Evangelina Evans, University of Colorado at Boulder; Marcus Holzinger, University of Colorado at Boulder; Daniel Scheeres, University of Colorado at Boulder
Keywords: astrography, cislunar space,
Abstract:
Cislunar space has become a region of interest as commercial and defense sectors seek to expand the operational capabilities of space-based assets into the cislunar domain. To effectively navigate and use this region in space, its foundational astrography needs to be defined by mapping key trajectories in the Earth-Moon system [1]. But first, let’s establish criteria for evaluating what makes a trajectory strategically valuable in the space domain.
A spacecraft’s trajectory through cislunar space is primarily dependent on two factors: delta-v (velocity changes, representative of fuel-cost) and time of flight (TOF), reflecting fuel efficiency and timely maneuverability. These two factors quantitatively measures a trajectory; qualitative characteristics can be considered as well. Analogous to the concept of maritime chokepoints which represent convergent lines of commerce across the high seas, a number of feasible trajectories can exist between two locations (or orbits) in cislunar space. While each trajectory is defined by its own propulsive maneuvers, they may travel along similar pathways or converge through a distinct region in space. Identifying where and how these lines of commerce exist in cislunar space is beneficial to space traffic management and space situational awareness. Additional qualifications for a strategic trajectory stem from application-based implications such as the detectability of a satellite along the trajectory and spaceflight safety.
The Earth-Moon Lagrange points have previously been identified as key regions in cislunar space. In recent years, the field has directed research of the Earth-Moon system to the L1 and L2 Lagrange points attributed to development of NASA’s lunar gateway [2-4]. The triangular Lagrange points, L4 and L5, are gaining notice as strategic regions for space infrastructure and space situational awareness due to their stability and diverse viewing geometry of the Earth-Moon system [5]. L3 remains less studied with efforts designing two-impulse transfers from Earth to L3 [6]. The common objective between most work is designing transfers specifically from Earth orbit to libration point orbits (LPOs) to place assets in-orbit about the Lagrange points. Recent research has limited the direction of travel as departing from Earth [2-6]. To encompass all spaceflight applications, including those that are modernly achievable or futuristic such as manned missions and asteroid mining, trajectories returning from cislunar regions to Earth-orbit must be researched as well. The results of recent work have also focused on identifying transfers between specific, often pre-determined, orbits or orbit families (e.g. geostationary transfer orbit (GTO) to near rectilinear halo orbit (NRHO) in the case of lunar gateway) [2]. Developing a rudimentary understanding of cislunar astrography will require more generalized, high-level results that analyze trajectories traveling from various cislunar regions to the domain of Earth-orbit (all orbits extending out to and including geosynchronous Earth orbit (GEO)).
Strategic trajectories from the Earth-Moon L3, L4, and L5 equilibrium points to Earth-orbits are modeled according to the Circular Restricted Three-Body Problem (CR3BP) dynamics. Given an initial impulsive maneuver at the Lagrange point, trajectories are numerically integrated for a one-month period. Trajectories with a perigee intersecting the domain of Earth-orbit are flagged as trajectories of interest. A second impulsive maneuver is then used as a circularizing burn to inject into Earth-orbit at the perigee altitude, pro- versus retro-grade direction is determined by and corresponds to the direction of the incoming trajectory’s velocity vector at perigee. Results will discuss the tradespace of trajectories transferring from the Lagrange points to the common Earth-orbit regimes of GEO, half-GEO, and LEO. A survey of the trajectories will identify the minimum-delta-v and minimum-TOF members and determine strategic attributes of the pathways traveled through space. Applications and operational scenarios for the trajectories will be analyzed as well as implications on spacecraft detectability. Through these methods of analysis, we will contribute to the mapping of strategic regions of interest within cislunar space, critical to step in defining the foundations of astrography for the Earth-Moon system.
References:
[1] Shaw, John E., et al. “Sailing the New Wine-Dark Sea.” AEther: A Journal of Strategic Airpower & Spacepower 1.1 (2022): 35-44.
[2] Locoche, Slim, et al. “Cis-lunar Transfer Vehicle: Mission Analysis for an ESA Transfer Vehicle to the Gateway.” ESA GNC-ICATT (2023).
[3] Gordon, Dawn Perry. “Transfers to Earth-Moon L2 Halo Orbits.” Master of Science Thesis, Purdue University, Indiana (2008).
[4] Rausch, Raoul R. “Earth to Halo Orbit Transfer Trajectories.” Master of Science Thesis, Purdue University, Indiana (2005).
[5] Ren, Jing, et al. “A trajectory design and optimization framework for transfers from the Earth to the Earth-Moon triangular L4 point.” Advances in Space Research 69.2 (2022): 1012-1026.
[6] Davis, Kathryn, et al. “Transfers to Earth–Moon L3 halo orbits.” Acta Astronautica 88 (2013): 116-128.
Date of Conference: September 17-20, 2024
Track: Cislunar SDA