A Model for Spacecraft Formation Dynamics Including Aerodynamic Drag Effects

Exploitation of formation flying in Low Earth Orbit requires accurate modeling of the dynamics, including atmospheric drag. Attempts available in literature focus on the use of simple density models involved in the forcing term to allow for a closed form solution of the linearized equations. This paper takes a different approach suggested by classical general perturbation theory, and proposes a solution of the full dynamics as a sequence of problems related to the increasing order of the terms taken into account. With the help of symbolic mathematic software, the solution is expressed in an easy-to-implement way, suitable for on board computer characteristics. The accuracy of this solution is validated by a comparison with a standard numerical propagation. The overall approach is especially interesting in view of an inexpensive, autonomous orbital control of spacecraft formations. The findings of a possible control strategy simulation are provided as an example