In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force that varies in strength as the inverse square of the distance …

It can be shown that, in general, Kepler’s problem is equivalent to the two-body problem, in which two masses, M and m, move solely due to the influence of their mutual gravitational attraction.

The granddaddy of all problems in dynamical systems is the so-called Kepler problem. Isaac Newton invented the calculus in order to solve the equations he had discovered while studying Kepler's laws …

Problem: For a satellite orbiting a planet, transfer between coplanar circular orbits can be affected by an elliptic orbit with perigee and apogee distances equal to the radii of the respective circles as shown in …

This is called the Kepler problem since it was Kepler who discovered that the orbits of planets were elliptical, and explaining this was the rst major triumph of Newtonian mechanics.

There are two methods that we can use to solve this problem. The first uses material that we have already developed, and the second introduces a new idea that is extremely useful.

The most important “three-body problem” in the 17th and 18th centuries involved finding the motion of the moon, due to gravitational interaction with both the sun and the earth.