Why Halley did not discover proper motion and why Cassini did

Frank Verbunt; Marc van der Sluys

REVIEW 3 major objections 6 minor 26 references

Why Halley did not discover proper motion and why Cassini did

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Modern reanalysis shows Halley's 1717 latitude comparisons do not establish stellar proper motion, while Cassini's 1738 Arcturus measurement does.

desk verdict The core quantitative claim is right — Halley's data fail significance testing — but the 'Cassini first' verdict rests on an unexamined premise about where a 509 CE occultation was observed. read the letter →

arxiv 1909.13636 v1 pith:YX3NTCXA submitted 2019-08-29 physics.hist-ph astro-ph.SR

Frank Verbunt , Marc van der Sluys This is my paper · ORCID

classification physics.hist-phastro-ph.SR

keywords propermotionEdmondHalleyJacquesCassinieclipticlatitudemeasurementerrorstarcataloguesAldebaranoccultationArcturus

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

The paper reopens the question of who first detected stellar proper motion. It argues that Halley's 1717 claim, based on comparing the latitudes of Aldebaran, Sirius, Arcturus, and Betelgeuse in Ptolemaios's and Brahe's catalogues with contemporary positions, collapses once measurement errors are included: the reported differences lie within the one-sigma latitude errors of those old catalogues. The paper also reconstructs the 11 March 509 lunar occultation of Aldebaran with modern lunar theory and the Earth's rotation correction, concluding that the observation was almost certainly made in Alexandria, where no occultation occurred, and that the required accuracy was beyond contemporary reach. By contrast, it shows that Jacques Cassini's 1738 study, using a re-reduction of Brahe's altitudes and comparing Richer's 1672 with his own 1738 measurements of Arcturus, yielded a latitude change significant at about the one-arcminute level — the first significant detection of proper motion.

What carries the argument

The central instrument is the catalogue latitude error budget: the one-$\sigma$ uncertainty $\sigma_\beta$ in ecliptic latitude for each source ($\simeq 23'$ for Ptolemaios, $2'$ for Brahe, $0.5'$ for Flamsteed, $\lesssim 1'$ for Cassini's reductions), used as the yardstick for whether a measured latitude difference $\Delta\beta$ is significant. For the occultation test, the load-bearing object is the topocentric lunar position relative to Aldebaran, computed from a modern lunar ephemeris with the Earth's rotation correction $\Delta T$; the result turns on lunar parallax and on where the observation was made.

What would settle it

A decisive test is independent historical evidence on the site of Heliodorus's observation: if the report is pinned to Athens from the career or textual details, the paper's rejection of Halley's occultation argument fails on its own numbers, because under the Athens assumption the true 509 position of Aldebaran lies just inside the lunar limb at closest approach.

Watch

Extended reading notes

Core claim

The paper argues that Halley's 1717 comparison of ecliptic latitudes for Aldebaran, Sirius, Arcturus, and Betelgeuse is not statistically meaningful. Against Ptolemaios the one-$\sigma$ latitude error is $\sigma_\beta \simeq 23'$, and against Brahe it is about $2'$, so the reported differences—tens of arcminutes in the first case, up to $4.5'$ in the second—fall inside the noise, especially because the old catalogues have non-Gaussian error tails and Halley selected the most promising stars. On the occultation side, the paper reconstructs the 11 March 509 event with modern lunar theory and the Earth's clock correction, and concludes that the observation was almost certainly made in Alexandria, where Aldebaran was not occulted; the precision needed to settle the question was beyond Boulliau's and Halley's reach. The positive result is Cassini's: re-reducing Brahe's meridian altitudes with improved refraction and obliquity, and comparing Richer's 1672 and his own 1738 measures of Arcturus, Cassini found a latitude change of about $-2'$ (and $5'$ from the re-reduced 1584 Brahe observation), well above the $\lesssim 1'$ errors of those measurements. That is the first significant evidence for proper motion, while Cassini's null results for other stars are confirmed and his one positive case for the star $\beta$ Aquilae is not supported by the error budget.

Load-bearing premise

The paper's rejection of Halley's occultation argument rests on accepting that Heliodorus's 11 March 509 observation was made in Alexandria rather than Athens; if the site was Athens, the paper's own computation places Aldebaran about $1.4'$ inside the lunar limb at closest approach, undercutting the dismissal.

Editorial extensions

If this is right

Halley's 1717 paper should no longer be cited as the discovery of proper motion: its latitude differences are consistent with the known errors of Ptolemaios and Brahe.
The first secure detection becomes Cassini's 1738 Arcturus result, a latitude change of about $-2'$ between Richer's 1672 measurement and Cassini's own.
Cassini's negative results for Sirius, Aldebaran, and Betelgeuse are valid, but his claimed significant change for the star $\beta$ Aquilae is not supported by the error budget.
Historical credit for discovering proper motion shifts from Halley's 1717 paper to Cassini's 1738 study.

