Analytic theory of orbit contraction
Abstract
The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 December 1977
 Bibcode:
 1977STIN...7830022V
 Keywords:

 Equations Of Motion;
 Numerical Analysis;
 Orbit Calculation;
 Orbital Mechanics;
 Satellite Orbits;
 Aerodynamic Forces;
 Differential Equations;
 Gravitational Effects;
 Lagrange Multipliers;
 Poincare Problem;
 Astrophysics