, N, or A) are output, refraction is not modelled and the interfering body marker is 'x' instead of the 'm' reserved for Earth's Moon.



STATISTICAL UNCERTAINTIES
  Output for asteroids and comets can include formal +/- 3-standard-deviation 
statistical orbit uncertainty quantities. There is a 99.7% chance the actual 
value is within given bounds.  These statistical calculations assume 
observational data errors are random. If there are systematic biases (such as 
timing, reduction, or star-catalog errors), results can be optimistic. Because
the epoch covariance is mapped using linearized variational partial 
derivatives, results can also be optimistic for times far from the solution 
epoch, particularly for objects having close planetary encounters.

NOTE: "n.a." is output if a requested quantity is not available for selected 
      object. For example, azimuth and elevation for a geocentric ephemeris,
      or uncertainties for an object with no covariance in the database.


SPECIFIC QUANTITIES
  1. Astrometric RA & DEC: 
        Adjusted for light-time only. With respect to the Earth mean equator 
        and equinox of the reference Epoch. If FK4/B1950.0 frame output is 
        selected, elliptic aberration terms are added.

        Labels:  R.A._(ICRF/J2000.0)_DEC  (HMS/DMS format)
                 R.A._( FK4/B1950.0)_DEC  (HMS/DMS format)
                 R.A._(J2000.0)_DEC.      (degree format)
                 R.A._(B1950.0)_DEC.      (degree format)

  2. Apparent RA & DEC:
        Apparent right ascension and declination of the target with respect
     to the center/site body's true-equator and Earth equinox of-date. For
     non-Earth sites with rotational models, the origin of RA is the meridian 
     containing the Earth equinox of J2000.0. For non-Earth sites without 
     rotational models, RA and DEC are with respect to the REFERENCE FRAME
     (FK4/B1950 or ICRF/J2000.0) coordinate system. Adjusted for light-time, 
     the gravitational deflection of light, stellar aberration, precession and 
     nutation. There is an optional (approximate) correction for atmospheric 
     refraction (Earth only).

        Labels:  R.A._(a-apparent)__DEC.  (airless, HMS/DMS format)
                 R.A._(r-apparent)__DEC.  (refracted, HMS/DMS format)
                 R.A._(a-appar)_DEC.      (airless, degrees format)
                 R.A._(r-appar)_DEC.      (refracted, degrees format)

  3. Rates; RA & DEC
        The rate of change of apparent RA and DEC (airless). d(RA)/dt is
     multiplied by the cosine of declination. Units are ARCSECONDS PER HOUR.
     
        Labels:  dRA*cosD d(DEC)/dt

  4. Apparent AZ & EL:
        Apparent azimuth and elevation of target. Adjusted for light-time, 
     the gravitational deflection of light, stellar aberration, precession and
     nutation. There is an optional (approximate) correction for atmospheric
     refraction (Earth only). Azimuth measured North(0) -> East(90) -> 
     South(180) -> West(270). Elevation is with respect to plane perpendicular
     to local zenith direction.  TOPOCENTRIC ONLY. Units: DEGREES

        Labels:  Azi_(a-appr)_Elev  (airless)
                 Azi_(r-appr)_Elev  (refracted)

  5. Rates; AZ & EL
        The rate of change of target apparent azimuth and elevation (airless). 
     d(AZ)/dt is multiplied by the cosine of the elevation angle. TOPOCENTRIC 
     ONLY. Units are ARCSECONDS PER MINUTE.

        Labels:  dAZ*cosE d(ELV)/dt

  6. X & Y satellite offset & position angle
        Satellite differential coordinates WRT the central body along with the
     satellite position angle. Differential coordinates are defined in RA as
          X=[(RA_sat - RA_primary)*COS(DEC_primary)],
     and in DEC as
          Y=(DEC_sat-DEC_primary).  
     Non-Lunar satellites only. "SatPANG" is CCW angle from the North Celestial
     Pole to a line from planet center to satellite center.  
     Units: ARCSECONDS (X & Y) and DEGREES (position angle)

        Labels:  X_(sat-primary)_Y SatPANG

  7. Local Apparent Sidereal Time
        The angle measured westward in the body true-equator of-date plane 
     from the meridian containing the body-fixed observer to the meridian 
     containing the true Earth equinox (defined by intersection of the true 
     Earth equator of date with the ecliptic of date). For non-Earth sites,
     a somewhat different definition is used. The value returned is measured
     from the observer meridian to the meridian containing the Earth equinox 
     of the J2000.0 system. TOPOCENTRIC ONLY. Units are HH MM SS.ffff or 
     decimal hours (HH.ffffffffff)

        Labels:  L_Ap_Sid_Time

  8. Airmass
        RELATIVE optical airmass; a measure of extinction. The ratio between
     the absolute optical airmass at the target's refracted position to the 
     absolute optical airmass at zenith. Based on work of Kasten and Young 
     (Applied Optics, vol. 28 no. 22, 15-Nov-1989). AVAILABLE ONLY FOR 
     TOPOCENTRIC EARTH SITES WITH THE TARGET ABOVE THE HORIZON.  Unitless.

        Labels:  a-mass

  9. Vis mag. & Surf Bright
        Approximate (apparent) visual magnitude & surface brightness, where
     surface brightness is the average visual magnitude of a square-arcsecond
     of the illuminated portion of the apparent disk).

     Planets & satellites: Value for Pluto includes Charon. The Sun's altitude
      above the Saturn ring-plane is not considered for Saturn.  When the Moon
      is at phase angles < 7 deg.  (within 1 day of full), the computed
      magnitude tends to be ~ 0.12 too small.  For observing sites not on the
      Earth or Moon, planet and satellite magnitudes are not available (but
      Sun, comet and asteroid values are). For planets and satellites, values
      are available only for solar phase angles in the range generally visible
      from Earth. This is to avoid extrapolation of models beyond their valid
      (data-based) limits.

     Asteroids & comets: Surface brightness is returned for asteroids only
      if a radius is known. Magnitudes are, in principle, accurate to about
      +/- 0.1 magnitude. However, measurement and calibration issues mean
      values should be treated as uncertain at the +/- 1.0 magnitude level.
      In practice, for solar phase angles > 90 deg, the error could exceed
      1 magnitude. No values are output for phase angles greater than 120
      degrees, since the errors could be large and unknown. Some comets have
      custom magnitude laws that are described at the end of the requested
      ephemeris output.

     Units are (none) and VISUAL MAGNITUDES PER SQUARE ARCSECOND.

     Magnitude laws:
       Sun
         APmag= M - 5 + 5*log10(d), where M=4.83, d=distance from Sun (parsecs)
       Asteroids
         APmag= H + 5*log10(delta) + 5*log10(r) -2.5*log10((1-G)*phi1 + G*phi2)
       Comets
         T-mag=M1 + 5*log10(delta) + k1*log10(r)
         N-mag=M2 + 5*log10(delta) + k2*log10(r) + phcof*beta
       Chiron:
         Computed using asteroid magnitude law with H= 6.5, G=0.15
       Wilson-Harrington
         Computed using asteroid magnitude law, H= 15.99, G= 0.15
       Elst-Pizzaro:
         Computed using asteroid magnitude law, H= 14.0, G= 0.15

     Surface brightness:
         S-brt= V + 2.5*log10(k*PI*a*b')
 
        Labels:  APmag S-brt  (Non-comet with known dimensions)
                 APmag        (Non-comet with unknown dimensions)
                 T-mag N-mag  (comets; total & nuclear magnitudes)

 10. Illuminated fraction
        Portion of target object circular disk illuminated by Sun (phase),
     as seen by observer.  Units are PERCENT.

        Labels:  Illu%

 11. Defect of illumination
        Angular width of target circular disk diameter not illuminated by Sun. 
     Available only if target radius is known.  Units are ARCSECONDS.

        Labels:  Def_illu

 12. Angular separation/visibility
        The angle between the center of a non-lunar target body and the center
     of the primary body it revolves around, as seen by the observer. Units are 
     ARCSECONDS.
 
        Non-lunar natural satellite visibility codes (limb-to-limb):

      /t = Transitting primary body disk, /O = Occulted by primary body disk,
      /p = Partial umbral eclipse,        /P = Occulted partial umbral eclipse,
      /u = Total umbral eclipse,          /U = Occulted total umbral eclipse,
      /- = Target is the primary body,    /* = None of above ("free and clear")
     
     ... the radius of major bodies is taken to be the equatorial value (max) 
     defined by the IAU2009 system. Atmospheric effects and oblateness aspect
     are not currently considered in these computations. Light-time is included.

        Labels:   ang-sep/v

 13. Target angular diameter
        The angle subtended by the disk of the target seen by the observer, if
     it was fully illuminated. The target diameter is taken to be the IAU2009
     equatorial diameter.  Oblateness aspect is not currently included. Units 
     are ARCSECONDS.

        Labels: Ang-diam

 14. Obs sub-long & sub-lat
        Apparent planetographic ("geodetic") longitude and latitude (IAU2009 
     model) of the center of the target seen by the OBSERVER at print-time. 
     This is NOT exactly the same as the "sub-observer" (nearest) point for 
     a non-spherical target shape, but is generally very close if not an 
     irregular body shape. Light travel-time from target to observer is taken 
     into account. Latitude is the angle between the equatorial plane and the 
     line perpendicular to the reference ellipsoid of the body. The reference 
     ellipsoid is an oblate spheroid with a single flatness coefficient in 
     which the y-axis body radius is taken to be the same value as the x-axis 
     radius. For the gas giants only (Jupiter, Saturn, Uranus and Neptune), 
     these longitudes are based on the Set III prime meridian angle, referred 
     to the planet's rotating magnetic field. Latitude is always referred to 
     the body dynamical equator.  Note there can be an offset between the 
     dynamical pole and the magnetic pole. The direction of positive longitude
     (east or west) will be indicated in the description at the end of the
     requested ephemeris.  Units are DEGREES.

        Labels: Ob-lon Ob-lat

 15. Solar sub-long & sub-lat
       Apparent planetographic ("geodetic") longitude and latitude of the Sun
     (IAU2009) as seen by the observer at print-time.  This is NOT exactly the 
     same as the "sub-solar" (nearest) point for a non-spherical target shape, 
     but is generally very close if not an irregular body shape. Light 
     travel-time from Sun to target and from target to observer is taken into 
     account.  Latitude is the angle between the equatorial plane and the line 
     perpendicular to the reference ellipsoid of the body. The reference 
     ellipsoid is an oblate spheroid with a single flatness coefficient in 
     which the y-axis body radius is taken to be the same value as the x-axis 
     radius. For the gas giants only (Jupiter, Saturn, Uranus and Neptune), 
     these longitudes are based on the Set III prime meridian angle, referred 
     to the planet's rotating magnetic field. Latitude is always referred to 
     the body dynamical equator. Note there can be an offset between the 
     dynamical pole and the magnetic pole. The direction of positive longitude
     (east or west) will be indicatedin the descripton at the end of the
     requested ephemeris. Units are DEGREES.

