Using the Translation Theorem for the Automated Stationkeeping of Extremely-Low Lunar Missions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915262744231936 |
|---|---|
| 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 |