Investigation of near-rectilinear halo orbit search and rescue using staging L1/L2 Lyapunov and distant retrograde orbit families

Cislunar space is a region of growing interest with nations investing resources to cultivate long presence habitations on the lunar surface. With this increased attention and expansion of missions, both crewed and uncrewed, the likelihood of a mishap or a spacecraft becoming impaired and unable to continue its mission will also increase. The present research adds to the field of cislunar mission operations and trajectory analysis by investigating search and rescue (SAR) operations via rendezvous and proximity operations (RPO) with an impaired notional spacecraft located in a Near-Rectlinear Halo Orbit (NRHO). This research compares the response times of rescuer spacecraft located in sample distant retrograde orbits (DROs) and $L_1$/$L_2$ Lyapunov orbits for the timely far rendezvous with the impaired spacecraft located in the NRHO. This will simulate a variety of far rendezvous whereby the impaired spacecraft’s location within the NRHO and the rescuer spacecraft in the $L_1$/$L_2$ Lyapunov and DRO orbit families are varied. A series of minimum time optimal control problems are posed using the circular restricted three-body problem (CR3BP) dynamics, and pseudospectral methods are used to find solutions given an example maximum $\Delta V$ constraint of 3 km/s. The results reinforces our intuition that rendezvous time of flight (TOF) between orbits within the $L_1$, $L_2$, and DRO families and the targeted NRHO correlate with proximity to the NRHO, with the shortest far rendezvous times in each family found to be approximately 6 hours, 4.5 hours, and 10 hours respectively. The results further show that a constellation of two rescue spacecraft could be positioned within the three orbit families to achieve far rendezvous with the chosen NRHO in under one day.