        Labels: Sl-lon Sl-lat

 16. Sub Solar Pos. Ang & Dis
        Target "sub-solar" point position angle (CCW with respect to direction
     of true-of-date Celestial North Pole) and angular distance from the 
     "sub-observer" point (center of disk) at print time. Negative distance 
     indicates the sub-solar point is on the hemisphere hidden from the 
     observer.  Units: DEGREES and ARCSECONDS

        Labels: SN.ang SN.ds

 17. N. Pole Pos. Ang & Dis 
        Target's North Pole position angle (CCW with respect to direction of 
     true-of-date Celestial North Pole) and angular distance from the 
     sub-observer point (center of disk) at print time. Negative distance 
     indicates N.P. on hidden hemisphere. Units: DEGREES and ARCSECONDS

        Labels: NP.ang NP.ds 

 18. Helio eclip. lon & lat
        Geometric heliocentric (J2000 or B1950) ecliptic longitude and latitude
     of target at the instant light leaves it to be observed at print time
     (print time minus 1-way light-time).  Units: DEGREES

        Labels: hEcl-Lon hEcl-Lat

 19. Helio range & range-rate 
        Heliocentric range ("r", light-time corrected) and range-rate ("rdot")
     of the target center or surface point at the instant light seen by the
     observer at print-time would have left the target (print-time minus
     down-leg light-time). The Sun-to-target distance traveled by a ray of
     light emanating from the center of the Sun that reaches the target at
     some instant and is recordable by the observer one down-leg light-time
     later at print-time.  Units: AU and KM/S

        Labels:    r       rdot

 20. Observer range & range rate 
        Target apparent range ("delta") & range-rate ("delta-dot") relative
     to observer.  Units are AU and KM/S.

        Labels:   delta  deldot

 21. One-Way Light-time
        Target 1-way light-time, as seen by observer. The elapsed time since 
     light (observed at print-time) left or reflected off the target. 
     Units are MINUTES.

        Labels:  1-way_LT

 22. Speed wrt Sun & obsrvr
        Magnitude of velocity of target with respect to the Sun center and the
     observer at the time light left the target to be observed. Units are KM/S. 

        Labels:  VmagSn VmagOb

 23. Sun-Observer-Target angle
        Target's apparent solar elongation seen from observer location at
     print-time.  If negative, the target center is behind the Sun. Units 
     are DEGREES.
 
        For observing centers with defined rotation models, an additional
     marker is output under the column labelled '/r' (for relative position).
     If there is no rotation model associated with the observing center, 
     no /r column will be present. Under this column,

            /T indicates target trails Sun (evening sky) 
            /L indicates target leads Sun  (morning sky)
 
        NOTE: The S-O-T solar elongation angle is the total separation in any
     direction. It does not indicate the angle of Sun leading or trailing.

        Labels: S-O-T /r
 
 24. Sun-Target-Observer angle, phase angle & phase angle bisector direction
        "S-T-O" is the Sun->Target->Observer angle; the measurable interior 
     vertex angle at target center formed by a vector to the apparent center 
     of the Sun at reflection time on the target and a vector to the observer 
     at print-time.

     "phi" is the PHASE ANGLE at the observer's location at print time. The
     difference with S-T-O is due to down-leg stellar aberration affecting 
     apparent target position but not apparent solar illumination direction.  
     When computing phase, Horizons uses "phi", not "S-T-O".

     "PAB-LON" and "PAB-LAT" are the ICRF/J2000 or FK4/B1950 ecliptic longitude
     and latitude of the phase angle bisector direction; the outward directed 
     angle bisecting the arc created by the apparent vector from Sun to target 
     center and the astrometric vector from observer to target center. For an 
     otherwise uniform ellipsoid, the time when its long-axis is perpendicular 
     to the PAB direction approximately corresponds to lightcurve maximum (or 
     maximum brightness) of the body. PAB is discussed in Harris et al., Icarus
     57, 251-258 (1984).  Units: DEGREES, DEGREES, DEGREES, DEGREES

        Labels: S-T-O      phi  PAB-LON  PAB-LAT
 
 25. Target-Observer-Moon (or Interfering_Body) / Illum%
        Apparent elongation angle, seen by the observer, between the target 
     body center and the center of a potential visually interfering body (such 
     as the Moon but, more generally, the largest body in the system except for
     the one the observer is on). Also output is the fraction of the lunar (or 
     IB) disk that is illuminated by the Sun. A negative elongation angle 
     indicates the target center is behind the interfering body. The specific
     interfering body for an observing site is given in the output header.
     Units are DEGREES and PERCENT.

        Labels: T-O-M/Illu%   (Earth observer, 'M' denoting "Moon")
                T-O-I/Illu%   (Non-Earth observer)

 26. Observer-Primary-Target angle
       Apparent angle between a target satellite, its primary's center and
     an observer at print time. Units: DEGREES

        Labels: O-P-T

 27. Sun-target position angle; radius & -vel
        The position angles of the extended Sun->target radius vector
     ("PsAng") and the negative of the target's heliocentric velocity vector 
     ("PsAMV"), as seen in the plane-of-sky of the observer, measured CCW 
     from reference frame North Celestial Pole. Small-bodies only. 
     Units are DEGREES. 

        Labels: PsAng PsAMV
        
 28. Orbit Plane Angle
        Angle between observer and target orbital plane, measured from center 
      of target at the moment light seen at observation time leaves the target. 
      Positive values indicate observer is above the object's orbital plane,
      in the direction of reference frame +z axis. Small-bodies only. 
      Units: DEGREES.

        Labels:  PlAng

 29. Constellation ID
        The 3-letter abbreviation for the constellation name of target's
      astrometric position, as defined by the IAU (1930) boundary delineation.

        Labels: Cnst

 30. CT-UT =
        Difference between uniform Coordinate Time scale ("ephemeris time") a
     Earth-rotation dependent Universal Time. Prior to 1962, the difference is
     with respect to UT1 (CT-UT1). For 1962 and later, the delta is with
     respect to UTC (CT-UTC).  Values beyond the next July or January 1st may
     change if a leap-second is introduced at later date. Units:SECONDS

        Labels: CT-UT

 31. Observer Ecliptic Longitude & Latitude
       Observer-centered Earth ecliptic-of-date longitude and latitude of 
     the target's apparent position, corrected for light-time, the 
     gravitational deflection of light, stellar aberration and possibly
     atmospheric refraction (if requested). Although centered on the observer,
     the values are expressed relative to coordinate basis directions defined
     by the Earth's true equator-plane, equinox direction, and ecliptic plane
     at print time. Units: DEGREES

        Labels: ObsEcLon    ObsEcLat

 32. Target North Pole RA & DEC
        Right Ascension and Declination (IAU2009 rotation model) of target 
     body's North Pole direction at the time light left the body to be 
     observed at print time. Consistent with requested reference frame; 
     ICRF/J2000.0 or FK4/B1950.0 RA and DEC.  Units: DEGREES.

        Labels: N.Pole-RA  N.Pole-DC

 33. Galactic Latitude
        Observer-centered Galactic System II (post WW II) latitude and latitude
     of the target's apparent position (corrected for light-time, stellar
     aberration, precession, nutation and the deflection of light due to the
     Sun and the most massive body in the planet's system). Units: DEGREES

        Labels: GlxLon GlxLat

 34. Local Apparent Solar Time
        Local Apparent SOLAR Time at observing site. This is the time indicated
     by a sundial. TOPOCENTRIC ONLY.  Units are HH.fffffffffff (decimal hours)
     or HH MM SS.ffff (sexagesimal hours)

 35. Earth to Site Light-time
        Instantaneous light-time of the station with respect to Earth center 
     at print-time. The geometric (or "true") separation of site and Earth 
     center, divided by the speed of light.  Units: MINUTES

        Labels: 399_ins_LT

 36. Plane-of-sky RA and DEC pointing uncertainty
        Uncertainty in Right-Ascension and Declination. Output values are the 
     formal +/- 3 standard-deviations (sigmas) around nominal position. 
     Units: ARCSECONDS

        Labels: RA_3sigma DEC_3sigma
 
 37. Plane-of-sky error ellipse
        Plane-of-sky (POS) error ellipse data. These quantities summarize the
     target's 3-dimensional 3-standard-deviation formal uncertainty volume 
     projected into a reference plane perpendicular to the observer's 
     line-of-sight.

        Labels:

         SMAA_3sig = Angular width of the 3-sigma error ellipse semi-major
                      axis in POS. Units: ARCSECONDS.

         SMIA_3sig = Angular width of the 3-sigma error ellipse semi-minor
                      axis in POS. Units: ARCSECONDS.

         Theta     = Orientation angle of the error ellipse in POS; the
                      clockwise angle from the direction of increasing RA to
                      the semi-major axis of the error ellipse, in the
                      direction of increasing DEC.  Units: DEGREES.

         Area_3sig = Area of sky enclosed by the 3-sigma error ellipse.
                      Units: ARCSECONDS ^ 2.

 38. Plane-of-sky ellipse RSS pointing uncertainty
       The Root-Sum-of-Squares (RSS) of the 3-standard deviation plane-of-sky 
     error ellipse major and minor axes.  This single pointing uncertainty 
     number gives an angular distance (a circular radius) from the target's 
     nominal position in the sky that encompasses the error-ellipse. 
     Units: ARCSECONDS.

       Labels: POS_3sigma

 39. Uncertainties in plane-of-sky radial direction
       Range and range rate (radial velocity) formal 3-standard-deviation
     uncertainties.  Units: KM, KM/S

       Labels: RNG_3sigma RNGRT_3sig
 
 40. Radar uncertainties (plane-of-sky radial direction)
       Doppler radar uncertainties at S-band (2380 MHz) and X-band (8560 MHz)
     frequencies, along with the round-trip (total) delay to first-order.
     Units: HERTZ and SECONDS

       Labels: DOP_S-sig  DOP_X-sig  RT_delay-sig

 41. True anomaly angle
       Apparent true anomaly angle of the target's heliocentric orbit position;
     the angle in the target's instantaneous orbit plane from the orbital 
     periapse direction to the target, measured positively in the direction of 
     motion.  The position of the target is taken to be at the moment light seen
     by the observer at print-time would have left the center of the object. 
     That is, the heliocentric position of the target used to compute the true 
     anomaly is one down-leg light-time prior to the print-time. Units: DEGREES

       Labels: Tru_Anom

 42. Local apparent hour angle
       Local apparent HOUR ANGLE of target at observing site. The angle between
     the observer's meridian plane, containing Earth's axis of-date and local
     zenith direction, and a great circle passing through Earth's axis-of-date
     and the target's direction, measured westward from the zenith meridian to
     target meridian along the equator. Negative values are angular times UNTIL
     transit.  Positive values are angular times SINCE transit.
     Exactly 24_hrs/360_degrees. EARTH TOPOCENTRIC ONLY. Units: sHH.fffffffff
     or HH MM SS.fff  (decimal or sexagesimal angular hours)

       Labels: L_ap_Hour_Ang

CLOSE-APPROACH TABLES

For asteroids and comets, a close-approach table may be requested. Output is produced only when the selected object reaches a minimum distance within a set spherical radius from a planet, Ceres, Pallas, or Vesta.

