Orbital elements by date for the orbits of the planets

PlanetL (°)a (au)ei (°)Ω (°)ϖ (°)


h m s

This script provides the details of orbits of the planets (eccentricity, ascending nodes, argument of perihelion, etc.) at a given date. See the explanation below. It could be used for low precision calculations of the location of the planets, but is not suitable for high precision calculations (such as conjunctions or occultations) since pertubations are not taken into account. It will be reasonably accurate for recent historical dates or dates in the near future, but should not be relied on for dates in the far future or distant past. The number of digits given above should not be interpreted as an indication of accuracy.

In the table:
L is the mean longitude of the planet (degrees);
a is the semimajor axis of the orbit (au);
e is the eccentricity of the orbit;
i is the inclination to the plane of the ecliptic (degrees);
Ω is the longitude of the ascending node (degrees);
ϖ is the longitude of the perihelion (degrees).
See the diagram below for more details.

The algorithm is from Jean Meeus Astronomical Algorithms (2nd ed) Chapter 31 and is based on JL Simon et al (1994) "Numerical expresssions for precession formulae and mean elements for the Moon and Planets", Astronomy and Astrophysics 282 pp663-683. It was coded by Richard Kaye

Diagram showing coordinate system used for orbital elements

The diagram above shows the orbit of a planet as seen from the sun. The points and angles in the table and diagram are as follows. (All angles are as subtended at the sun.)

Richard Kaye, http://www.rwkaye.co.uk/.