A nonlinear dynamical model of relative motion for the orbiting debris problem
Abstract
A nonlinear dynamical model of relative motion is presented for the orbital breakup problem. The model is applied to the analysis of debris density, starting at the time of breakup and proceeding until the cloud rings the earth. A linear relative motion model generalizing the Clohessy and Wiltshire equations to all eccentricity and secular J(2) is produced, and selected higherorder terms are added. It is shown that an improvement over linear relative motion methods is achieved for the expanding debris cloud. The inverse of the relative motion transformation enables an analysis of debris differentially at a location in space as a function of initial breakupspread velocity statistics. The structure of a debris cloud is considered, and it is concluded that debris density increases by four orders of magnitude around the wellknown pinched features of the cloud and at locations internal to the cloud.
 Publication:

Astrodynamics 1989
 Pub Date:
 1990
 Bibcode:
 1990asdy.conf..393H
 Keywords:

 Dynamic Models;
 Orbital Lifetime;
 Space Debris;
 Spacecraft Motion;
 Nonlinearity;
 Spacecraft Breakup;
 Astrodynamics