Reading between the lines

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

Beyond the paper: the error-budget test supplies a template for auditing other early proper-motion claims, such as I-Hsing's eighth-century north-south shifts, which the paper mentions but does not quantify.
Beyond the paper: because the occultation result changes by about $6'$ if Earth's rotation is assumed constant, similar ancient near-occultation reports may be more useful as constraints on the history of $\Delta T$ than as evidence about stellar motions.
Beyond the paper: if the observing site were ever shown to be Athens, Halley's Aldebaran argument would be partially rehabilitated, since the paper's own Athens calculation shows an occultation only if Aldebaran lay north of its zero-proper-motion 509 position.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

You should know two things about this paper. First, the main quantitative argument is solid: once you put realistic errors on Ptolemy's latitudes (~23′) and Brahe's (~2′), none of the four stars Halley used shows a significant latitude change, and the paper reproduces Halley's arithmetic closely enough to show exactly where the signal came from. Second, the positive claim that Jacques Cassini's 1738 Arcturus study is the first significant evidence for proper motion is plausible but not as airtight as the Halley part, because it depends on dismissing a 509 CE Aldebaran occultation that the authors want to relocate from Athens to Alexandria.

What's genuinely new: earlier authors (van de Kamp, Brandt) had already smelled trouble with Halley's Aldebaran and Betelgeuse, but this is the first time all four stars get a proper significance test against HIPPARCOS ground truth, with the obliquity error and catalog noise both taken into account. The selection-bias point is good too — Halley chose stars that looked like they moved. The occultation section is methodologically careful: modern lunar ephemeris, Morrison–Stephenson ΔT, and a sensitivity test running from ΔT = 5620 s down to 11 s. And they give Cassini real credit while noting that Cassini himself was inconsistent about when to trust Ptolemy — the treatment of the historical actors is fair.

The soft spot is exactly where the stress test points. The paper's own Table 3 shows that in Athens at closest approach the Moon's center sits at latitude −5.343°, with Aldebaran's true 509 position at −5.573° — about 1.4′ inside the limb. So if Heliodorus's observation was genuinely made in Athens, the text does support a southward-moving Aldebaran, meaning it corroborates Halley's inference. The paper's fallback — that the accuracy needed to decide was beyond Boulliau and Halley, and that the Greek text's details are unreliable — is real, but it proves Halley couldn't have made the case rigorously, not that the observation carries no evidentiary weight. The location premise comes from Neugebauer's reading of Heliodorus's career, and the paper doesn't re-examine it; the Greek text never names the site. To their credit, the authors flag all this explicitly, including the ligature ambiguity in the Appendix.

Minor: the Cassini claim is asserted as significant from error estimates rather than shown through the same significance machinery used against Halley; the arithmetic is simple enough that this is unlikely to change the verdict, but a formal number would close the loop. No code accompanies the paper, which is a nuisance but not a blocker given the detailed tables.

Who's it for: historians of astronomy and textbook writers, plus anyone who wants a clean worked example of why pre-statistical-era claims need error bars before being quoted. I'd send it to a serious referee. The referee's main jobs: pressure the Alexandria premise, and ask for the Cassini significance calc.

Referee Report

3 major / 6 minor

Summary. The paper re-examines Edmond Halley's 1717 claim to have detected proper motion in four bright stars (Aldebaran, Sirius, Arcturus, Betelgeuse) by comparing contemporaneous latitudes with those from Ptolemaios and Brahe. Using modern astrometric data (HIPPARCOS) and published error estimates for the historical catalogs, the authors show that Halley's latitude differences are consistent with catalog noise and do not constitute significant evidence for proper motion. They also analyze the lunar occultation of Aldebaran on 11 March 509, arguing that it was 'almost certainly' observed in Alexandria rather than Athens, and that in Alexandria no occultation occurred; even for Athens, the paper argues, the required lunar calculation was beyond the accuracy of Halley and his contemporaries. Finally, the paper credits Jacques Cassini's 1738 study of Arcturus as the first significant evidence for proper motion, based on an improved redetermination of Brahe's latitudes and a comparison with Richer's and his own measurements.

