Formation Design in Eccentric Orbits Using Linearized Equations of Relative Motion

Abstract

Geometrical methods for formation flying design based on the analytical solution to Hill’s equations have been previously developed and used to specify desired relative motions in near circular orbits. These approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a particular geometrical shape. A comparable set of geometrical relationships for formations in eccentric orbits, where Hill’s equations are not valid, is presented. The use of these relationships to investigate formation designs and their evolution in time is demonstrated.