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arxiv: 2606.05601 · v1 · pith:2P3GLAKGnew · submitted 2026-06-04 · 🌌 astro-ph.IM

Station-Keeping Approach for Extremely Low Lunar Orbits with Solar Sailing

Jack Yarndley , Gregory Lantoine , Roberto Armellin This is my paper

Pith reviewed 2026-06-27 23:57 UTC · model grok-4.3

classification 🌌 astro-ph.IM
keywords solar sailstation-keepingextremely low lunar orbiteLLOeccentricity vectorconvex optimizationlunar gravitypropellant free
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The pith

Solar sails can maintain spacecraft in extremely low lunar orbits for at least one year without any propellant.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a method to keep spacecraft in orbits less than 50 kilometers above the Moon using only solar sails for station-keeping. These orbits are normally unstable due to the Moon's uneven gravity, which quickly increases eccentricity and risks impact. By using two optimization stages that exploit the predictable motion of the eccentricity vector, the authors show a realistic sail-equipped craft can stay in the desired regime for a full year. This matters because it allows long-term close-up lunar observations and operations without carrying fuel for corrections.

Core claim

A two-stage framework is introduced for solar sail station-keeping in eLLOs. The first stage uses mixed-integer second-order cone programming to select orbit and sail configurations that leverage the translational behavior of the eccentricity vector. The second stage applies sequential convex programming with lossless convexification to generate high-fidelity trajectories. A case study shows that a realistic solar sail spacecraft can be maintained in the eLLO regime for at least one year without propellant expenditure.

What carries the argument

Two-stage optimization framework with MISOCP for favorable configuration selection based on eccentricity vector translation and SCP for trajectory refinement using convexified solar sail dynamics.

If this is right

  • The approach works with control updates as infrequent as once per month.
  • The method has low sensitivity to model uncertainties.
  • Indefinite station-keeping in eLLOs may be feasible with solar sails.
  • Propellant-free sustained operations become possible at altitudes below 50 km around the Moon.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This could enable new classes of lunar science missions that require prolonged low-altitude data collection.
  • The technique might apply to station-keeping around other small bodies with irregular gravity fields.
  • Combining this with occasional low-thrust corrections could further extend mission durations.

Load-bearing premise

Predictable behavior in the eccentricity vector from the lunar translation theorem can be leveraged by solar sail control to counteract perturbations in extremely low lunar orbits.

What would settle it

A high-fidelity simulation or actual flight data showing that the eccentricity vector grows uncontrollably and leads to surface impact within one year despite the proposed sail control strategy would disprove the feasibility claim.

Figures

Figures reproduced from arXiv: 2606.05601 by Gregory Lantoine, Jack Yarndley, Roberto Armellin.

Figure 1
Figure 1. Figure 1: SRP acceleration components for the non-ideal flat-plate solar sail model relative to the sail normal and Sun [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Definition of the cone angle α and clock angle β in the local Sun-pointing frame FSN used to parameterize the solar sail attitude. It is also customary to define the orientation of the solar sail in terms of the cone angle α and clock angle β. These angles are defined in a rotating frame FSN with respect to the Sun, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Normalized feasible SRP acceleration set for a representative non-ideal flat-plate solar sail with NEA [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Geometry of the conical umbra-penumbra shadow model used to scale the solar-sail SRP acceleration by the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Moon-shadow geometry for several 50-km polar lunar orbits, illustrating the short penumbra transition and [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Modeled acceleration magnitudes over 5 days for a 50-km polar lunar orbit, showing the relative scales of [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Two-stage station-keeping workflow: translation-based MISOCP search followed by high-fidelity SCP [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Short eccentricity-vector propagations from multiple initial conditions, with panel (b) showing the relative [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Geometric construction of the lossless control-convex constraint used in the SCP formulation to bound [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Average shadow factor over one orbital revolution and corresponding orbit–Sun phase angle for start epochs [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: One-day reachability of the eccentricity vector and semi-major axis under central-body-plus-SRP dynamics [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Maximum eccentricity over 60 days as a function of the initial eccentricity-vector location for ballistic [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Maximum eccentricity over 1 year as a function of the initial eccentricity-vector location for ballistic [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Grid-search results for the 60-day case: minimum achievable maximum eccentricity versus inclination and [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Grid-search results for the 1-year case: minimum achievable maximum eccentricity versus inclination and [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: SCP-refined 60-day station-keeping solution for the best grid-search configuration, including sail attitude, [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: SCP-refined 1-year station-keeping solution for the best grid-search configuration, including sail attitude, [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: SCP-refined eccentricity-vector trajectories for control update intervals from 0.5 to 28 days; black dots [PITH_FULL_IMAGE:figures/full_fig_p023_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Open- and closed-loop Monte Carlo trajectory ensembles for the 60-day case relative to the nominal reference [PITH_FULL_IMAGE:figures/full_fig_p024_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Representative control profiles for open- and closed-loop Monte Carlo realizations for the 60-day case. [PITH_FULL_IMAGE:figures/full_fig_p025_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Distributions of the minimum semi-major axis, maximum semi-major axis, and maximum eccentricity [PITH_FULL_IMAGE:figures/full_fig_p026_21.png] view at source ↗
read the original abstract