User-specifications for this table can include the time-span to check, the radius of detection for planets and asteroids, the maximum uncertainty in time-of-close-approach before the table is automatically cut-off, and whether to output optional error ellipse information projected into the B-plane

The B-plane mentioned above is defined by the three orthogonal unit vectors T, R, and S (the origin being the body center). T lies in the B-plane, pointing in the direction of decreasing celestial longitude. R lies in the B-plane, pointing in the direction of decreasing celestial latitude (south). S is directed along the relative velocity vector at body encounter, perpendicular to the B-plane, and thus R and T. The B vector is the vector in the plane from the body to the point where the incoming object's velocity asymptote pierces the R-T plane. Note the B-plane is defined only when the incoming object is hyperbolic with respect to the body.

For objects with covariances, statistical quantities are output for each close-approach. All tabulated statistical quantities (MinDist, MaxDist, TCA3Sg, Nsigs and P_i/p) are based on a linearized covariance mapping in which higher-order (small) terms in the variational partial derivatives of the equations of motion are dropped.

Due to possible non-linearities in any given object's actual dynamics, this can result in significant errors at epochs distant in time from the solution epoch. Consequently, long linearized mappings (thousands, or hundreds, or sometimes just dozens of years from the present time) should be considered approximate, pending additional analysis, especially in these cases:

           A) objects with numerous close planetary encounters (dozens), 
           B) objects with very close planetary encounters (< 0.01 AU),
           C) objects with very short data arcs (days or weeks).

While linearized projections will tend to indicate such cases with obviously rapid uncertainty growth, the specific numbers output can tend to understate orbit uncertainty knowledge.

Possible output quantities are described below. "Nominal" effectively means "highest-probability for the given orbit solution", although there can be other possible orbits of equal probability. If there is no covariance, no statistical quantities are returned.

 Date (CT) =
   Nominal close-approach date (Coordinate Time). Calendar dates prior to 
1582-Oct-15 are in the Julian calendar system.  Later calendar dates are 
in the Gregorian system.

 Body =
   Name or abbreviation of the planetary body or major asteroid being
closely approached by the selected small-body.

 CA Dist =
   Nominal close-approach distance at the close-approach time. Units: AU

 MinDist = 
   Minimum close-approach distance possible (formal 3 standard-deviations 
with linearized covariance mapping). Units: AU

 MaxDist =
   Maximum close-approach distance possible (formal 3 standard-deviations
with linearized covariance mapping). Units: AU

 Vrel =
   Relative velocity of the object and the body it is approaching at the
nominal time of close-approach. Units: KM/S

 TCA3Sg =
   Close-approach-time 3-standard deviation uncertainty.  Units: MINUTES

 SMaA   =
   3-sigma error ellipse semi-major axis projected into the B-plane at nominal
time of closest-approach. Units: KM

 SMiA   =
   3-sigma error ellipse semi-minor axis projected into the B-plane at nominal
time of closest-approach. Units: KM

 Gamma  =
   Orientation angle of error ellipse in the B-plane. Counter-clockwise 
angle from the B vector to the semi-major axis of the error ellipse. 
Units: DEGREES 

 Nsigs  =
   The number of standard deviations (sigmas) required for the error ellipse 
to intersect the body being closely approached. Units: STANDARD DEVIATIONS

 P_i/p  =
   Linearized probability of the object impacting the body. Non-zero values
less than approximately 0.001 may not be numerically significant due to the
linearization process.

UNDERSTANDING RISE, TRANSIT AND SET INDICATORS

There are 2 ways the system can be used to mark rise, transit and set (RTS) conditions: activate the RTS-only print option OR produce a general observer table with step-size less than 30 minutes.

NORMAL_TABLE RTS-MARKER MODE

RTS is indicated automatically during normal observer table generation, when the step-size is less than 30 minutes. Markers are placed to indicate the event occurred at some point in the previous step. Thus, precision of the indicator depends on the step-size selected. For this mode, rise and set are always with respect to the true-visual-horizon reference plane (TVH), described below.

RTS-ONLY PRINT MODE

The advantage of this mode is it allows production of a more compact RTS table over a longer time-span than does the "normal" table generation mode.

When RTS-only print is selected, the program will search for the events at a user-specified resolution, from 1 to 9 minutes. Output will be generated ONLY for these three events. The marker symbols in the table indicate that the event took place sometime in the previous step interval.

This RTS-only mode can be turned on at two different points in the program:

  1. Preferably, when specifying the ephemeris/search step-size
  2. ... but also in the "change defaults" prompt structure

Three types of criteria are available for the rise and set conditions, relative to an input elevation angle (nominally 0 degrees). Select by specifying, when prompted at #1 or #2, one of these symbols:

TVH
True visual horizon plane. The horizon seen by an observer on the reference ellipsoid. Allows for horizon dip effect and refraction, but not local topography.
GEO
Geometric horizon plane. The horizon is defined by the plane perpendicular to the reference ellipsoid local zenith (no horizon dip). Refraction is allowed for.
RAD
Radar case. Geometric horizon plane, no refraction.

For example, when prompted for the step-size, one could enter "5 min GEO' to search, at five-minute steps, for the refracted rise/set relative to the geometric horizon.

BACKGROUND DESCRIPTION

Rise and set elevations are taken to be the maximum of 0 or the input elevation cut-off value [0-90 deg], set in the "change defaults" prompt section. Thus, if there are local hills, one could set the cut-off at 10 degrees and get RTS relative to that elevation.

At low elevations, these rise/set times should be viewed as approximations, realistically good to perhaps only 1-2 minutes at the horizon due to local atmospheric variation and topography.

To speed RTS-only searches, use the largest step-size compatible with the required accuracy. For example, considering the inherent atmospheric instability at the horizon, one should rarely need to identify rise/set to better than 5 minute accuracy. Setting a search-step of 5 minutes will then produce a table 5 times faster than 1 minute searching.

The program computes approximate refraction angles assuming yellow-light observations at 10 deg C sea-level with pressure of 1010 millibars. Corrected coordinates should be accurate to < 10 arcsec, but errors may be much larger near the horizon (+- 0.3 deg) or fluctuate unpredictably with local weather.

Both Moon and Sun rise/set are based on when the refracted upper limb of the object reaches the specified elevation. Transit is based on the center of the target body.


CONSTELLATION IDENTIFICATION

One output value that may be requested for an observer table is the constellation it is observed to be in (corrected for light-time). The output field will contain a three letter abbreviation of the constellation name, from the list shown below.

Constellation boundaries are those delineated by Gould (1877) and Delporte (1930) under the auspices of the International Astronomical Union.

        _______________________________________________________________
       | Abbrev. | Constellation Name | | Abbrev. | Constellation Name |
       |_________|____________________|_|_________|____________________|
       | And     | Andromeda          | | Leo     | Leo                |
       | Ant     | Antila             | | LMi     | Leo Minor          |
       | Aps     | Apus               | | Lep     | Lepus              |
       | Aqr     | Aquarius           | | Lib     | Libra              |
       | Aql     | Aquila             | | Lup     | Lupus              |
       | Ara     | Ara                | | Lyn     | Lynx               |
       | Ari     | Aries              | | Lyr     | Lyra               |
       | Aur     | Auriga             | | Men     | Mensa              |
       | Boo     | Bootes             | | Mic     | Microscopium       |
       | Cae     | Caelum             | | Mon     | Monoceros          |
       | Cam     | Camelopardis       | | Mus     | Musca              |
       | Cnc     | Cancer             | | Nor     | Norma              |
       | CVn     | Canes Venatici     | | Oct     | Octans             |
       | CMa     | Canis Major        | | Oph     | Ophiuchus          |
       | CMi     | Canis Minor        | | Ori     | Orion              |
       | Cap     | Capricornus        | | Pav     | Pavo               |
       | Car     | Carina             | | Peg     | Pegasus            |
       | Cas     | Cassiopeia         | | Per     | Perseus            |
       | Cen     | Centaurus          | | Phe     | Phoenix            |
       | Cep     | Cepheus            | | Pic     | Pictor             |
       | Cet     | Cetus              | | Psc     | Pisces             |
       | Cha     | Chamaeleon         | | PsA     | Pisces Austrinus   |
       | Cir     | Circinus           | | Pup     | Puppis             |
       | Col     | Columba            | | Pyx     | Pyxis              |
       | Com     | Coma Berenices     | | Ret     | Reticulum          |
       | CrA     | Corona Australis   | | Sge     | Sagitta            |
       | CrB     | Corona Borealis    | | Sgr     | Sagittarius        |
       | Crv     | Corvus             | | Sco     | Scorpius           |
       | Crt     | Crater             | | Scl     | Sculptor           |
       | Cru     | Crux               | | Sct     | Scutum             |
       | Cyg     | Cygnus             | | Ser     | Serpens            |
       | Del     | Delphinus          | | Sex     | Sextans            |
       | Dor     | Dorado             | | Tau     | Taurus             |
       | Dra     | Draco              | | Tel     | Telescopium        |
       | Equ     | Equuleus           | | Tri     | Triangulum         |
       | Eri     | Eridanus           | | TrA     | Triangulum Australe|
       | For     | Fornax             | | Tuc     | Tucana             |
       | Gem     | Gemini             | | UMa     | Ursa Major         |
       | Gru     | Grus               | | UMi     | Ursa Minor         |
       | Her     | Hercules           | | Vel     | Vela               |
       | Hor     | Horologium         | | Vir     | Virgo              |
       | Hya     | Hydra              | | Vol     | Volans             |
       | Hyi     | Hydrus             | | Vul     | Vulpecula          |
       | Ind     | Indus              | |         |                    |
       | Lac     | Lacerta            | |         |                    |
       |_________|____________________|_|_________|____________________|

SPK File Generation

Introduction:

An SPK file is a binary file which may be smoothly interpolated to retrieve an object's position and velocity at any instant within the file time-span. Such files may be used as input to visualization and mission design programs, allowing them to quickly retrieve accurate target body observation and data analysis ephemerides without having to repeatedly integrate equations of motion. An SPK file could be considered a "recording" of the integrator.

SPK stands for "Spacecraft and Planet Kernel". It is a file element of the SPICE system devised and maintained by the NAIF (Navigational and Ancillary Information Facility) team at JPL. SPK files may hold ephemerides for any kind of spacecraft, vehicle or solar system body, but the SPK files produced by Horizons are only for comets and asteroids.

