Safety analysis for near rectilinear orbit close approach rendezvous in the circular restricted three-body problem

On the road to a human exploration of Mars, several mission scenarios beyond Low Earth Orbit have been identified by the International Space Exploration Coordination Group (ISEGC) as significant landmarks. One fundamental step being considered includes the establishment of a new space station on a Near Rectilinear Orbit (NRO), at one of the libration points of the Earth-Moon system. In this context, the ability to rendezvous in cis-lunar space, necessary for the station deployment and its overall operability, could rely on the combined use of the NASA/ESA Orion Multi-Purpose Crew Vehicle and the Space Launch System (SLS), both currently under development. The Near Rectilinear Orbits (NROs) selected for this work have already been studied in literature but, to the author's knowledge, never considered for a rendezvous analysis. In this paper, a design of Orion's NRO close approach rendezvous strategy is developed using the Circular Restricted Three-Body Problem (CRTBP) as a baseline framework. First, different linear models used to describe cis-lunar relative motion, as the CRTBP linearized relative equations, the Clohessy-Wiltshire equations and the Straight Line equations are discussed and compared. Second, a direct two-impulse transfer is implemented as a tool to compare the results obtained from the linear models and the full non-linear relative model. It is shown that the error introduced by linear models is not generally satisfactory for high-precision maneuvers, especially in orbital regions where the lunar influence is highly predominant, such as the periselene. Third, different close approach strategies are implemented, taking into account Orion’s sensor suite, the existing requirements for a LEO rendezvous and the peculiar deep-space conditions. Fourth, a stochastic analysis is performed to validate and compare the results. Finally, a general close approach rendezvous strategy is built so that the safety of the procedure is ensured throughout the whole mission. The requirements deriving from this analysis are then discussed and compared with the ones currently employed for a rendezvous in Low Earth Orbit. The pivotal point of this work is represented by the development of an algorithm to solve a Lambert's Three-Body Problem with the full non-linear relative CRTBP dynamics.

Sulla strada per una esplorazione umana di Marte, numerose missioni oltre la Low Earth Orbit (LEO) sono state identificate dall'International Space Exploration Coordination Group (ISEGC) come pietre miliari. In questo contesto, un passo fondamentale considerato è il posizionamento di una stazione spaziale su una Near Rectilinear Orbit (NRO). La capacità di effettuare un rendezvous in un contesto di problema dei 3 corpi diventa così fondamentale, anche alla luce del possibile utilizzo della capsula Orion per questo tipo di missioni. Le Near Rectilinar Orbits sono state già analizzate in letteratura ma mai prese in considerazione per uno studio di rendezvous. In questo lavoro, è stata sviluppata una strategia di close-approach rendezvous basata sulle NRO e sul problema dei 3 corpi. Dapprima, diversi modelli lineari sono stati comparati per verificarne l'accuratezza nel descrivere il moto relativo e per verificare la possibilità di utilizzare un targeting relativo lineare. Questo tipo di analisi non ha fornito risultati soddisfacenti e dunque un algoritmo non-lineare è stato implementato. Successivamente, il moto relativo in 3 corpi è stato analizzato e sono state messe in luce le principali differenze con il moto a 2 corpi. Sulla base di questo, sono stati ridefiniti i safety requirements legati al close-approach rendezvous e, infine, una traiettoria ottima in termini di safety e consumo di carburante è stata generata.