Renewed interest in cislunar space has created opportunities for sustained operations in extremely low-lunar orbits (eLLOs), where altitudes below 50~km enable close surface proximity. However, these orbits are strongly perturbed by the irregular lunar gravity field, leading to rapid eccentricity growth, high station-keeping costs or even surface impact. Recent advances in our understanding of the lunar `translation theorem' have revealed predictable behavior in the eccentricity vector, offering new opportunities for efficient control. This paper introduces a two-stage framework for solar sail station-keeping in eLLOs. First, a mixed-integer second-order cone programming (MISOCP) approach leverages the translational behavior of the eccentricity vector to identify orbit and sail configurations favorable for station-keeping. Second, a lightweight sequential convex programming (SCP) formulation refines these into high-fidelity trajectories, enabled by a recently developed lossless convexification of solar sail dynamics. A case study inspired by the Lunar Reconnaissance Orbiter (LRO) mission demonstrates that a realistic solar sail spacecraft can be maintained within the eLLO regime for at least 1~year without propellant expenditure, suggesting that longer-duration, or even indefinite station-keeping, may be feasible. The approach remains effective at reduced control update frequencies (down to monthly) and exhibits low sensitivity to uncertainties.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces a two-stage framework for solar-sail station-keeping in extremely low lunar orbits (eLLOs): a mixed-integer second-order cone program (MISOCP) that selects orbit and sail configurations by leveraging predictable eccentricity-vector translation from the lunar translation theorem, followed by a sequential convex programming (SCP) refinement step that uses a lossless convexification of solar-sail dynamics. A Lunar Reconnaissance Orbiter-inspired case study claims that a realistic solar-sail spacecraft can be maintained inside the eLLO regime for at least one year with zero propellant expenditure, and that the approach remains effective at monthly control updates with low sensitivity to uncertainties.

Significance. If the central claim is validated, the work would demonstrate a practical route to propellant-free, long-duration operations at altitudes below 50 km, which is of clear operational value for lunar remote-sensing and surface-proximity missions.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (MISOCP stage): the framework explicitly rests on the lunar translation theorem supplying predictable eccentricity-vector behavior that can be exploited for control selection. The theorem is stated for unforced motion; once continuous solar-sail acceleration is introduced, the eccentricity-vector dynamics are no longer guaranteed to obey the same translation rule. The manuscript must demonstrate (analytically or numerically) that the controlled trajectories remain sufficiently close to the unforced translation behavior for the MISOCP-selected configurations to retain their station-keeping property.
  2. [Case-study section] Case-study section: the abstract reports a successful one-year station-keeping result but supplies no quantitative validation details (e.g., maximum eccentricity excursion, position error statistics, or Monte-Carlo sensitivity runs). Without these metrics it is impossible to judge whether the 1-year claim is robust or merely a single nominal trajectory.
minor comments (1)
  1. The phrase 'low sensitivity to uncertainties' is used without defining the uncertainty sources or reporting the associated sensitivity metrics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation and validation of the results.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (MISOCP stage): the framework explicitly rests on the lunar translation theorem supplying predictable eccentricity-vector behavior that can be exploited for control selection. The theorem is stated for unforced motion; once continuous solar-sail acceleration is introduced, the eccentricity-vector dynamics are no longer guaranteed to obey the same translation rule. The manuscript must demonstrate (analytically or numerically) that the controlled trajectories remain sufficiently close to the unforced translation behavior for the MISOCP-selected configurations to retain their station-keeping property.

    Authors: We acknowledge that the lunar translation theorem is derived for unforced motion and that continuous solar-sail acceleration introduces a perturbation whose effect on eccentricity-vector translation must be quantified. The MISOCP stage employs the theorem to identify configurations in which the sail acceleration remains a small, directed perturbation relative to the dominant gravitational translation. The subsequent SCP stage enforces the full nonlinear dynamics. To address the concern directly, we will add a new numerical subsection in §3 that compares eccentricity-vector evolution for the selected configurations under unforced motion versus the controlled SCP trajectories. This will demonstrate that the deviation remains below a threshold (to be quantified) sufficient to preserve the station-keeping property identified by the MISOCP. revision: yes

  2. Referee: [Case-study section] Case-study section: the abstract reports a successful one-year station-keeping result but supplies no quantitative validation details (e.g., maximum eccentricity excursion, position error statistics, or Monte-Carlo sensitivity runs). Without these metrics it is impossible to judge whether the 1-year claim is robust or merely a single nominal trajectory.

    Authors: We agree that the case-study section would be strengthened by explicit quantitative metrics. The current manuscript presents the one-year result primarily through trajectory plots and a qualitative description of the LRO-inspired scenario. In the revision we will augment the case-study section with the requested statistics: maximum eccentricity excursion, position-error time histories (mean and RMS), and Monte-Carlo results under representative uncertainties in initial state, sail optical properties, and lunar gravity model. These additions will allow readers to assess the robustness of the one-year claim beyond the nominal trajectory. revision: yes

Circularity Check

0 steps flagged

Minor reliance on external recent advance in lunar translation theorem; derivation remains self-contained

full rationale

The paper's two-stage MISOCP+SCP framework explicitly invokes the lunar translation theorem as an external input to leverage predictable eccentricity-vector behavior for selecting favorable sail configurations. No equations, fitted parameters, or self-citations are shown to reduce the 1-year station-keeping result to a tautological input or prior author work by construction. The central claim therefore retains independent content from the convex optimization steps and high-fidelity refinement, consistent with a low circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; none can be extracted.

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discussion (0)

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Reference graph

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