ABSTRACT
Many physical systems are described by differential equations. As an example, we consider the two-body problem (the Kepler prob-
lem). It concerns the motion of two bodies under mutual gravitation. By placing a reference frame at one of the bodies, the problem can be reduced to the motion of a single body in a central gravitational force field. The force is expressed by the universal law of gravitation
F = −µ x‖x‖3 ,
where the gravitational constant and the total mass of the system are normalized to 1. At every position x in the phase space R3 \ {(0, 0, 0)} there is a force vector that points towards the origin and has its magnitude inverse proportional to the square of the distance to the origin. The motion of the body is governed by the second order differential equation
d2x
dt2 = − x‖x‖3 .
