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REVIEW 3 major objections 5 minor 49 references

Eclipses by Artificial Satellites to Measure the Angular Sizes of Stars

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Pith's one-line read Eclipses of bright stars by artificial satellites and the Moon can measure stellar angular diameters below the optical diffraction limit, down to about 0.1 milliarcseconds for the brightest targets.

desk verdict A promising feasibility study for measuring stellar diameters via satellite occultations, but the headline numbers rest on an unvalidated straight-edge model for satellites that needs a careful check. read the letter →

arxiv 2608.11161 v1 pith:5E2FPPAT submitted 2026-08-11 astro-ph.IM astro-ph.SR

classification astro-ph.IMastro-ph.SR
keywords occultationimagingstellarangulardiametersFresneldiffractionphotoncountingartificialsatelliteconstellationslunarsuper-resolutionastronomyBayesianinference
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Most stars are too small and distant for even the largest telescopes to resolve, because the diffraction limit of a 10-metre telescope sits at tens of milliarcseconds at optical wavelengths. This paper argues that watching a star wink out behind a fast-moving foreground object bypasses that limit, because the star's angular size is encoded in the time-dependent diffraction pattern of the occulting edge. Using artificial satellites in low and medium Earth orbit, and the Moon, the authors estimate that sub-2-milliarcsecond resolution becomes available for roughly $10^4$ stars per year, with a few dozen to a hundred stellar diameters measured to better than 0.5 milliarcseconds. The practical requirement is microsecond-level photon counting, which fast silicon photomultiplier instruments have already demonstrated.

What carries the argument

The load-bearing object is the Fresnel diffraction integral for a straight-edged mask, which acts as a 'negative point-spread function': instead of forming an image, the occulting edge blocks light and imprints a damped oscillatory fringe pattern on the total detected flux. The angular Fresnel scale $\theta_F = \sqrt{\lambda D_{\mathrm{OM}}/2}/D_{\mathrm{OM}}$ sets the fringe spacing, and a star's angular diameter $\theta_*$ suppresses the fringe amplitudes through an amplitude-suppression factor and a small phase shift, approximated by a WKB expression. This converts spatial structure on the stellar disc into a temporal signal that an ultra-fast photon counter can record, with the fringe period fixing $\theta_F$ and the fringe damping fixing $\theta_*$.

What would settle it

Occult a bright star whose angular diameter is already known from long-baseline interferometry with a variety of satellites, using a microsecond photon counter; if the recovered diameters disagree between satellites, or if a point-like star produces fringes that deviate from the straight-edge Fresnel prediction, the edge model is falsified. A tabletop version would diffract a laser around a razor edge with added panel gaps and test whether the predicted high-order fringes survive.

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Extended reading notes

Core claim

The paper's central claim is that occultation imaging is no longer a rare-event technique: the thousands of artificial satellites now in orbit make it a population-scale survey tool. When a satellite edge crosses the line of sight, it casts a Fresnel diffraction pattern that sweeps past the observer on microsecond timescales, and the finite angular diameter of the background star damps the amplitude of the higher fringes in that pattern. The authors simulate photon-counting observations, analyse them with a Bayesian model that handles Poisson shot noise, and show that stellar diameters are recovered without bias. In their estimates, navigation satellites in medium Earth orbit deliver sub-milliarcsecond resolution for bright stars and outperform lunar occultations once the background star is dimmer than roughly tenth magnitude, while low-Earth-orbit satellites provide hundreds to thousands of intermediate-resolution events per night. The resolution limit is set by photon shot noise and the angular Fresnel scale, not by telescope aperture.

Load-bearing premise

The entire prediction rests on treating each satellite as a clean, opaque, straight-edged screen; a real satellite with solar panels, gaps, antennas, and changing orientation could distort the Fresnel fringe pattern from which the stellar diameter is read.

