On Szebehely's Equation and its Connection with Dainelly's / Whittaker's Equations
Abstract
In this paper we prove that Szebehely's equation implies the condition necessary and sufficient in order that the DainelliWhittaker formulas be obtained from a potential function. Thus, we prove that Szebehely's equation is not only a necessary condition to be satisfied by the potential U(ěc x) but is also a sufficient condition. This was shown by Broucke and Lass (1977) using a procedure different from ours. We obtain also a first order partial differential equation for the function g^{2} (ěc x) appearing in the paper of Broucke and Lass. This equation, being of a quite simple structure, is quite adequate for its integration, and this is shown by examples.
 Publication:

Celestial Mechanics
 Pub Date:
 May 1984
 DOI:
 10.1007/BF01231096
 Bibcode:
 1984CeMec..33...85G
 Keywords:

 Celestial Mechanics;
 Orbit Calculation;
 Trajectory Analysis;
 Whittaker Functions;
 Orbital Mechanics;
 Partial Differential Equations;
 Potential Theory;
 Astronomy