Anomalies for Planetary Motion

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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 .



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send