Using the Translation Theorem for the Automated Stationkeeping of Extremely-Low Lunar Missions

Fuente: arXiv
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Main Authors: Yarndley, Jack, Lara, Martin, Holt, Harry, Armellin, Roberto
Format: Preprint
Published: 2025
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author Yarndley, Jack
Lara, Martin
Holt, Harry
Armellin, Roberto
author_facet Yarndley, Jack
Lara, Martin
Holt, Harry
Armellin, Roberto
contents Extremely-Low Lunar Orbits (eLLOs) (altitudes $\leq 50$ km) exhibit severe perturbations due to the highly non-spherical lunar gravitational field, presenting unique challenges to orbit maintenance. These altitudes are too low for the existence of stable `frozen' orbits, and naive stationkeeping methods, such as circularization, perform poorly. However, mission designers have noticed a particular characteristic of low lunar orbits, which they have found useful for stationkeeping and dubbed the "translation theorem", wherein the eccentricity vector follows a predictable monthly pattern that is independent of its starting value. We demonstrate this feature results from the low orbital eccentricity combined with the dominant effect of a particular subset of sectoral and tesseral harmonics. Subsequently, automated stationkeeping strategies for eLLOs are presented, utilizing this theorem for eccentricity vector control. Several constraints within the eccentricity vector plane are explored, including circular, annular, and elevation-model derived regions, each forming distinct stationkeeping strategies for varying orbital configurations. Subsequently, the optimal control profiles for these maneuvers within the eccentricity plane are obtained using Sequential Convex Programming (SCP). The proposed strategies offer computational simplicity and clear advantages when compared to traditional methods and are comparable to full trajectory optimization.
format Preprint
id arxiv_https___arxiv_org_abs_2504_19559
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Using the Translation Theorem for the Automated Stationkeeping of Extremely-Low Lunar Missions
Yarndley, Jack
Lara, Martin
Holt, Harry
Armellin, Roberto
Instrumentation and Methods for Astrophysics
Earth and Planetary Astrophysics
Extremely-Low Lunar Orbits (eLLOs) (altitudes $\leq 50$ km) exhibit severe perturbations due to the highly non-spherical lunar gravitational field, presenting unique challenges to orbit maintenance. These altitudes are too low for the existence of stable `frozen' orbits, and naive stationkeeping methods, such as circularization, perform poorly. However, mission designers have noticed a particular characteristic of low lunar orbits, which they have found useful for stationkeeping and dubbed the "translation theorem", wherein the eccentricity vector follows a predictable monthly pattern that is independent of its starting value. We demonstrate this feature results from the low orbital eccentricity combined with the dominant effect of a particular subset of sectoral and tesseral harmonics. Subsequently, automated stationkeeping strategies for eLLOs are presented, utilizing this theorem for eccentricity vector control. Several constraints within the eccentricity vector plane are explored, including circular, annular, and elevation-model derived regions, each forming distinct stationkeeping strategies for varying orbital configurations. Subsequently, the optimal control profiles for these maneuvers within the eccentricity plane are obtained using Sequential Convex Programming (SCP). The proposed strategies offer computational simplicity and clear advantages when compared to traditional methods and are comparable to full trajectory optimization.
title Using the Translation Theorem for the Automated Stationkeeping of Extremely-Low Lunar Missions
topic Instrumentation and Methods for Astrophysics
Earth and Planetary Astrophysics
url https://arxiv.org/abs/2504.19559