Significance. If the authors' analysis is correct, the paper revises the standard historical narrative that Halley discovered proper motion, assigning that role to Jacques Cassini. The strength of the paper is its transparent, quantitative re-analysis: the latitude comparison is anchored to HIPPARCOS astrometry and to independent catalog error estimates (Verbunt & van Gent), and the occultation discussion uses a modern lunar ephemeris and explicitly acknowledges the effect of ΔT uncertainty. The statistical argument that Halley's inferred latitude shifts fall within the measurement noise of the ancient catalogs is convincing and properly accounts for the selection of stars with apparently high proper motion. The paper also provides a careful philological transcription of the Heliodorus text, which is a useful addition.

major comments (3)

[Occultation of Aldebaran by the Moon: modern; Table 3] The attribution of the observation site to Alexandria is adopted from Neugebauer (ref. 9) without critical examination, yet the authors' own calculations show that the site is decisive: at closest approach in Athens the Moon's topocentric latitude (-5.343°) puts Aldebaran (correct latitude -5.573°) 1.4′ inside the lunar limb, whereas in Alexandria the star is well outside the limb. Since the Greek text does not specify the site, the assertion that the observation was 'almost certainly made in Alexandria' is load-bearing and needs either a detailed philological defense or an explicit conditional framing.
[Cassini; Table 4] The claim that Cassini's Arcturus proper motion is significant is stated without a formal error propagation; the authors give the uncertainties of individual latitudes (better than 1′ for the Brahe redetermination, better than 0.5′ for Richer and Cassini), but they do not compute the combined uncertainty of the -2′ change between 1672 and 1738, so the significance is asserted rather than demonstrated.
[Abstract; Discussion] The conclusion that Cassini's Arcturus study 'provides the first significant evidence for proper motion' is a strong historical claim that is not supported by a systematic survey of pre-1738 candidates; the paper only dismisses Halley's arguments and mentions I-Hsing, so the 'first' should either be qualified (e.g., 'among the studies examined here') or supported with a more comprehensive historical review.

minor comments (6)

[Table 2] The Brahe-to-Halley columns for Aldebaran and Betelgeuse contain only three entries while the header lists four columns (a)-(d); the authors should insert dashes or an explanatory note to clarify which comparison is missing.
[Introduction; Occultation of Aldebaran by the Moon: Halley] The spelling of the star's name is inconsistent: 'Palilicium' in the introduction and 'Pallicium' in the occultation section; please standardize.
[Occultation of Aldebaran by the Moon: modern] The phrase 'after the lighting of the lamps' is translated; it might help readers to have a footnote on the approximate local time corresponding to this phrase.
[Cassini] In the list of differences for several stars (e.g., '20′′ for Antares (66′′)'), the meaning of the parenthetical values should be stated explicitly to avoid confusion.
[References] The citation for the libTheSky VISLIMIT implementation (reference 23) should include a proper software citation or URL.
[Introduction] The discussion of Macrobius is interesting but speculative; consider moving it to a footnote or adding a reference to scholarly interpretations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the analysis is anchored to external astrometric and lunar-theory benchmarks, and its self-citations are to independently calibrated catalogue-error studies.

full rationale

The paper's central claims are derived by comparing historical star positions and occultation computations against external standards: HIPPARCOS astrometry for the true positions and proper motions, ELP/MPP02 lunar theory for the Moon's position, and Morrison & Stephenson for ΔT. The error estimates for Ptolemaios and Brahe are taken from earlier published catalogue studies (Verbunt & van Gent), which were themselves calibrated against HIPPARCOS data; they are not fitted to Halley's Δβ values. Table 2 replicates Halley's computation and then compares it with independent modern computations, rather than using Halley's claimed differences as the target of a fit. The conclusion that Halley's latitude differences are insignificant follows from comparing his differences with independently established catalogue uncertainties. The occultation discussion does not reduce to its inputs either: the authors compute the Moon's topocentric position from modern lunar theory, and the assumption that the observation was made in Alexandria is adopted from Neugebauer on historical grounds, not manufactured by the paper or derived from the desired conclusion. Any weakness in that premise is a historical-accuracy concern, not circularity. The Cassini evaluation likewise uses independent error estimates and modern positions. The self-citations are to external, falsifiable catalogue-error results and are not load-bearing in a circular sense. Overall, no step in the derivation equates the conclusion with its inputs by construction.

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

All quantitative inputs come from external catalogues, modern astrometric surveys, and published ephemerides; the paper fits no new parameters. The historical conclusions rest on accepted error distributions, the reliability of HIPPARCOS, and site/text interpretations flagged in the text.

assumptions (6)

