Anomalies for Planetary Motion
![](/img/demonstrations-branding.png)
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
The Kepler motion of a planet (brown dot) around a star (yellow dot) follows an ellipse. Given a semimajor axis and eccentricity
, the current position of the planet at time
since the perihelion passage is given by the true anomaly
. To determine this, we first have to calculate the eccentric anomaly
from the mean anomaly
.
Contributed by: Thomas Müller (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Kepler's third law gives a relation between the semimajor axis and the period
of a planet,
, where
is the gravitational constant and the solar mass is set equal to 1. The mean anomaly is defined as
, where
is the time since the perihelion passage of the planet. To obtain the eccentric anomaly, we have to solve the Kepler equation
. The true anomaly can be determined via
. The distance between the star and the planet is given by
.
Permanent Citation