Potential users are advised that programming and science/math skills at an advanced college level are needed to utilize these files. Users must have a computer with 25-50 Mbytes of disk space, 8 Mbytes of available RAM and a FORTRAN or C compiler. The user's own code must be capable of calling FORTRAN or C modules. Internet FTP capability is needed to obtain the necessary SPICE components as well as the SPK files generated by Horizons.

   For information on SPK files in general, contact
 
               Charles.H.Acton-Jr@jpl.nasa.gov (NAIF Team Leader)
 
   or see web site http://pds-naif.jpl.nasa.gov/.

Horizons Implementation:

SPK files can be produced on demand using the Horizons telnet interface. Horizons allows a maximum of 20 small-bodies per SPK file. To construct an SPK for a comet or asteroid, Horizons retrieves the latest orbit solution and numerically integrates the object's trajectory over a user-specified time span less than 200 years. Internal data from the integrator is written directly to the SPK file as this occurs. When a users' application program reads the SPK file, that data can be used to reconstruct the integrator state to within machine precision limits.

SPK files are capable of storing trajectory data with a fidelity greater than 1 millimeter (more accurately than should ever be required).

Summary information is stored in the SPK file comment area. It can be read using the "spacit" or "commnt" utility in the SPICE Toolkit distribution.

Files produced autonomously by Horizons users are considered informal file releases and should not be used for purposes affecting the safety and success of spacecraft hardware or missions without first contacting the JPL Solar System Dynamics Group:

       Donald.K.Yeomans@jpl.nasa.gov (Supervisor, 818-354-2127) 
       Jon.D.Giorgini@jpl.nasa.gov   (SSDG analyst).  

This is because an object's orbit solution may be insufficiently determined over the chosen time-span to be suitable for some high-precision purposes, due to the quantity of measurements available for an object, the time-span they cover, and the object's dynamical path.

Although not stored in an SPK file, the statistical uncertainty of the trajectory as a function of time may be available from the JPL Horizons system. This can help interpret the accuracy of the trajectory.

The orbit solutions used to produce SPK files on demand are updated in Horizons as new measurements are made. Therefore, a trajectory in an SPK file may be superceded by more recent solutions. Check the orbit solution number for an object (given as "source" in the SPK file comments area) against the latest Horizons entry to determine if an updated orbit solution is available.


STATEMENT OF EPHEMERIS LIMITATIONS

To produce an ephemeris, observational data (optical, VLBI, radar & spacecraft) containing measurement errors are combined with dynamical models containing modeling imprecisions. A best fit is developed to statistically minimize those errors. The resulting ephemeris has an associated uncertainty that fluctuates with time.

For example, only a limited percentage of asteroid orbits are known to better than 1 arcsec in the plane-of-sky over significant periods of time. While 1991 JX center-of-mass was known to within 30 meters along the line-of-sight during the 1995 Goldstone radar experiment, errors increase outside that time-span. Uncertainties in major planet ephemerides range from 10cm to 100+ km in the state-of-the-art JPL/DE-405 ephemeris, used as the basis for spacecraft navigation, mission planning and radar astronomy.

Cartesian state vectors are output in all their 16 decimal-place glory. This does not mean all digits are physically meaningful. The full-precision may be of interest to those studying the ephemerides or as a source of initial conditions for subsequent integrations.

On top of this basic uncertainty, the mass parameter (GM) used to compute osculating element output is rarely known to better than 5 significant figures.

For observer angular output tables, purely local atmospheric conditions will affect "refraction-corrected" apparent places by several arcseconds, more at the horizon.

Small-body elements are reported in the optical frame (i.e. FK5/J2000.0). This frame is currently thought to differ by no more than 0.01 arcseconds from the ICRF of the planetary ephemeris DE-405. Until a generally agreed upon transformation from one frame to the other is defined and implemented, they will be treated by this program as being the same.

The Earth is assumed to be a rigid body and solid Earth tides affecting station location are not included. Of course, precession and nutation effects are included, as is polar motion. CT-TAI terms less than 20 usec are omitted. These and other Earth-model approximations result in topocentric station location errors, with respect to the reference ellipsoid, of less than 20 meters. However, many optical site positions (latitude and longitude) are reported far less accurately and can be many kilometers off.

Solar relativistic effects are included in all planet, lunar and small body dynamics, excluding satellites. Relativity is included in observables via 2nd order terms in stellar aberration and the deflection of light due to gravity fields of the Sun (and Earth, for topocentric observers).

Deflections due to other gravity fields can potentially have an effect at the 10^-4 arcsec level but are not currently included here. Satellites of other planets, such as Jupiter could experience deflections at the 10^-3 arcsec level as well. Light time iterations are Newtonian. This affects light-time convergence at the millisecond level, position at ~10^-6 arcsec level.

For many small natural satellites, the orbit orientation is well known, but the position of the body along the ellipse is not. Errors may be significant, especially for the lesser satellites of outer planets. Satellite osculating elements output by Horizons should NOT be used to initialize a separate integration or extrapolation. Such elements assume Keplerian motion (two point masses, etc.) which does not match, for example, kinematic models such as a precessing ellipse, used for some satellites. One would do better extrapolating mean orbital elements at http://ssd.jpl.nasa.gov/sat_elem.html.

Spacecraft in low Earth orbit (such as ISS, HST, Swift, GALEX) need frequent updates to maintain high accuracy. LEO predicts more than a few days into the future can have 10s or 100's of km of error. If accurate predicts are needed, and the last update was more than a few days ago, an update can be done on request. For interplanetary spacecraft, users having high-precision applications (such as mission data reduction) should contact JPL Solar System Dynamics to verify the status of the specific trajectory in Horizons.

IF YOUR CAREER OR SPACECRAFT DEPENDS ON A NON-LUNAR NATURAL SATELLITE OR SMALL-BODY EPHEMERIS, CONTACT JPL BEFORE USING IT. YOU MUST HAVE ADDITIONAL INFORMATION TO CORRECTLY UNDERSTAND EPHEMERIS LIMITATIONS AND UNCERTAINTIES.

LONG-TERM EPHEMERIS

SOLAR SYSTEM MODEL:

The JPL DE-406/LE-406 extended ephemeris covers the interval from 3000 B.C. to A.D. 3000. This ephemeris is identical to the shorter DE-405 in the sense it is the same data-fit (solution) and the same numerical integration as DE-405. However, it has been stored with slightly less accuracy to reduce its size.

For the Moon, DE-406 recovers the original integrator state to within 1 meter, other bodies within 25 meters (maximum error). This difference can be less than the uncertainty associated with the trajectory solution itself, thus is insignificant for all but the most specialized circumstances. The short-span version, DE-405, recovers the integrator state to the millimeter level.

Horizons uses the long-term DE-406/LE-406 for the following objects:

            Objects                      ID code #
            ---------------------------  -------------------
            All planet barycenters       0,1,2,3,4,5,6,7,8,9 
            Sun                          10 
            Moon                         301
            Mercury                      199
            Venus                        299
            Earth                        399
            Mars                         499

Satellites and outer solar-system planet-centers each have various shorter intervals, as warranted by their observational data arc. Comets and asteroids are available only over the A.D. 1599 to A.D. 2200 interval of the DE-405 ephemeris they are integrated against. (Only a few dozen small-bodies have sufficiently well-known orbits to justify rigorous integration over time-spans of hundreds of years.)

PRECESSION MODEL:

For the time-span of 1799-Jan-1 to 2202-Jan-1, the official IAU precession model [16] of Lieske is used. As published, this model is valid for only ~200 years on either side of the J2000.0 epoch. This is due to round-off error in the published coefficients and truncation to a 3rd order polynomial in the expressions for the Euler rotation angles. Therefore, outside this interval, the long-term precession and obliquity model [17] of Owen is used to maintain accuracy in the calculation of apparent ("of-date") quantities.

This model is a rigorous numerical integration of the equations of motion of the celestial pole using Kinoshita's model for the speed of luni-solar precession.

NUTATION MODEL:

The IAU (1980) model [18] of Wahr is used. This is the same table printed in the 1992 Explanatory Supplement to the Astronomical Almanac. Note there is an error in the Explanatory Supplement for the Node term, given on p. 114 as:

                        OMEGA = 135deg 2'40.280" + ...

This system uses the correct formulation:

                        OMEGA = 125deg 2'40.280" + ... 

UNIVERSAL TIME (CT -> UT Conversion):

This program internally uses the CT time-scale of the ephemerides (the independent variable in the equations of motion). To produce the more familiar Universal Time (UT) output tied to the Earth's rotation, it is necessary to use historical reconstructions of old or ancient observations of constrained events, such as eclipses, to derive a CT-UT difference. This program currently uses the analyses of [12-15] as follows:

    Span                   CT-UT offset  ("delta-t")   Type Argument (T=...)
    ---------------------  -------------------------- ----- -------------------
    3000 BC to  500 BC     (31*T*T) - 20                UT1 cent. since JD1820
    500 BC  to AD 1620     Stephenson cubic spline fit
    AD 1620 to AD 1962     Smoothed table               UT1
    AD 1962 to Present     EOP file                     UTC

   Values prior to 1962 above are adjusted for compatibility with the Horizons
planetary ephmeris lunar tidal acceleration (n_dot) of -25.7 "/century^2 as
follows:

  delta_(CT-UTC) = -0.911*(n_dot + 26)*T*T, where T =  (year - 1955.5) / 100

        For epochs after 1962, the calculation is as follows:

                  CT - UTC = (CT - TAI) + (TAI - UTC)
... where
         
          CT  - TAI = 32.184 + 1.657E-3 * SIN( M + 0.01671*SIN(M) )
                  M = 6.239996 +  T * 1.99096871E-7
                  T = CT or TAI seconds past J2000.0 epoch

          TAI - UTC = interpolated from current EOP file.

... dropping terms less than about 20 usec in CT-TAI.

As one progresses to earlier times, particularly those prior to the 1620 telescopic data span, uncertainties in UT determination generally (though not always and not uniformly) increase due to less precise observations and sparser records. At A.D. 948, uncertainty (not necessarily error) can be a few minutes. At 3000 B.C., the uncertainty in UT is about 4 hours. The TT time scale, being uniform, does not have this uncertainty, but is not directly related to Earth's rotation (local time) either.

GREENWICH MEAN SIDEREAL TIME:

GMST, used for topocentric ephemerides, is related to UT1 using an expression consistent with the IAU 1976 system of constants, as shown on p. 50 of the Explanatory Supplement (1992), along with the new more accurate 1997 IAU equinox equation.

HIGH PRECISION EARTH ORIENTATION PARAMETER (EOP) MODEL

The EOP file is currently updated twice a week based on GPS and other Earth-monitoring measurements. Horizons uses it to obtain calibrations for UT1-UTC, polar motion and nutation correction parameters necessary to determine the rotation from the Earth-fixed reference frame to an inertial reference frame. The EOP file provides data from 1962 to the present, with predictions about 78 days into the future from the date of file release. For times outside the available interval, Horizons uses the last value available in the file as constants. For CT-UT calculations, it switches to the different models described above.