domain assumption The latitude errors of the Ptolemy and Brahe catalogues are characterized by sigma_beta=23' and 2' with non-Gaussian tails, as derived in Verbunt & van Gent (2012, 2010).
Used as the significance yardstick for Halley's Delta-beta values in the 'Latitude differences: modern' section; if these uncertainties were substantially smaller, Halley's differences for Sirius and Arcturus might become significant.
domain assumption HIPPARCOS astrometry provides correct reference positions and proper motions for the four stars.
Serves as the external ground truth for the d-beta values in Table 1 and the true Delta-beta values in Table 2 (van Leeuwen 2007).
domain assumption The modern lunar ephemeris (ELP/MPP02, Chapront & Francou 2003) and Earth rotation model (Delta-T=5620 +/- 140 s from Morrison & Stephenson 2004) accurately predict the Moon's position for 11 March 509.
Underpins the occultation calculations in Table 3; the authors perform a sensitivity test with Delta-T=11 s.
domain assumption Neugebauer's inference that Heliodorus's observation was made in Alexandria, not Athens, is accepted.
Used in the modern occultation section to argue that no occultation occurred; if the site were Athens, Halley's inferred southward proper motion of Aldebaran would be qualitatively supported.
domain assumption The transcribed Greek text in the Appendix refers to Aldebaran, dates to 11 March 509, and supports the reading 'six fingers' as an alternative to 'half a finger'.
The textual interpretation (with the <te> emendation and the ambiguous numeral) is load-bearing for assessing whether the description matches an occultation at all.
standard math The standard precession and obliquity equations (Seidelman 1992) are valid for the epochs involved.
Used to convert positions between epochs; these are standard celestial mechanics.

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Cite this review

Pith. "Pith review of Why Halley did not discover proper motion and why Cassini did." pith.science (2026). https://pith.science/paper/YX3NTCXA

@misc{pith2026190913636,
  author       = {Pith},
  title        = {Pith review of: Why Halley did not discover proper motion and why Cassini did},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YX3NTCXA}},
  note         = {Machine review of arXiv:1909.13636}
}

read the original abstract

In 1717 Halley compared contemporaneous measurements of the latitudes of four stars with earlier measurements by ancient Greek astronomers and by Brahe, and from the differences concluded that these four stars showed proper motion. An analysis with modern methods shows that the data used by Halley do not contain significant evidence for proper motion. What Halley found are the measurement errors of Ptolemaios and Brahe. Halley further argued that the occultation of Aldebaran by the Moon on 11 March 509 in Athens confirmed the change in latitude of Aldebaran. In fact, however, the relevant observation was almost certainly made in Alexandria where Aldebaran was not occulted. By carefully considering measurement errors Jacques Cassini showed that Halley's results from comparison with earlier astronomers were spurious, a conclusion partially confirmed by various later authors. Cassini's careful study of the measurements of the latitude of Arcturus provides the first significant evidence for proper motion.

Figures

Figures reproduced from arXiv: 1909.13636 by the authors.

**Figure 2.** Motion of the Moon along the sky for the period of a month centered on March 11, 509. The dashed line gives the geocentric position, i.e. the direction of the line that connects the center of the Earth to the center of of the Moon. The angle between the lunar orbit and the Earth equator causes a monthly oscillation. The solid line gives the topocentric position in Athens of the southernmost point of the Moon, showin… view at source ↗

**Figure 3.** Relative positions of the Moon and Aldebaran at the moment of closest approach and at the moment of first visibility of Aldebaran for Athens (top) and for Alexandria (below) on 11 March 509, computed with modern knowledge. The black crescents correspond to the illuminated part of the Moon. The upper position of Aldebaran is the correct one, the lower position is computed assuming no proper motion between 1690 and 50… view at source ↗

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Toomer, Ptolemy’s Almagest, 2nd ed

G. Toomer, Ptolemy’s Almagest, 2nd ed. Princeton: Princeton University Press, 1998. Prepared using sagej.cls 14 Journal Title XX(X)

work page 1998

[2] [2]

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Macrobius. In somnium Scipionis Commentarii . ±400, I.xvii.16. available at: http://digiliblt.lett.unipmn.it

work page

[3] [3]

Brahe, Astronomiae Instauratae Progymnasmata

T. Brahe, Astronomiae Instauratae Progymnasmata . Prague: Brahe, 1602; we use the edition by Dreyer J, Tychonis Brahe Dani Scripta Astronomica, V ol. II, Kopenhagen, Gyldendal, 1916, obliquity p.18, geographical latitude Uraniborg p.25, proper motion p.234, star catalogue p.258

work page 1916

[4] [4]

Halley, Considerations on the change of the latitudes of some of the principal ﬁxt stars

E. Halley, Considerations on the change of the latitudes of some of the principal ﬁxt stars. Philosophical Transactions Roy Soc 1717; 30: 736–738

work page

[5] [5]

Bullialdus, Astronomia philolaica

I. Bullialdus, Astronomia philolaica. Paris: Piget, 1645, p.171 (available at https://www.e-rara.ch/zut/content/pageview/156143)

work page

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Cassini, Des variations que l’on observe dans la situation et dans le mouvement de diverses ´etoiles ﬁxes

J. Cassini, Des variations que l’on observe dans la situation et dans le mouvement de diverses ´etoiles ﬁxes. M´emoires de Mathematique et de Physique 1738; 331–346

work page

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van de Kamp, Dark companions of stars

P. van de Kamp, Dark companions of stars. Space Sci Rev 1986; 43: 231

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Brandt, St

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