Use of nonspherical gravity harmonics for relative motion GN/C (category 2)
Abstract
Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multivehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as ClohessyWiltshire type) from the farfield to the nearfield interface, i.e., within 1 nm and; (3) close proximity motion  the nearfield motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of nonspherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the ClohessyWiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to nonspherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).
 Publication:

Automated Rendezvous and Capture Review. Executive Summary
 Pub Date:
 1991
 Bibcode:
 1991arcr.nasaR....H
 Keywords:

 Algorithms;
 Gravitation;
 Gravitational Effects;
 Harmonics;
 Mathematical Models;
 Numerical Analysis;
 Orbital Mechanics;
 Equations Of Motion;
 Far Fields;
 Near Fields;
 Perturbation;
 Spacecraft Design, Testing and Performance