Because EOP values are fit to data, it is possible an ephemeris may differ slightly from one produced days or weeks or months later, especially, if the original ephemeris extended into the predicted region of the EOP file. The most recent ephemeris will be more accurate, but if it is necessary to reproduce results exactly, contact JPL. EOP files are archived and the one used in your initial run (indicated in your output) can be retrieved. Generally, any numeric change will be very small and almost always negligible in a practical sense.

BODY ROTATIONS:

The current IAU rotational models for the planets and satellites are simply extended in time as necessary.


BACKGROUND

  • Comet and asteroid orbits are INTEGRATED from initial conditions stored in the JPL-maintained DASTCOM database.

  • Planet and satellite ephemerides are INTERPOLATED from files previously generated by JPL, such as the DE-405 (or higher) planetary ephemeris.

  • SMALL BODY DATA SCREENS are from the JPL DASTCOM database. These display constants ARE ACTUALLY USED to produce the ephemeris.

  • MAJOR BODY DATA SCREEN CONSTANTS are from "Astrometric and Geometric Properties of Earth and the Solar System", Charles Yoder (JPL), published in "Global Earth Physics: A Handbook of Physical Constants", AGU Reference Shelf 1.

  • MAJOR BODY DATA SCREEN CONSTANTS are presented for your information (FYI) only and ARE NOT USED to generate the ephemeris output (see below). While an effort has been made to insure their accuracy, suitability of these DISPLAY constants for any given purpose must be determined by individual users. Users should be aware there is often more than one determination in the literature for many of these constants and that they are subject to revision as more data are accumulated.

SOURCES AND REFERENCES FOR PRIMARY EPHEMERIS DATA

Planets

Standish, E.M., XX Newhall, J.G. Williams, and W.M. Folkner. JPL Planetary and Lunar Ephemerides, DE403/LE403. JPL Interoffice Memorandum 314.10-127 dated May 22, 1995.

Natural Satellites

                                               Ephemeris
Satellite            Theory                    References
-----------------    ---------------------     ----------------------

Phobos & Deimos      MARSAT (Analytic)         Jacobson et al. (1989)

Galileans            GALSAT(E5, Analytic)      Lieske (1995)
Minor Jovians        Precessing ellipse        Jacobson (1994) 
Outer Jovians        Numerical Integration     Jacobson (1991)

Major Saturnians     Numerical Integration     Jacobson (1996a)
Phoebe               Numerical Integration     Jacobson (1996c) 
Inner Saturnians     Precessing ellipse        Jacobson (1995)
Saturn co-orbiters   Numerical Integration     Jacobson (1995) 
Saturn librators     Numerical Integration     Jacobson (1995) 

Major Uranians       GUST (Analytic)           Laskar & Jacobson (1987)
Minor Uranians       Precessing ellipse        Jacobson (1996b)

Triton               Numerical Integration     Jacobson et al. (1991)
Nereid               Numerical Integration     Jacobson et al. (1991)
Inner Neptunians     Precessing ellipse        Owen et al. (1991)      

Charon               Dynamic conic             Tholen (1990)        

References For Natural Satellite Ephemerides:

  1. Jacobson, R.A., 1991. Outer Jovian Satellite Ephemerides for the Galileo Project. JPL Interoffice Memorandum 314.6-1261 (JPL internal document).

  2. Jacobson, R.A., 1994. Revised Ephemerides for the Inner Jovian Satellites. JPL Interoffice Memorandum 314.10-101 (JPL internal document).

  3. Jacobson, R.A., 1995. The Orbits of the Minor Saturnian Satellites. Bulletin, American Astronomical Society, vol. 27, No.3, p. 1202-1203.

  4. Jacobson, R.A., 1996a. Update of the Major Saturnian Satellite Ephemerides. JPL Interoffice Memorandum 312.1-96-012 (JPL internal document).

  5. Jacobson, R.A., 1996b. Updated Ephemerides for the Minor Uranian Satellites. JPL Interoffice Memorandum 312.1-96-014 (JPL internal document).

  6. Jacobson, R.A., 1996c. Update of the Ephemeris for Phoebe. JPL Interoffice Memorandum 312.1-96-024 (JPL internal document).

  7. Jacobson, R.A., Synnott, S.P., and Campbell, J.K., 1989. The Orbits of the Satellites of Mars from Spacecraft and Earthbased Observations. Astronomy and Astrophysics, 225, 548.

  8. Jacobson, R.A., Riedel, J.E. and Taylor, A.H., 1991. The Orbits of Triton and Nereid from Spacecraft and Earthbased Observations. Astronomy and Astrophysics, 247, 565.

  9. Laskar, J. and Jacobson, R.A., 1987. GUST86. An Analytic Ephemeris of the Uranian Satellites. Astronomy and Astrophysics, 188, 212.

  10. Lieske, J.H., 1995. Galilean Satellite Ephemerides E5. JPL Engineering Memorandum 312-583 (JPL internal document).

  11. Owen, W.M., Vaughan, R.M., and Synnott, S.P., 1991. Orbits of the Six New Satellites of Neptune. Astronomical Journal, 101, 1511.

  12. Tholen, D. and Buie, M.W., 1990. Further Analysis of Pluto-Charon Mutual Event Observations - 1990. Bulletin, American Astronomical Society, vol. 22, No.3, p. 1129.

Comets and Asteroids

Sources of Orbital Elements for Comets and Asteroids

  1. Minor Planet Circulars (MPC) published by the Minor Planet Center, 60 Garden St., Cambridge, Massachusetts 02138 http://cfa-www.harvard.edu/cfa/ps/mpc.html

  2. The Lowell Observatory Database of Asteroid Orbits (E.L.G. Bowell) http://www.lowell.edu

  3. Solar System Dynamics Group/Jet Propulsion Laboratory (JPL) D.K. Yeomans, Supervisor

Cometary Magnitude Parameters

  1. International Comet Quarterly (D.W.E. Green, editor), 60 Garden St., Cambridge, Massachusetts, 02138

  2. Charles Morris, Jet Propulsion Laboratory, Pasadena, California 91109

Asteroid Physical Parameters

Radius and Albedo:

  1. Tedesco, E.F. (1995) "IMPS Diameters and Albedos V1.0" Planetary Data System - Small Bodies Node (PDSSBN) (M. A'Hearn, University of Maryland, College Park, Maryland) http://pdssbn.astro.umd.edu

  2. McFadden, L.A. et al. (1989) In Asteroids II, p. 456.

  3. Williams, J.G. (1990) Private Communication.

Taxonomic Type ("Spectral Type"):

  1. Tholen, D.J. (1989) "Asteroid Taxonomy V1.0" Planetary Data System - Small Bodies Node (PDSSBN) (M. A'Hearn, University of Maryland, College Park, Maryland) http://pdssbn.astro.umd.edu

  2. Binzel, R.P. and Xu, S. (1993) Science 216:186-191.

Rotation Period:

  1. Harris, A.W. (1996) "Asteroid Lightcurve Derived Data V2.0" Planetary Data System - Small Bodies Node (PDSSBN) (M. A'Hearn, University of Maryland, College Park, Maryland) http://pdssbn.astro.umd.edu

Magnitude Parameters:

  1. Minor Planet Circulars (MPC) published by the Minor Planet Center, 60 Garden St., Cambridge, Massachusetts 02138 http://cfa-www.harvard.edu/cfa/ps/mpc.html

Constants and Model References

Major body (planet/satellite) GM and AU definitions ACTUALLY USED (as opposed to the FYI data screens) are from the DE405 ephemeris, a significant improvement over the earlier DE-200. Other planet and satellite constants used by this software, such as radii, rotation and orientation, are based on the following sources:

1.
`Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 2009', Celestial Mechanics and Dynamical Astronomy 82: 83-110, 2002.

2.
`The Astronomical Almanac', 1993.

3.
`Planetary Geodetic Control Using Satellite Imaging', Journal of Geophysical Research, Vol. 84, No. B3, March 10, 1979, by Thomas C. Duxbury.

4.
Letter from Thomas C. Duxbury to Dr. Ephraim Lazeryevich Akim, Keldish Institute of Applied Mathematics, USSR Academy of Sciences, Moscow, USSR.

Most values are from the `IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 2009'. The exceptions are:

  • The second nutation precession angle (M2) for Mars is represented by a quadratic polynomial in the IAU2009 report. Current software cannot handle this term (which is extremely small), so the polynomial is truncated to a linear one.

  • The expressions for the pole and prime meridian of Neptune given in the IAU report include trigonometric terms which current software doesn't yet handle. These terms are omitted.

  • For several satellites, the IAU2009 report either gives a single radius value or a polar radius and a single equatorial radius. Current software uses a triaxial ellipsoid model that requires three radii. In the cases listed below, additional values have been supplied in order to allow the software to function.

The affected satellites are:

       Body      NAIF ID code 
       ----      ------------
       Thebe     514
       Metis     516
       Helene    612
       Caliban   716      (no IAU value)
       Sycorax   717      (no IAU value)
       Larissa   807
       Vesta     20000004 (no IAU value)

Airmass computation is based on:

5.
Kasten, F., Young, A., "Revised Optical Air Mass Tables and Approximation Formula", Applied Optics, vol 28, no. 22, p. 4735-4738, Nov. 15, 1989.

Refraction computation is based on [6-7]:

6.
Saemundsson, T., Sky & Telescope, July, 1986, p.70.

7.
Meeus, J., "Astronomical Algorithms", 1991, p. 101-102.

Constellation identification based on [8-9,(10-11)]:

8.
Roman, N.G. 1987, "Identification of a Constellation from a Position", Publ. Astronomical Society of the Pacific 99, 695-699.

9.
Warren, Wayne H., Jr., (1997, GSFC) private communication.

10.
Delporte, E. 1930, Delimitation Scientifique des Constellations, Cambridge, Cambridge University Press.

11.
Gould, B.A., 1877, Uranometria Argentina, mapas (Buenos Aires, Argentina: Observatorio Nacional)

Long-term CT-UT offset calculations based on:

12.
priv. comm. Morrison (1980).

13.
Stephenson, F.R., Houlden, M.A., Atlas of Historical Eclipse Maps, Cambridge Univ. Press, p X, (1986).

14.
Stephenson, F.R, Morrison, L.V., "Long-term Changes in the Rotation of the Earth: 700 B.C. to A.D. 1980", Phil. Trans. R. Soc. London 313, 47-70 (1984)

15.
Stephenson, F.R., Morrison, L.V., "Long-term Fluctuations in the Earth's Rotation: 700 BC to AD 1990", Phil. Trans. R. Soc. London 351, p. 165-202 (1995)

Precession (IAU) from 1799-Jan-1 to 2202-Jan-1:

16.
Lieske, J., "Precession Matrix Based on IAU (1976) System of Astronomical Constants", Astron. Astrophys. 73, 282-284, 1979.

