This is documentation for Mathematica 5.2, which was
based on an earlier version of the Wolfram Language.

Mathematica in Celestial Mechanics: A Sampling

# Zero Velocity Curves in the Restricted Three Body Problem

Let and be bipolar coordinates and the smaller mass.

# Series Solution of Newton's Equation

Let R[t] be the radius vector, r[t] the length. Then we can write . f[t] and g[t] can be calculated iteratively by series expansion using the equation of motion.

Here is the actual computation.

# Poisson Series Expansion for the Center in Kepler Motion

The motion of the so-called center in Kepler motion cannot be expressed in closed form, but a series approximation can be calculated in the following way.

Here is the 2,2 approximation.

Here is the more accurate 6,6 approximation.

# Riemann Surface for the Kepler Equation

One of the most important equations in celestial mechanics is the Kepler equation:

Here is a picture of a part the Riemann surface of the function over the complex m-plane. The branch points at are clearly visible .