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, in right ascension,
Dec., and in distance, r, from the Keplerian formulation
described in the links below.
||1800 -- 2050
||3000 BC to 3000 AD
||10|| 1|| 200
|| 400|| 15||4000
||5|| 2|| 300
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
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: