Darin C. Koblick, Raytheon Intelligence and Space; Joseph S. Choi, Raytheon Intelligence and Space
Keywords: Boomerang Orbit, Earth Gravity Assist Trajectory, Novel Lunar Plane Change
Abstract:
International interest in lunar exploration has increased since the early 1990s; subsequent missions to the moon over the next half a decade will likely exceed those over the last half-century. Dozens of international teams plan to send orbiters, small satellites, rovers, and crewed missions to the Moon as we envision a permanent presence. Many of these missions will require dedicated support infrastructure such as lunar communications and navigation services like NASAs LunaNet and ESAs Moonlight initiatives. Lunar satellite constellations will need to operate at different orbital inclinations for enhanced surface coverage, long term orbital stability, and geometric diversity.
Low altitude lunar orbits may be unstable as large gravitational perturbations caused by mascons tug them down crashing the space vehicle into the surface. Frozen Low Lunar Orbits (LLO) are of interest to many mission designers because their eccentricity (altitudinal variation) and argument of perigee remain fixed over time. Maintaining a constant altitude is ideal for lunar reconnaissance missions and requires few orbital maintenance maneuvers. Previously published research has identified four orbital inclinations (e.g., 27°, 50°, 76°, and 86°), ideal for frozen LLOs, permitting a satellite to remain in orbit indefinitely. Transferring to/from these orbital planes via single impulse maneuver at the nodal crossing increases the required ?V proportional to the angular difference, if instead of thrusting, the Earths gravitational field were used to change inclination (lunar boomerang transfer) the required ?V approaches a constant value and cover any inclination change (regardless of amount).
A lunar boomerang transfer consists of two impulsive maneuvers: the first maneuver, coplanar with the insertion orbit, raises the apolune near the Earths sphere of influence (SOI), and the second maneuver, occurring at the intersection of transfer orbit and the desired LLO altitude, lowers the apolune until its circularized. Lunar boomerang transfers may be found using nonlinear optimization methods to solve for the apolune, argument of perilune, and epoch (relative positions of the Earth and with respect to the moon) of the transfer orbit. All trajectories are propagated using numerical integration of a point mass Earth/Lunar gravity model, where the inertial location of the moon is determined from the DE440 planetary ephemeris, directly accessible from NASAs open-source SPICE implementation.
A numerical optimization technique is developed to change the inclination of any orbit using a two-impulse transfer that exploits Earths gravity. We present the analytic single-impulse plane change ?V solution as well as the three-impulse plane change, often known as a bi-elliptic transfer for comparison. These inclination changes, bounded analytically by the Jacobi Constant, allow for full 180º inclination changes. We found that Earth gravity assisted inclination changes require less ?V when required inclination change angles were greater than 45º vs single impulse instantaneous maneuvers. For circular lunar orbit altitudes greater than 100 km, the total ?V required for an Earth gravity assisted inclination change is less than 1.4 km/s (regardless of the angle) with transfer times below ten days. Earth gravity assist trajectories enable a spacecraft to reduce its ?V deployment costs up to 60% allowing for larger payload SWaP and enhanced mission capabilities.
Date of Conference: September 27-20, 2022
Track: Cislunar SSA