This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.

 Mathematica in Celestial Mechanics: A Sampling The advanced symbolic and other capabilities of Mathematica make it the ideal tool for solving problems in the field for which calculus and much of modern mathematics was originally invented. 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 .