Editorial extensions

If this is right

  • Occultations by medium-Earth-orbit navigation satellites yield about ten events per night at resolutions better than roughly 3 milliarcseconds, independent of lunar phase.
  • Lunar occultations reach about 0.1 milliarcsecond resolution for the brightest stars, at a rate of roughly once per week; navigation satellites take over for fainter stars, where the Moon's scattered light dominates the noise.
  • Low-Earth-orbit satellite constellations can in principle generate more than one hundred thousand sub-diffraction-limited events per day, with the practical rate limited by telescope pointing overhead to a few hundred per night.
  • The required detector speed already exists in demonstrated fast photon-counting imagers with nanosecond-scale timing, and in large Cherenkov telescope arrays.
  • Because precision scales with photon shot noise and the Fresnel scale, the method's resolution depends only weakly on aperture size and wavelength, so it complements rather than replaces diffraction-limited telescopes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if real satellites are not clean straight edges, the predicted fringe pattern would be corrupted; modelling each satellite as a compound mask with panels, gaps, antennas, and orientation would yield concrete predictions for how recovered diameters and event rates change.
  • Beyond the paper: the same time-domain logic applies to any artificial object with a known ephemeris, including debris and future constellations, so the survey power of the method will grow as the orbital population changes.
  • Beyond the paper: pairing these angular diameters with existing parallax measurements would turn the method into a physical-radius census for supergiants and binary stars, which is where the population-level payoff would be largest.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. Fung et al. propose using high-speed photon-counting detectors to record Fresnel diffraction patterns during occultations of bright stars by artificial satellites (Starlink in LEO, GPS-like satellites in MEO) and by the Moon, and to infer stellar angular diameters below the telescope diffraction limit. They derive a straight-edge Fresnel model (Eq. 1), define the angular resolution as the 95% upper bound of the posterior for a point source (Eq. 7), simulate Poissonian light curves for MEO occultations, validate a Bayesian inference pipeline on injected diameters (Fig. 5), and compute event rates for LEO, MEO, and lunar masks (Eqs. 11-13). The headline claims are <2 milliarcsecond resolution for ~10^4 stars per year, with ~10^1-10^2 stellar diameters constrained to better than 0.5 milliarcseconds, using SPINA-type detectors with ~1 microsecond timing.

Significance. If the idealized edge model is adequate, this is a genuinely clever and potentially transformative route to population-scale stellar angular diameters, complementary to intensity interferometry and far cheaper than constructing very large diffraction-limited telescopes. The Bayesian treatment of the photon-starved regime, the explicit statistical definition of resolution, and the validation with injected signals are clear strengths. However, the significance of the artificial-satellite results is conditional on treating each satellite as an opaque straight half-plane; the paper does not yet demonstrate this for real spacecraft. The lunar-occultation component is on much firmer ground, since the lunar limb is a long-established straight-edge approximation.

major comments (3)
  1. [§2.1, Eq. (1); Table 1] The half-plane Fresnel model is not justified for artificial satellites. For GPS-like MEO, the Fresnel scale D_F = sqrt(lambda*D_OM/2) is about 2 m at lambda = 500 nm, comparable to the bus, solar panels, and gaps of a navigation satellite; for LEO, D_F is roughly 0.3-0.4 m, comparable to Starlink dimensions. A finite, multi-edged, partially transparent screen produces a coherent superposition of edge waves rather than the single-edge pattern of Eq. (1), and the projected silhouette changes with attitude on the ~100 microsecond timescale of the event. Since the claimed <0.5 mas precision corresponds to a small change in fringe amplitude, unmodelled three-dimensional structure can plausibly bias the inferred stellar diameter. The authors should simulate Fresnel diffraction from realistic satellite silhouettes (or at least from rectangular or gapped screens) over a range of orientations and show that the inferred diameter bias is below the quoted precision.
  2. [§3.1, Eq. (8); Fig. 5] The validation pipeline assumes theta(t) = omega*t with the angular speed known from external tracking, and it does not marginalize over the projected edge velocity or orientation. Section 2.2 notes that omega*cos(phi) can be determined empirically, but this is not implemented in the likelihood (Eq. 8) or in the bias check (Fig. 5). For satellite events, an error in the assumed angular rate or a time-varying attitude directly shifts the phase of the diffraction fringes and can mimic the amplitude suppression that constrains theta_*. The reported sigma_theta values are therefore conditional on exactly known kinematics; a sensitivity analysis or marginalization over omega*cos(phi) is needed before the quoted precision can be taken as realistic.
  3. [§4.2, Eqs. (12)-(13); Fig. 8] The event-rate calculation assumes circular non-overlapping orbits and multiplies the single-satellite swept solid angle by N_mask. Real LEO constellations have many satellites in shared orbital planes, so track overlap can be substantial, and visibility effects such as Earth shadow, sky background near the Moon, and satellite illumination are not included. The authors correctly label this as a coarse estimate, but the abstract's '~10^4 stars every year' and the cumulative rate curves in Fig. 8 are headline numbers. A rate estimate using current ephemerides and accounting for orbit overlap would calibrate the claim; alternatively the numbers should be presented as upper limits or order-of-magnitude estimates.
minor comments (5)
  1. [§2.1, Eq. (5)] The phase-misalignment term 'pi*theta_*^2/8' is dimensionally inconsistent as written; it should be pi*theta_*^2/(8*theta_F^2) in angular units, or the equation should be expressed using normalized variables x = theta/theta_F and a = theta_*/theta_F.
  2. [§2.3] The statement that occultation resolution is independent of wavelength relies on a flat SED with f_lambda proportional to lambda and on a cancellation between the Fresnel-scale growth and photon-counting SNR; this should be presented as a special illustrative case, not as a general property of the method.
  3. [§2.2] The text contains a typo: 'Kelper's law' should read 'Kepler's law'.
  4. [Fig. 5] The middle panel states that bias is consistent with zero, but no error bars or numeric bias values are shown; please include the measured bias and scatter so the reader can verify the claim.
  5. [Code and Data Availability] The source code is available only 'on reasonable request'; since the paper presents reproducible simulations, making the code public would strengthen the manuscript.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the paper is a forward model from stated physical assumptions, and the claimed resolution and event-rate numbers are not fitted inputs relabelled as predictions.

