Juan Ojeda Romero, John Hopkins Applied Physics Lab; Fouad Khoury, Johns Hopkins Applied Physics Laboratory
Keywords: Multibody Astrodynamics, Cislunar Rendezvous and Proximity Operations, Relative Motion, Bicircular Restricted Four Body Problem, Circular Restricted Three-Body Problem, Dynamical Systems Theory
Abstract:
As NASA moves to enable a more permanent human presence beyond Earth orbit, the current state-of-the-art spacecraft guidance, navigation, and control (GNC) technologies need to be developed in order operate spacecraft in more challenging dynamical environments. Notably, NASAs Artemis program seeks a return to the Moon and plans to leverage the lunar surface and surrounding cislunar region as a proving ground to test and employ new technologies for coordinating spacecraft to meet near and long term human exploration objectives. For example, NASAs proposed orbiting platform, Gateway, which is proposed as the first deep-space station beyond low Earth orbit is expected to orbit near the Moon in a 9:2 Lunar Synodic Resonant NRHO (Near Rectilinear Halo Orbit) and serve as a staging location for missions to the lunar surface and beyond. A critical element of these future space architectures warrant the capability to coordinate multiple spacecraft relative to one another to accomplish mission objectives such as rendezvous and proximity operations. As a result, the need arises to advance relative motion GNC technologies in flight regimes simultaneously governed by multiple gravitational influences from the Moon, Earth, and Sun.
Most of the previous work in relative motion modeling has been confined to near-Keplerian orbit regimes where the gravitational influence on spacecraft is assumed to stem from a single primary body and additional perturbations can be approximated to first-order effects. Recently, relative motion in more complex dynamical regimes, like the Circular Restricted Three-Body Problem (CRTBP) model has been investigated but these models ignore the nontrivial influence of the Sun on certain trajectories in the cislunar vicinity. Moreover, additional some mission requirements, including NASAs proposed rendezvous operations between the Orion spacecraft and Gateway, stipulate that proximity operations are performed with Sun-lit geometries. The Bi-Circular Restricted Four-Body Problem (BCRFBP) is a lower-fidelity model that incorporates the gravitational influence of all three celestial bodies within one dynamical model. In the Sun-Earth-Moon, SEM, system, the model is derived in either the Earth-Moon rotating frame or the Sun-B1 rotating frame, where B1 is the Earth-Moon barycenter. The SEM BCRFBP model is an extension of the Earth-Moon Circular Restricted Three-Body Problem (CRTBP) model with the added gravitational influence of the Sun. Although the BCRFBP model is not coherent, e.g., the motion of the Earth, Moon, and Sun are assumed to be along the same orbital plane, it offers an intermediate fidelity representation of the complex dynamics before transitioning to the higher-fidelity ephemeris model.
In this investigation, a framework to characterize relative dynamics between two spacecraft (identified as a target and chaser) in the BCRFBP is presented. Initially, the nonlinear relative equations of motion of a chaser relative to a target spacecraft are parameterized and formulated with respect to the Moons center. These equations, derived in the target spacecrafts LVLH (Local-Vertical-Local-Horizontal), are then linearized with respect to the targets position and verified along three periodic orbits that exist within the BCRFBP model. These orbits lie in regions near the vicinity of the Moon and Earth-Moon L1 and L2 Lagrange points and include a 9:2 Lunar Synodic Resonant NRHO and a 3:1 L1 Northern Halo Orbit. Once verified, these linearized relative equations of motion are used to implement a relative guidance & control strategy to maneuver the chaser relative to the target spacecraft along each of these three reference orbits.
In this work, two rendezvous and proximity operations (RPO) scenarios between a target and chaser spacecraft are explored along the three orbits defined in the BCRFBP. In the first scenario, a Sun-influenced ballistic lunar transfer (BLT) is leveraged to produce a chaser spacecraft launch trajectory towards a 3:1 L1 Northern Halo Orbit where a target spacecraft is assumed to reside. Upon insertion along the halo orbit, the chaser spacecraft will perform a number of active loitering maneuvers relative to the target spacecraft with the objective of achieving terminal rendezvous with some specified time of flight (TOF). Next, in the second scenario, the target and chaser spacecraft configuration is used to model rendezvous operations between the Orion spacecraft and NASAs Gateway orbiting platform. In this example, the rendezvous trajectory is computed to incorporate specific solar geometry so that the relative approach is in a sun lit region of the orbit. The results of this investigation underscore
the benefit of characterizing spacecraft relative dynamics in the BCRFBP to model rendezvous and proximity operations in a multibody gravitational environment.
Date of Conference: September 19-22, 2023
Track: Conjunction/RPO