Precession (long-term) before 1799-Jan-1 and after 2202-Jan-1:

17.
Owen, William M., Jr., (JPL) A Theory of the Earth's Precession Relative to the Invariable Plane of the Solar System, Ph.D. Dissertation, University of Florida, 1990.

Nutation:

18.
Table 1,"Proposal to the IAU Working Group on Nutation", John M. Wahr and Martin L. Smith 1979. Adopted 1980.

ACKNOWLEDGEMENTS

This software reflects the underlying contributions of several people at JPL:

        Design/implementation : Jon Giorgini 
                                Don Yeomans
    
        Cognizant Eng.        : Jon Giorgini   

        Ephemerides           : Myles Standish  (Planetary ephemerides)
                                Bob Jacobson    (Satellites)
                                Jay Lieske      (Satellites)

        Contributors          : Paul Chodas     (some subroutines)
                                Alan Chamberlin (web interface, database)
                                The NAIF group (SPICELIB)
                                 (esp. Chuck Acton, Bill Taber, Nat Bachman) 
                                Ray Wimberly    (database maintenance)
                                Mike Keesey     (comet orbits, database)

Address queries to Jon.D.Giorgini@jpl.nasa.gov, who is solely responsible for any errors or omissions. Solar System Dynamics Group, Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109 USA.

The system described in this document was developed at the Jet Propulsion Laboratory (Solar System Dynamics Group, Supervisor: D.K. Yeomans), California Institute of Technology, under contract with the National Aeronautics and Space Administration.

The Horizons system may be formally referenced as:

Giorgini, J.D., Yeomans, D.K., Chamberlin, A.B., Chodas, P.W., Jacobson, R.A., Keesey, M.S., Lieske, J.H., Ostro, S.J., Standish, E.M., Wimberly, R.N., "JPL's On-Line Solar System Data Service", Bulletin of the American Astronomical Society 28(3), 1158, 1996.

Appendices/Examples

These examples demonstrate a few of the different types of Horizons functions. Additional functions and customizable output types are available.


Major body data screen

JPL Horizons, vers SUN-1.12 
`?' for brief intro, `?!' for more details 
System news updated MAR 04, 1997 -- IMPORTANT!
 
Horizons> saturn
*******************************************************************************
 Revised: Sep 12, 1996                Saturn                                699
 
 PHYSICAL DATA:
  Mass (10^24 kg)       =   568.46        Density (g/cm^3)       =  0.6873
  Equat. radius (1 bar) = 60268+-4 km     Polar radius (km)      = 54364+-10
  Volumetric mean radius= 58232+-6 km     Flattening             =  0.09796

  Rotation period       = 10h 39m 22.4s   Rot. rate(10^-4 rad/s) =  1.63785 
  m = w^2a^3/GM         =  0.15481        Hydrostatic flat., fh  =  0.09829
  Inferred rot. period  = 10.61+-0.02 hr  ks = 3*J2/m            =  0.317
  Mom. of inert. I/MRo^2=  0.210          I/MRo^2 (upper bound)  =  0.231 
  Rocky core mass (Mc/M)=  0.1027         Y factor (He/H ratio)  =  

  GM (km^3/s^2)         = 37,931,187      GM 1-sigma (km^3/s^2)  = +-100
  Equ. grav, ge (m/s^2) =  8.96+-0.01     Pol. grav, gp (m/s^2)  = 12.14+-0.01

  Geometric albedo      =  0.47           Visual magnitude V(1,0)= -8.88
  Vis. mag. (opposition)= +0.67           Obliquity to orbit     = 26.73 deg
  Sidereal orbit period = 29.423519 yr    Sidereal orbit period  = 10746.940 d
  Mean daily motion     = 0.0334979 deg/d Mean orbit velocity    =  9.6624 km/s

  Atmos. temp. (1 bar)  = 134+-4 K        Heat flow/mass (x10^7) = 15 erg/gm*s
  Planetary Solar Const =  15.04 W/m^2    Dipole tilt/offset     = 0.0deg/0.0Rp 
  Escape velocity (km/s)=  35.5           Mag.dip.mom(gauss-Rp^3)= 0.21
  Aroche(ice)/Rp        =  2.71           Hill's sphere rad. Rp  = 1100
*******************************************************************************
 Select ... [E]phemeris, [F]tp, [K]ermit, [M]ail, [R]edisplay, ?,  : 

Asteroid data screen

JPL Horizons, vers SUN-1.12 
`?' for brief intro, `?!' for more details 
System news updated MAR 04, 1997 -- IMPORTANT!
 
Horizons> 1620;
*******************************************************************************
JPL/DASTCOM3                1620 Geographos                1997-Apr-02 11:13:16
Rec #:  1620            soln data arc: 1951-1994           # obs: 903          
 
FK5/J2000.0 osculating elements (AU, DAYS, DEG, period in Julian years):       
 
  EPOCH=  2450400.5 != 1996-Nov-13.0000000 (TDB)                               
    EC= .335457434         QR= .8277437479999999  TP= 2450545.8223853          
    OM= 337.3533493        W= 276.7579416         IN= 13.340954                
    A= 1.24558424          MA= 256.9668602        ADIST= 1.663424732           
    PER= 1.39017           N= .708997032          ANGMOM= .018086079           
    DAN= 1.06344           DDN= 1.15085           L= 256.7672741               
    B= -43.9920798                                TP= 1997-Apr-07.3223853      
 
Physical parameters (KM, SEC, rotational period in hours):
    GM= n.a.               RAD= .900              ROTPER= 5.223                
    H= 15.6                G= .150                B-V= .890                    
    ALBEDO= .326           STYP=  S                                            
 
ASTEROID comments: 
1: soln ref.= JPL#37,     1951 RA       radar( 3 delay, 4 Dop.)
2: dim.= 5.11x1.85km: Ostro, Nature, May 1995; other: McFadden, Asteroids II.
*******************************************************************************
 Select ... [E]phemeris, [F]tp, [K]ermit, [M]ail, [R]edisplay, ?,  : 

Comet data screen

JPL Horizons, vers SUN-1.12 
`?' for brief intro, `?!' for more details 
System news updated MAR 04, 1997 -- IMPORTANT!
 
Horizons> 20181;
*******************************************************************************
JPL/DASTCOM3                     Halley                    1997-Apr-02 11:13:57
Rec #: 20181            soln data arc: 1835-1989           # obs: n.a.         
 
FK5/J2000.0 osculating elements (AU, DAYS, DEG, period in Julian years):       
 
  EPOCH=  2446480.5 != 1986-Feb-19.0000000 (TDB)                               
    EC= .967276875         QR= .587103582         TP= 2446470.9589491          
    OM= 58.8601271         W= 111.8656638         IN= 162.2421694              
    A= 17.94154996         MA=.1237401            ADIST= 35.295996338          
    PER= 75.9973           N= .012969228          ANGMOM= .018487217           
    DAN= 1.80537           DDN= .84911            L= 191.5461888               
    B= -56.6792985                                TP= 1986-Feb-09.4589491      
 
Physical & non-grav parameters (KM, SEC; A1 & A2 in AU/d^2):
    GM= n.a.               RAD= 5.6               A1= 3.88D-10                 
    A2= 1.55D-10           M1= 5.5                M2= 13.                      
    k1= 8.                 k2= 5.                 PHCOF= .030                  
 
COMET comments 
1: soln ref.= IHW 61,        radius ref. is Belton,M (1991)            
2: k1=8, k2=5, phase coef.=0.03; ref. for magnitude laws is ICQ 1994 Handbook
*******************************************************************************
 Select ... [E]phemeris, [F]tp, [K]ermit, [M]ail, [R]edisplay, ?,  :

Small-body search

JPL Horizons, vers SUN-1.12 
`?' for brief intro, `?!' for more details 
System news updated MAR 04, 1997 -- IMPORTANT!
 
Horizons> dan > 0.9; dan < 1.1; in < 5;
 
Comet & asteroid parameter search:
 DAN > 0.9; DAN < 1.1; IN < 5.;
Continue [ =yes, n=no, ? ] : 
*******************************************************************************
JPL/DASTCOM3               Small-body Search Results       1997-Apr-02 11:15:45

 Comet & asteroid parameter search:      
    DAN > 0.9; DAN < 1.1; IN < 5.;

 Matching small-bodies: 

    Record #  Epoch-yr   Name
    --------  --------   ----
      3361      1996     Orpheus                
      3757      1996     1982 XB                
      4581      1996     Asclepius              
     11809      1996     1988 XB                
     13616      1997     1996 RG3               
     14591      1996     1989 UP                
     14594      1996     1990 HA                
     14621      1996     1991 VG                
     14662      1996     1992 UY4               
     14682      1996     1993 KA2               
     14721      1996     1994 CC                
     14778      1996     1989 VB                
     14779      1996     1990 OS                
     15081      1996     1995 FF                
     16153      1996     1996 GT                
     16263      1996     1996 MQ                

 (16 matches found)
*******************************************************************************
 Select ... [F]tp, [K]ermit, [M]ail, [R]edisplay,  :

Satellite Observer Ephemeris (Io)