full rationale

The derivation chain starts from the Fresnel straight-edge model (Eq. 1), integrates it over a stellar disc (Eq. 3), treats n0, thetaF, DeltaT, and the Moon flux as known or chosen inputs, simulates Poisson light curves (Eq. 8), and then performs a Bayesian inversion for theta* (Eq. 10). The resolution theta_res is defined (Eq. 7) as the 95% upper bound of the posterior for a point source, and the numbers quoted in the abstract are outputs of this simulated forward model, not quantities fitted to data and then re-reported as predictions. The star-count calibration (Eq. 11) uses the external Gaia catalogue, and the SPINA detector parameters come from prior instrument papers by the same group, but those self-citations supply hardware performance numbers rather than the central physics claim; the Fresnel diffraction and occultation formalism is standard and independently citable. The validation in Section 3.3 recovers injected theta* values with the same generative model used to create the mock data; that tests the statistical pipeline, not the physical model, and the paper does not claim otherwise. The main residual concern is physical fidelity: real satellites are finite, partially transparent, multi-edged bodies rather than ideal half-planes, and an unmodelled 3D silhouette could distort the fringe amplitudes (Section 2.1, Eq. 1). That is a modelling and correctness risk, not a circularity, because the prediction does not reduce to its input by construction.

Assumptions & free parameters 6 free parameters · 8 assumptions · 0 invented entities

The central feasibility numbers rest on several hand-chosen parameters and modeling axioms. The forward diffraction model is standard, but the application to satellites depends on the straight-edge assumption, Poisson noise assumptions, and the event-rate inputs (satellite counts, sizes, and the Gaia luminosity function). No new physical entities are introduced. The free parameters are inputs to a forward model, not fitted to the target result, so the circularity burden is low.

