Satellites and Riemannian geometry

Abstract

In an axially symmetric three-dimensional Riemann-spacegik(u1,u2)−u3 represents the cyclic parameter-, a gravitational potential ϕ(u1,u2) is given. For all masspoints with equal total energy and equal angular momentum there exists a function Ψ(u1,u2) by means of which the equations of motion can be reduced to a simple ordinary second-order differential equation. The function ϕ can be interpreted as the velocity with which the masspoint moves in the two-dimensional spaceu1,u2.