$$SOH
*******************************************************************************
JPL On-Line Ephemerides                                                Horizons
*******************************************************************************
TARGET BODY    : Io                        (501)  {Source : JUP100}
OBSERVER SITE  : Los Angeles
*******************************************************************************
EXECUTION DATE : Wed Apr  2 11:24:38 1997  (Pasadena time)
REQUESTED BY   : PORT_LOGIN
INERTIAL FRAME : ICRF/J2000.0
ROTATION SOURCE: IAU94-05B
TARGET RADII   : 1830.0 x 1818.7 x 1815.3 (km)
PRIMARY BODY   : Jupiter     
START TIME     : 1996 OCT 09 15:00 TT 
STOP  TIME     : 1996 OCT 11 04:00 TT 
STEP (MINUTES) : 60
APPARENT COORDS: AIRLESS  
RA FORMAT      : HMS
TIME FORMAT    : CAL 
ELEV. CUTOFF   : -90 DEG
AIRMASS CUTOFF : 38.0000
DAYLIGHT CUTOFF: NO 
***************************************************************************************************************************************************************
 Date (TT)  HR MN     R.A._(ICRF/J2000.0)_DEC RA__(offset)__DEC a-mass APmag S-brt Illu%  ang-sep/v Ob-lon Ob-lat Sl-lon Sl-lat      delta      deldot 1-way_LT
***************************************************************************************************************************************************************
$$EOH
$$SOE
1996 Oct  9 15:00 *m  18 42 53.79 -23 18 38.5   -70.06    -8.71   n.a.   5.5   5.1  99.1 .649E+02/* 324.62  -1.66 313.56  -1.40  5.1917897109  36.3876  43.1788
1996 Oct  9 16:00 *m  18 42 56.00 -23 18 36.5   -54.67    -7.63   n.a.   5.5   5.1  99.1 .508E+02/* 333.09  -1.66 322.03  -1.40  5.1926382827  34.1111  43.1859
1996 Oct  9 17:00 *m  18 42 58.29 -23 18 34.3   -38.09    -6.38   n.a.   5.5   5.1  99.1 .356E+02/* 341.56  -1.66 330.50  -1.40  5.1934300912  31.6801  43.1924
1996 Oct  9 18:00 *m  18 43 00.63 -23 18 32.1   -20.67    -4.99   n.a.   5.5   5.1  99.1 .196E+02/* 350.03  -1.66 338.97  -1.40  5.1941621034  29.1514  43.1985
1996 Oct  9 19:00 *m  18 43 02.99 -23 18 29.7    -2.81    -3.50   n.a.   5.5   5.1  99.1 .434E+01/o 358.50  -1.66 347.44  -1.40  5.1948326692  26.5829  43.2041
1996 Oct  9 20:00 *m  18 43 05.35 -23 18 27.2    15.11    -1.92   n.a.   5.5   5.1  99.1 .140E+02/u   6.96  -1.66 355.91  -1.40  5.1954415240  24.0317  43.2092
1996 Oct  9 21:00 *m  18 43 07.68 -23 18 24.7    32.70    -0.30  7.063   5.5   5.1  99.1 .300E+02/u  15.43  -1.66   4.38  -1.40  5.1959897590  21.5530  43.2137
1996 Oct  9 22:00 *m  18 43 09.96 -23 18 22.2    49.57     1.33  3.334   5.5   5.1  99.1 .455E+02/*  23.90  -1.66  12.85  -1.40  5.1964797604  19.1992  43.2178
1996 Oct  9 23:00 *m  18 43 12.17 -23 18 19.6    65.36     2.93  2.344   5.5   5.1  99.1 .601E+02/*  32.37  -1.66  21.32  -1.40  5.1969151232  17.0183  43.2214
1996 Oct 10 00:00 *m  18 43 14.27 -23 18 17.1    79.72     4.47  1.960   5.5   5.1  99.1 .734E+02/*  40.84  -1.66  29.79  -1.40  5.1973005419  15.0535  43.2246
1996 Oct 10 01:00 *   18 43 16.26 -23 18 14.6    92.36     5.91  1.838   5.5   5.1  99.1 .850E+02/*  49.31  -1.66  38.26  -1.40  5.1976416853  13.3426  43.2275
1996 Oct 10 02:00 N   18 43 18.12 -23 18 12.3   102.99     7.22  1.901   5.5   5.1  99.1 .949E+02/*  57.78  -1.66  46.73  -1.40  5.1979450573  11.9173  43.2300
1996 Oct 10 03:00     18 43 19.83 -23 18 10.0   111.40     8.38  2.186   5.5   5.1  99.1 .103E+03/*  66.26  -1.66  55.21  -1.40  5.1982178495  10.8031  43.2323
1996 Oct 10 04:00     18 43 21.39 -23 18 07.9   117.40     9.36  2.913   5.5   5.1  99.1 .108E+03/*  74.73  -1.66  63.68  -1.40  5.1984677884  10.0191  43.2343
1996 Oct 10 05:00     18 43 22.78 -23 18 06.0   120.86    10.13  5.184   5.5   5.1  99.1 .111E+03/*  83.20  -1.66  72.15  -1.40  5.1987029809   9.5778  43.2363
1996 Oct 10 06:00     18 43 24.00 -23 18 04.3   121.72    10.69 28.833   5.5   5.1  99.1 .112E+03/*  91.68  -1.66  80.63  -1.40  5.1989317588   9.4856  43.2382
1996 Oct 10 07:00     18 43 25.06 -23 18 02.8   119.95    11.01   n.a.   5.5   5.1  99.1 .111E+03/* 100.15  -1.66  89.10  -1.40  5.1991625270   9.7423  43.2401
1996 Oct 10 08:00     18 43 25.96 -23 18 01.5   115.59    11.10   n.a.   5.5   5.1  99.1 .107E+03/* 108.63  -1.66  97.58  -1.40  5.1994036130  10.3416  43.2421
1996 Oct 10 09:00     18 43 26.69 -23 18 00.4   108.75    10.95   n.a.   5.5   5.1  99.1 .100E+03/* 117.10  -1.66 106.05  -1.40  5.1996631219  11.2714  43.2443
1996 Oct 10 10:00     18 43 27.28 -23 17 59.7    99.55    10.56   n.a.   5.5   5.1  99.1 .920E+02/* 125.58  -1.66 114.53  -1.40  5.1999487949  12.5136  43.2467
1996 Oct 10 11:00     18 43 27.73 -23 17 59.1    88.21     9.94   n.a.   5.5   5.1  99.1 .816E+02/* 134.05  -1.66 123.00  -1.40  5.2002678731  14.0446  43.2493
1996 Oct 10 12:00  m  18 43 28.06 -23 17 58.9    74.96     9.11   n.a.   5.5   5.1  99.1 .694E+02/* 142.53  -1.66 131.48  -1.40  5.2006269673  15.8357  43.2523
1996 Oct 10 13:00 Nm  18 43 28.28 -23 17 58.8    60.09     8.08   n.a.   5.5   5.1  99.1 .558E+02/* 151.01  -1.66 139.96  -1.40  5.2010319330  17.8528  43.2557
1996 Oct 10 14:00 *m  18 43 28.42 -23 17 59.0    43.92     6.87   n.a.   5.5   5.1  99.1 .409E+02/* 159.49  -1.66 148.44  -1.40  5.2014877549  20.0575  43.2595
1996 Oct 10 15:00 *m  18 43 28.49 -23 17 59.4    26.80     5.51   n.a.   5.5   5.1  99.1 .252E+02/* 167.96  -1.66 156.92  -1.40  5.2019984392  22.4070  43.2637
1996 Oct 10 16:00 *m  18 43 28.53 -23 17 59.9     9.11     4.04   n.a.   5.5   5.1  99.1 .929E+01/t 176.44  -1.66 165.40  -1.40  5.2025669189  24.8547  43.2684
1996 Oct 10 17:00 *m  18 43 28.54 -23 18 00.5    -8.78     2.47   n.a.   5.5   5.1  99.1 .844E+01/t 184.92  -1.66 173.88  -1.40  5.2031949726  27.3514  43.2737
1996 Oct 10 18:00 *m  18 43 28.57 -23 18 01.2   -26.48     0.85   n.a.   5.5   5.1  99.1 .243E+02/* 193.40  -1.66 182.35  -1.40  5.2038831610  29.8452  43.2794
1996 Oct 10 19:00 *m  18 43 28.63 -23 18 01.9   -43.59    -0.79   n.a.   5.5   5.1  99.1 .400E+02/* 201.87  -1.66 190.83  -1.40  5.2046307845  32.2831  43.2856
1996 Oct 10 20:00 *m  18 43 28.74 -23 18 02.6   -59.74    -2.41   n.a.   5.5   5.1  99.1 .549E+02/* 210.35  -1.66 199.31  -1.40  5.2054358640  34.6120  43.2923
1996 Oct 10 21:00 *m  18 43 28.94 -23 18 03.2   -74.57    -3.98  6.596   5.5   5.1  99.1 .686E+02/* 218.83  -1.66 207.79  -1.40  5.2062951484  36.7796  43.2994
1996 Oct 10 22:00 *m  18 43 29.25 -23 18 03.8   -87.76    -5.46  3.239   5.5   5.1  99.1 .808E+02/* 227.31  -1.65 216.27  -1.40  5.2072041512  38.7356  43.3070
1996 Oct 10 23:00 *m  18 43 29.68 -23 18 04.2   -99.02    -6.82  2.309   5.5   5.1  99.1 .912E+02/* 235.78  -1.65 224.75  -1.40  5.2081572185  40.4335  43.3149
1996 Oct 11 00:00 *m  18 43 30.25 -23 18 04.3  -108.08    -8.03  1.947   5.5   5.1  99.1 .996E+02/* 244.26  -1.65 233.22  -1.40  5.2091476279  41.8315  43.3232
1996 Oct 11 01:00 *   18 43 30.98 -23 18 04.3  -114.77    -9.06  1.837   5.5   5.1  99.1 .106E+03/* 252.73  -1.65 241.70  -1.40  5.2101677213  42.8937  43.3316
1996 Oct 11 02:00 N   18 43 31.88 -23 18 04.1  -118.91    -9.90  1.911   5.5   5.1  99.1 .110E+03/* 261.21  -1.65 250.18  -1.40  5.2112090618  43.5917  43.3403
1996 Oct 11 03:00     18 43 32.96 -23 18 03.6  -120.43   -10.51  2.214   5.5   5.1  99.1 .111E+03/* 269.68  -1.65 258.65  -1.39  5.2122626232  43.9050  43.3491
1996 Oct 11 04:00     18 43 34.22 -23 18 02.8  -119.28   -10.89  2.986   5.5   5.1  99.1 .110E+03/* 278.15  -1.65 267.13  -1.39  5.2133189957  43.8225  43.3579
$$EOE
$$SOD
***************************************************************************************************************************************************************
Column meaning:
 
SOLAR PRESENCE
  Time tag is followed by a blank, then a solar-presence symbol:

        '*'  Daylight (refracted solar upper-limb on or above apparent horizon)
        'C'  Civil twilight/dawn
        'N'  Nautical twilight/dawn
        'A'  Astronomical twilight/dawn
        ' '  Night OR geocentric ephemeris

LUNAR PRESENCE
  The solar-presence symbol is immediately followed by a lunar-presence symbol:

        'm'  Refracted upper-limb of Moon on or above apparent horizon
        ' '  Refracted upper-limb of Moon below apparent horizon OR geocentric
             ephemeris
 
 R.A._(ICRF/J2000.0)_DEC =
   J2000.0 astrometric right ascension and declination of target. Corrected
for light-time. Units: HMS (HH MM SS.ff) and DMS (DD MM SS.f)
 
 RA_(offset)_DEC =
   The difference in RA and DEC between the center of a (non-lunar) natural
satellite target and the center of the planet it orbits (satellite-primary).
Units: ARCSECONDS
 
 a-mass =
   Relative optical airmass, TOPOCENTRIC, ABOVE HORIZON ONLY. Unitless.
 
