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Keplerian Elements for Approximate Positions of the Major Planets

This page contains sufficient information and data to allow computation of approximate positions for the planets. Formulae are provided in a PDF document due to the inability of HTML to effectively format mathematical expressions. Tables containing the required Keplerian elements are provided in plain ASCII text format to allow for both human and machine readability.

You are reminded that these formulae and data provide approximate positions for the planets. They should not be used unless the errors (tabulated below) are acceptable for your application. High precision ephemerides for the planets are available via our HORIZONS system.

Approximate Errors

Approximate errors, in right ascension, RA, declination, Dec., and in distance, r, from the Keplerian formulation described in the links below.

  1800 -- 2050 3000 BC to 3000 AD
  RA
(arcsec)
Dec.
(arcsec)
r
(1000 km)
RA
(arcsec)
Dec.
(arcsec)
r
(1000 km)
Mercury 1511 20151
Venus 2014 40308
Earth-Moon
Barycenter
2086 401515
Mars 40225 1004030
Jupiter 40010600 6001001000
Saturn 600251500 10001004000
Uranus 50 21000 2000 308000
Neptune 10 1 200 400 154000
Pluto 5 2 300 4001002500

Formulae for Computing Approximate Planetary Positions

Lower accuracy formulae for planetary positions have a number of important applications when one doesn't need the full accuracy of an integrated ephemeris. They are often used in observation scheduling, telescope pointing, and prediction of certain phenomena as well as in the planning and design of spacecraft missions.

Approximate positions of the major planets and Pluto may be found by using Keplerian formulae with their associated elements and rates. Such elements are not intended to represent any sort of mean; they are simply the result of being adjusted for a best fit. As such, it must be noted that the elements are not valid outside the given time-interval over which they were fit.

Since the combination of HTML with the large number of web browsers currently available do not render mathematical expressions reliably, the document containing the formulae and data required to compute approximate planetary positions is formatted as a PDF document.

Keplerian Elements

The data required for use in these formulae are available both in the above referenced PDF document and as ASCII plain text files (see below). There are two ASCII tables containing the Keplerian mean elements appropriate for specified time spans:

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