free parameters (6)
  • Moon residual brightness after masking = V = 2
    Assumed that 93% of the new Moon's area can be masked or subtracted, leaving a residual apparent magnitude of 2. This strongly affects the lunar occultation noise budget and the resolution and rate curves in Figs 6-8.
  • Observing bandwidth = +/-50 nm at 500 nm
    Chosen to avoid over-fitting unphysically high-order Fresnel fringes; truncates the fringe pattern and affects simulated light curves and resolution.
  • Telescope throughput x quantum efficiency = 30%
    Assumed end-to-end efficiency at 500 nm; sets the photon rate n0 for a given magnitude and aperture (Fig 4), which directly drives the resolution and rate numbers.
  • Satellite geometric angular sizes = Starlink 3.8e3 mas; GPS-like 1.0e2 mas
    Adopted typical satellite sizes at their orbital distances; directly sets the swept solid angle in the event-rate estimate (Eq 12).
  • Number of masks = Starlink 1e4; GPS-like 1e2
    Adopted current and planned constellation counts; scales the event rate linearly in Eq 13 and is a major driver of the headline annual rate.
  • Stellar luminosity function normalization = 3.139e-4 (10^{0.414 m*} - 1) deg^-2
    Calibrated power law using Gaia data (Eq 11); used to convert swept solid angle into occultation event rates. Gaia is incomplete for the bright stars that matter most for high-resolution events.
assumptions (8)
  • standard math Fresnel near-field diffraction integral describes the negative PSF of the mask
    Standard scalar diffraction theory; Eq 1 is used with the near-field approximation D_OM/D_MS << 1.
  • ad hoc to paper The mask can be approximated as an opaque infinite straight edge
    Section 2.1: 'If the angular size of the mask is much larger than the star, the geometry of the mask can be approximated as a straight edge [44].' Real satellites have finite, complex, possibly non-opaque shapes.
  • standard math Wavefronts from different regions of the stellar disc are uncorrelated, so intensities add
    Footnote 4 in Section 2.1; holds because the relevant optical path difference is set by the wavelength, not the Fresnel scale.
  • domain assumption The angular speed of the mask is known with high precision from external tracking
    Section 3.1: 'we assume the angular speed of the occulting mask is known from external constraints with high precision [45].' This fixes theta(t)=omega t in the likelihood.
  • domain assumption Photon counts follow Poisson statistics with negligible dark current and negligible satellite-reflected light
    Section 3.1, Eq 8 and surrounding text; assumes other photon sources are negligible for satellite occultations when the Sun is below the horizon.
  • domain assumption Satellite orbits are circular and their projected sky ribbons do not overlap
    Section 4.2: assumed for the simple solid-angle sweep estimate of event rates (Eqs 12-13).
  • domain assumption A uniform circular disc or a uniform box describes the stellar surface brightness
    Section 2.1, Eq 4; ignores limb darkening and other realistic intensity profiles.
  • domain assumption The Gaia-calibrated luminosity function gives the correct number density of bright stars
    Section 4.2, Eq 11; the paper notes Gaia is incomplete at the bright end, yet the event-rate estimates rely on this power law.

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Cite this review

Pith. "Pith review of Eclipses by Artificial Satellites to Measure the Angular Sizes of Stars." pith.science (2026). https://pith.science/paper/5E2FPPAT

@misc{pith2026260811161,
  author       = {Pith},
  title        = {Pith review of: Eclipses by Artificial Satellites to Measure the Angular Sizes of Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5E2FPPAT}},
  note         = {Machine review of arXiv:2608.11161}
}
abstract

Direct measurements of the angular sizes of stars (other than our Sun) are inherently limited by telescopes' optical diffraction limit. The spatial diffraction limit can be overcome by using time-domain information when stars are `eclipsed' by anything moving in the foreground: artificial satellites or the Moon (known as `lunar occultation imaging'). Here we analyse the angular resolution achievable by high-speed photon counting devices, when stars are eclipsed for several microseconds by one of the thousands of satellites now in low or mid-Earth orbit. We also build a full Bayesian statistical treatment for analysing simulated observations. We show that eclipses by the moon and satellites deliver $<2$ milliarcsecond resolution for $\sim$$10^4$ stars every year, with the diameters of $\sim$$10^1 - 10^2$ stars constrained to better than $0.5$ milliarcseconds. The application of satellites requires an ultra-fast, photon-resolving detector, capable of continuous readout with inter-frame delay controlled within $\lesssim 1$ $\mu$s. Such a fast rate can easily be handled by the SPINA instrument, which has demonstrated $8$ ns inter-frame delay, and potentially by the Cherenkov Telescope Array.

Figures

Figures reproduced from arXiv: 2608.11161 by the authors.

Figure 1
Figure 1. The geometry of occultation. During a brief flyby of an orbiting mask into the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Top panel: Light curves of a distant object of diameter [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. The unnormalised posterior probability of the inferred size of a star that is genuinely [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The mean number of photons n0 received from a star per microsecond (before or after an occultation), as a function of the star’s Gaia G-band magnitude [46] and the telescope’s effective aperture. This assumes telescope throughput and detector quantum efficiency of 30% …
Figure 5
Figure 5. Figure 5: Validation that the proposed Bayesian inference pipeline can measure stellar di [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: The attainable resolution limit θres with the occultation method on stars of different magnitudes, compared to the optical diffraction limit. Here, the diffraction limit of optical telescopes is defined at the observing wavelength λ500 ≡ 500 nm. The occultation-based r…
Figure 7
Figure 7. Figure 7: The occultation event rate of different foreground mask choices as a function of [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: The cumulative number of events observable every day as a function of angular [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

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