 APmag S-brt =
   Target's approximate apparent visual magnitude & surface brightness.
Units: none & VISUAL MAGNITUDES PER SQUARE ARCSECOND
 
 Illu% =
   Fraction of target circular disk illuminated by Sun (phase), as seen by
observer.  Units: PERCENT
 
 ang-sep/v =
  Target-primary angular separation and visibility. The angle between the
center of target object and the center of the primary body it revolves around,
as seen by the observer. Units: ARCSECONDS

  Satellite visibility codes:
    /t = Transitting primary body disk,  /o = Occulted by primary body disk,
    /p = Partial umbral eclipse,         /u = Total umbral eclipse,
    /- = Target is the primary body,     /* = None of above ("free and clear")
 
 Ob-lon Ob-lat =
   Observer sub-longitude and sub-latitude. The 1994 IAU planetographic
longitude and latitude of the center of the target disk seen by the observer.
Units: DEGREES
 
 Sl-lon Sl-lat =
   Solar sub-longitude and sub-latitude. The 1994 IAU planetographic longitude
and latitude of the center of the target disk seen from center of Sun.
Units: DEGREES
 
  delta  deldot =
   Target apparent range ("delta") and range-rate ("delta-dot") relative to
observer. Units: AU and KM/S
 
 1-way_LT =
   Target 1-way light-time, as seen by observer. Units: MINUTES


 Computations by ...
     Solar System Dynamics Group, Horizons On-Line Ephemeris System
     4800 Oak Grove Drive, Jet Propulsion Laboratory
     Pasadena, CA  91109   USA

***************************************************************************************************************************************************************
$$EOD
$$EOF

Asteroid Observer Ephemeris (1 Ceres)

$$SOH
*******************************************************************************
JPL On-Line Ephemerides                                                Horizons
*******************************************************************************
TARGET BODY    : 1 Ceres                          {Source : JPL#03-DASTCOM3}
OBSERVER SITE  : Los Angeles
*******************************************************************************
EXECUTION DATE : Mon Jul 21 17:12:21 1997  (Pasadena time)
REQUESTED BY   : PORT_LOGIN
TARGET RADII   : 466.5 (km)
PRIMARY BODY   : Sun         
START TIME     : 1996 OCT 06 00:00 TDT
STOP  TIME     : 1996 OCT 07 00:00 TDT
STEP (MINUTES) : 30
APPARENT COORDS: AIRLESS  
RA FORMAT      : HMS
TIME FORMAT    : CAL 
ELEV. CUTOFF   : -90 DEG
AIRMASS CUTOFF : 38.0000
DAYLIGHT CUTOFF: YES
*******************************************************************************
Initial heliocentric osc. elements wrt ecliptic and mean equinox of J2000.0:
  EPOCH=  2450600.5 != 1997-Jun-01.0000000 (TDB)                               
    EC= .07652422          QR= 2.558190529        TP= 2449830.0046917          
    OM= 80.5995101         W= 73.0340746          IN= 10.5840296               
Asteroid physical parameters:
    GM= 70.                RAD= 466.5             ROTPER= 9.075                
    H= 3.34                G= .120                B-V= .720                    
***************************************************************************************************************************************************************
 Date (TT)  HR MN     R.A._(airls-apparent)__DEC. Azi_(a-appr)_Elev a-mass APmag S-brt Illu%         r         rdot      delta      deldot 1-way_LT O-E-M/Illu%
***************************************************************************************************************************************************************
$$EOH
$$SOE

>..... Daylight Cut-off Requested .....<

1996 Oct  6 02:00 N   17 01 10.4781 -25 09 18.280 213.4996  22.6613  2.577   9.1   6.9  97.5  2.8700305659   1.1537  3.1706906223  22.4453  26.3698 135.7/ 35.3
1996 Oct  6 02:30 A   17 01 12.1722 -25 09 22.299 219.5902  18.9407  3.049   9.1   6.9  97.5  2.8700444581   1.1537  3.1709609359  22.4786  26.3721 135.3/ 35.1
1996 Oct  6 03:00     17 01 13.8683 -25 09 26.303 225.1703  14.7299  3.864   9.1   6.9  97.5  2.8700583497   1.1536  3.1712316315  22.5080  26.3743 135.0/ 34.8
1996 Oct  6 03:30     17 01 15.5666 -25 09 30.293 230.2794  10.1083  5.485   9.1   6.9  97.5  2.8700722406   1.1536  3.1715026573  22.5328  26.3766 134.7/ 34.5
1996 Oct  6 04:00     17 01 17.2675 -25 09 34.272 234.9708   5.1454  9.816   9.1   6.9  97.5  2.8700861309   1.1535  3.1717739555  22.5526  26.3788 134.4/ 34.3
1996 Oct  6 04:30     17 01 18.9711 -25 09 38.240 239.3036  -0.0998 32.554   9.1   6.9  97.5  2.8701000206   1.1535  3.1720454633  22.5671  26.3811 134.0/ 34.0
1996 Oct  6 05:00     17 01 20.6776 -25 09 42.200 243.3382  -5.5778   n.a.   9.1   6.9  97.5  2.8701139097   1.1534  3.1723171133  22.5759  26.3834 133.7/ 33.8
1996 Oct  6 05:30     17 01 22.3873 -25 09 46.154 247.1345 -11.2473   n.a.   9.1   6.9  97.5  2.8701277982   1.1534  3.1725888357  22.5789  26.3856 133.4/ 33.5
1996 Oct  6 06:00     17 01 24.1001 -25 09 50.104 250.7514 -17.0737   n.a.   9.1   6.9  97.5  2.8701416860   1.1533  3.1728605585  22.5759  26.3879 133.1/ 33.3
1996 Oct  6 06:30     17 01 25.8161 -25 09 54.053 254.2489 -23.0278   n.a.   9.1   6.9  97.5  2.8701555733   1.1533  3.1731322094  22.5669  26.3901 132.9/ 33.0
1996 Oct  6 07:00     17 01 27.5353 -25 09 58.002 257.6914 -29.0844   n.a.   9.1   6.9  97.5  2.8701694599   1.1532  3.1734037168  22.5522  26.3924 132.6/ 32.8
1996 Oct  6 07:30     17 01 29.2576 -25 10 01.954 261.1536 -35.2210   n.a.   9.1   6.9  97.5  2.8701833458   1.1531  3.1736750111  22.5318  26.3947 132.3/ 32.6
1996 Oct  6 08:00     17 01 30.9829 -25 10 05.910 264.7298 -41.4161   n.a.   9.1   6.9  97.5  2.8701972312   1.1531  3.1739460256  22.5061  26.3969 132.0/ 32.4
1996 Oct  6 08:30  m  17 01 32.7111 -25 10 09.873 268.5524 -47.6476   n.a.   9.1   6.9  97.5  2.8702111159   1.1530  3.1742166982  22.4755  26.3992 131.8/ 32.2
1996 Oct  6 09:00  m  17 01 34.4420 -25 10 13.846 272.8271 -53.8894   n.a.   9.1   6.9  97.5  2.8702250001   1.1530  3.1744869719  22.4405  26.4014 131.6/ 32.0
1996 Oct  6 09:30  m  17 01 36.1753 -25 10 17.828 277.9095 -60.1045   n.a.   9.1   6.9  97.5  2.8702388836   1.1529  3.1747567964  22.4016  26.4036 131.3/ 31.8
1996 Oct  6 10:00  m  17 01 37.9107 -25 10 21.823 284.4907 -66.2294   n.a.   9.1   6.9  97.5  2.8702527664   1.1529  3.1750261281  22.3594  26.4059 131.1/ 31.7
1996 Oct  6 10:30  m  17 01 39.6480 -25 10 25.831 294.1036 -72.1283   n.a.   9.1   6.9  97.5  2.8702666487   1.1528  3.1752949317  22.3147  26.4081 130.9/ 31.5
1996 Oct  6 11:00  m  17 01 41.3867 -25 10 29.853 310.5974 -77.4340   n.a.   9.1   6.9  97.5  2.8702805303   1.1528  3.1755631803  22.2682  26.4104 130.7/ 31.4
1996 Oct  6 11:30  m  17 01 43.1266 -25 10 33.891 342.3787 -80.9859   n.a.   9.1   6.9  97.5  2.8702944114   1.1527  3.1758308562  22.2205  26.4126 130.6/ 31.2
1996 Oct  6 12:00  m  17 01 44.8672 -25 10 37.944  25.6090 -80.5254   n.a.   9.1   6.9  97.5  2.8703082918   1.1527  3.1760979508  22.1726  26.4148 130.4/ 31.1
1996 Oct  6 12:30 Am  17 01 46.6082 -25 10 42.013  53.6083 -76.4572   n.a.   9.1   6.9  97.5  2.8703221716   1.1526  3.1763644650  22.1251  26.4170 130.2/ 31.0
1996 Oct  6 13:00 Nm  17 01 48.3492 -25 10 46.098  68.2105 -70.9796   n.a.   9.1   6.9  97.5  2.8703360507   1.1526  3.1766304092  22.0789  26.4192 130.1/ 30.9

>..... Daylight Cut-off Requested .....<

$$EOE
$$SOD
***************************************************************************************************************************************************************
Column meaning:
 
SOLAR PRESENCE
  Time tag is followed by a blank, then a solar-presence symbol:

        '*'  Daylight (refracted solar upper-limb on or above apparent horizon)
        'C'  Civil twilight/dawn
        'N'  Nautical twilight/dawn
        'A'  Astronomical twilight/dawn
        ' '  Night OR geocentric ephemeris

LUNAR PRESENCE
  The solar-presence symbol is immediately followed by a lunar-presence symbol:

        'm'  Refracted upper-limb of Moon on or above apparent horizon
        ' '  Refracted upper-limb of Moon below apparent horizon OR geocentric
             ephemeris
 
 R.A._(airls-apparent)__DEC. =
   Airless apparent right ascension and declination of target. Corrected for
light-time, stellar aberration, precession, nutation and deflection of light
due to the Sun & Earth.  Units: HMS (HH MM SS.ffff) and DMS (DD MM SS.fff)
 
 Azi_(a-appr)_Elev =
   Airless apparent azimuth and elevation of target. Corrected for light-time,
stellar aberration, precession, nutation and the deflection of light due to the
Sun and Earth. TOPOCENTRIC ONLY. Units: DEGREES
 
 a-mass =
   Relative optical airmass, TOPOCENTRIC, ABOVE HORIZON ONLY. Unitless.
 
 APmag S-brt =
   Asteroid's approximate apparent visual magnitude & surface brightness.
APmag = H + 5*log10(delta) + 5*log10(r) - 2.5*log10((1-G)*phi1 + G*phi2)
Units: none & VISUAL MAGNITUDES PER SQUARE ARCSECOND
 
 Illu% =
   Fraction of target circular disk illuminated by Sun (phase), as seen by
observer.  Units: PERCENT
 
 r       rdot =
   Target apparent heliocentric range ("r") and range-rate ("rdot") as seen
by observer. Units: AU and KM/S
 
  delta  deldot =
   Target apparent range ("delta") and range-rate ("delta-dot") relative to
observer. Units: AU and KM/S
 
 1-way_LT =
   Target 1-way light-time, as seen by observer. Units: MINUTES
 
 O-E-M/Illu% =
   Obj-Earth-Moon/Illum%; apparent angle seen by Earth observer and the percent
of the lunar disk illuminated by the Sun. Units: DEGREES and PERCENT


 Computations by ...
     Solar System Dynamics Group, Horizons On-Line Ephemeris System
     4800 Oak Grove Drive, Jet Propulsion Laboratory
     Pasadena, CA  91109   USA
     connect: telnet ssd.jpl.nasa.gov 6775

***************************************************************************************************************************************************************
$$EOD
$$EOF
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