Solution for the Lambert Problem in Multiples Stages Applied to a Satellite Constellation and a Study of Close Approaching Strategies for Rendezvous and Docking Operations
by
Gilberto Arantes, Jr
Center of Applied Space Technology and Microgravity ZARM
Coauthors: Evandro Marconi Rocco, Antonio Fernando Bertachini de Almeida Prado and Stephan Theil

The purpose of this work is to present an approach to solve the Lambert problem in the context of a constellation of service satellites that should be maneuvered, in a initial phase, to perform a rendezvous with a customer spacecraft. This operation could be necessary for missions as rescue, de-orbit of large space debris, or even maintenance in-orbit. A study was made analyzing the capacity for the rendezvous and docking (RVD) with customer spacecraft taken into account each service satellite, the time of flight and the fuel consumption constraints. The use of service satellites could avoid a new launch and replacement of stranded spacecrafts reducing the ownership cost. The Lambert problem was written by using universal variables and was solved by a methodology that consider a multi-stages in the optimization process. The use of those stages allowed to achieve accurate results in a reduced CPU time. In addition, a wide study by dealing in great numbers of close maneuvers in the last phase of RVD is presented and reviewed. Based on Clohessy-Wiltshire equations the close maneuvers was analyzed and a discussion about strategies to inspect, final approach and also safe departure of the customer spacecraft, in terms of safety and fuel consumption, is done. A survey of close approaching maneuvers in that context is presented. This work intends to cover the maneuvers issue for RVD problems from far to close ranges.

Date received: November 23, 2007