The Cost of Lunar South-Polar Geometry, and Surface Beacons as the Efficient Fix: a Dilution-of-Precision Analysis

Jul 16, 2026

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Lunar positioning, navigation, and timing (PNT) architectures place small constellations of satellites in elliptical lunar frozen orbits to serve the south pole, yet geometry there yields limited dilution of precision (DOP). A quantitative analysis shows that meeting terrestrial GNSS-like geometric quality requires roughly double the planned satellite count because visible satellites cluster within a narrow overhead angle. Time-averaged simulations give south-polar GDOP far above terrestrial levels, while adding a few near-horizon surface ranging beacons reduces median GDOP dramatically. The paper models beacon placement constrained by the airless-body geometric horizon and validates the geometry engine with independent DOP computation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

Introduction

The lunar south pole is the hard case

Contribution and relation to prior work

Related work

arXiv :2607 .06212v1 [ astro-ph .EP] 7 Jul 2026 The cost of lunar south-polar geometry, and surface beacons as the efficient fix: a dilution-of-precision analysis Chakshu Baweja Ashforde OÜ, Tallinn, Estonia [contact@ashforde.org](contact@ashforde.org) July 8, 2026 Abstract Lunar positioning, navigation, and timing (PNT) architectures, NASA’s Lunar Augmented Navigation Service (LANS), ESA’s Moonlight, and allied concepts, place a small number of satellites in elliptical lunar frozen orbits (ELFO) to serve the south-polar region prioritized for exploration [5, 7] . The satellite count, orbital geometry, and resulting position dilution of precision (DOP) have been studied [4] . We report a quantitative result that reframes the design trade: for a user at the lunar south pole, the satellite count needed to reach good geometry is roughly double what is currently planned, because the visible satellites cluster into a small solid angle overhead and dilution of precision is limited by their angular spread rather than their number. In a time-averaged simulation, orbit-only ELFO constellations of the planned size (4 to 6 satellites) give a south-polar median geometric DOP (GDOP) of ∼ 16 to 21, far worse than the GDOP ≈ 6 routine for terrestrial GNSS, and the constellation must grow to ≈12 satellites before the median GDOP crosses 6 . We then show that a small number of surface ranging beacons, the lunar analogue of terrestrial pseudolites and a configuration absent from the lunar PNT literature, reaches the same geometric quality far more cheaply by supplying the near-horizon diversity the overhead cluster lacks: three beacons on modestly elevated terrain around a −80◦ user cut the median GDOP from 16.2 to 1.6, a factor of about 10, moving the user from 15% to 100% of the time below GDOP 6, geometry a purely orbital solution reaches only near a 24-satellite fleet. We characterize the airless-body constraint that governs beacon placement: with no atmospheric refraction, surface-to-surface line of sight is bounded by the geometric horizon, so beacon siting on crater rims and elevated terrain is itself a design variable. Surface-beacon augmentation is the lowest-cost, highest-leverage improvement available to lunar south-polar PNT, deployable on assets already planned for the region. The geometry engine is Validated against an independent DOP computation; the constellation and beacon scenario are Modelled. Index terms: lunar PNT, LANS, Moonlight, ELFO, geometric dilution of precision, pseudolite, surface beacon, south pole, constellation geometry. 1 Introduction 1.1 The lunar south pole is the hard case The Artemis programme, Chandrayaan follow-ons, and commercial lunar landers converge on the same small region, the lunar south pole, where permanently shadowed regions hold volatiles and nearby peaks hold near-continuous sunlight. Precisely there, satellite-based PNT is at its weakest. A polar user sees only the satellites above the local horizon, and for a constellation optimized for global coverage from a handful of orbital planes, those satellites are few and poorly distributed in the sky. The lunar PNT community has responded with elliptical lunar frozen orbits (ELFO), whose apolune dwell over the south pole maximizes coverage time there, and has studied how satellite count and orbital parameters trade against coverage, dilution of precision, orbit-determination accuracy, and insertion cost [4, 7] . Our contribution is not to redo that trade but to point out a structural limit within it, and a remedy that lies outside the orbital segment entirely. 1.2 Contribution and relation to prior work Prior work has established that lunar orbital constellations suffer poor geometry near the Moon and has quantified the coverage/DOP trade for ELFO and Walker families (Section 2) . This paper adds two things. 1. The cost of south-polar geometry. We show quantitatively that reaching terrestrialGNSS-like DOP at the p

FAQs

Why does satellite-based PNT geometry become difficult at the lunar south pole?

A polar user sees only satellites above the local horizon, and for constellations optimized from a limited number of orbital planes, the visible satellites are few and poorly distributed, clustering into a small overhead solid angle.

What does the analysis say about the satellite count needed for good south-polar geometry?

To reach terrestrial GNSS-like DOP at the pole using an orbit-only ELFO constellation, the needed satellite count is roughly double the currently planned number (about 12 versus 4–6), because DOP is constrained by the angular spread of the visible set rather than by satellite count alone.

How do surface ranging beacons improve south-polar geometric quality, and what constraint affects their placement?

A small number of near-horizon surface beacons supplies angular diversity the overhead cluster lacks, cutting the median GDOP by about an order of magnitude (e.g., from around 16.2 to 1.6). Placement is governed by an airless-body horizon constraint: with no atmospheric refraction, line of sight is limited by the geometric horizon.

Jul 16, 2026

Upload by Miles