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REVIEW 2 major objections 5 minor 18 references

Small telescopes and simple models still recover the speed of light from Io’s eclipses, just as Roemer did 350 years ago.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-31 05:00 UTC pith:2VGLPVO2

load-bearing objection Clean didactic replication of Roemer with real multi-observer timings; the ~10% circular-model result is solid, the 298200 km/s headline is mostly a consistency check. the 2 major comments →

arxiv 2607.28512 v1 pith:2VGLPVO2 submitted 2026-07-30 physics.hist-ph astro-ph.IMphysics.class-phphysics.ed-ph

De mora luminis: Roemer's discovery 350 years later

Fabio Falchi , Riccardo Furgoni , Paolo Gattillo , Maurizio Francesio This is my paper
classification physics.hist-ph astro-ph.IMphysics.class-phphysics.ed-ph
keywords speed of lightRoemerIo eclipseshistorical astronomyJupiter satellitesdidactic experimentlight-travel time
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper repeats Ole Roemer’s 1676 experiment with eyes and telescopes comparable to those of the late 17th century. Timing the reappearances of Jupiter’s moon Io after eclipse, the authors show that even a uniform-circular-orbit model yields a speed of light within about 10 percent of the modern value. Adding elliptical-orbit corrections does not automatically improve the answer, because other orbital perturbations intervene. When a modern ephemeris supplies Io’s true synodic period, the same timings give c = (298200 ± 1900) km/s. The work is offered as a hands-on demonstration of how hypotheses, observations, and competing explanations interact, and it also recovers Roemer’s own 1677 attempt to confirm the finite speed of light with the Great Red Spot.

Core claim

Roemer’s method remains valid under period-comparable visual conditions: the authors’ eye and camera timings of Io emersions, reduced with the simplest uniform-circular geometry, already give c within roughly 10 percent of the accepted value; feeding the same timings a synodic period taken from modern ephemerides produces the weighted average c = (298200 ± 1900) km s⁻¹.

What carries the argument

The linear relation between the increase in Earth–Jupiter distance after opposition and the accumulated delay in successive Io emersions; the slope of that line is the speed of light.

Load-bearing premise

The most precise quoted value treats Io’s average orbital period extracted from modern planetarium software as an independent input, even though that software already incorporates the known speed of light.

What would settle it

Re-reduce the same raw emersion times using an Io synodic period measured solely from dynamical models that contain no light-travel-time terms; if the resulting slope then departs significantly from 3 × 10⁸ m/s, the high-precision claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Undergraduate labs can measure c to ~10 % with an 80–120 mm refractor, a stopwatch, and circular-orbit arithmetic.
  • Adding orbital eccentricity alone can worsen the answer; students must confront competing perturbations before trusting more complex models.
  • The same data set can be re-used to compare human versus digital detection thresholds and atmospheric-error budgets.
  • Roemer’s 1677 Great Red Spot timings supply an independent historical cross-check that light delay appears in Jupiter’s rotation as well as in Io’s eclipses.

Where Pith is reading between the lines

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

  • The didactic design deliberately keeps telescope aperture and timing precision near 17th-century limits so that students experience the same systematic floor Roemer faced.
  • Because the high-precision result is essentially a consistency test against modern ephemerides, the paper’s strongest first-principles claim remains the ~10 % circular-model recovery.
  • A multi-year campaign spanning Jupiter’s full radial-velocity cycle would map how much the uncorrected circular result wanders, quantifying when simple models succeed or fail.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The authors re-observe Io eclipse emersions with eye and small telescopes comparable to late-17th-century instruments, plus one CMOS series, over ~70 orbits after the 2023 opposition. They recover c ≈ 2.6×10^5 km s⁻¹ (within ~10–14% of the modern value) from a uniform-circular model of Earth–Jupiter distance versus observed delay (Table 5), show that an ellipticity-only correction for Jupiter can over-correct and worsen the result, and obtain a weighted average c = (298200 ± 1900) km s⁻¹ when the Io synodic period is taken from modern ephemerides after light-time removal (Table 6). They argue the exercise has strong didactic value and report an archival note that Roemer in 1677 also timed Great Red Spot meridian transits as an independent check.

Significance. For a history-of-physics / physics-education venue the work is valuable and largely successful. The tabulated timings (Table 2), explicit cloud exclusions, eye-versus-CMOS scatter, and regression statistics make the observational claim reproducible. The demonstration that a more ‘realistic’ elliptical correction need not improve c is pedagogically useful and well supported by the data and by Appleton’s earlier analysis. The archival GRS confirmation from the Roemer–Huygens correspondence is a genuine historical contribution. Strengths include transparent data reduction, period-comparable instrumentation, and an explicit didactic framing that links hypothesis, prediction, observation and alternative explanations.

major comments (2)
  1. [Abstract; §III; Table 6; §IV] Abstract and §III (‘Calculation knowing the “exact” value of the synodic period’): tephemeris = 152917.1 s is obtained by subtracting light-travel times that already assume the modern value of c from Stellarium/VSOP87 positions, then feeding that period into the slope fit that recovers c = (298200 ± 1900) km s⁻¹ (Table 6). The body text acknowledges the presumption (‘we now presume to know the speed of light’), but the Abstract and Conclusions present the figure as a determination of c from modern ephemerides. The result is properly a high-precision consistency check of the observers’ timings against known physics, not an independent first-principles measurement. The Abstract, the final paragraph of §III, and §IV should state this limitation explicitly and relegate the number to a test of observational quality.
  2. [§III (Elliptical orbits model; Variability of Io’s synodic period)] §III, uniform-circular and elliptical analyses: the paper correctly notes that other perturbations (Io–Europa–Ganymede resonance, inclination) remain after the ellipticity correction, yet it never quantifies their expected contribution over the 2023–24 window or shows residual O–C after the circular-model fit. A short residual table or a one-paragraph comparison with Appleton’s full perturbation budget would make the claim that ‘increasing complexity does not necessarily bring results closer to c’ fully load-bearing rather than qualitative.
minor comments (5)
  1. [§III] §III, paragraph beginning ‘Let’s start counting…’: typographical error ‘Juiter’ for ‘Jupiter’.
  2. [Table 2] Table 2: the ‘Difference with Stellarium’ row mixes signed means with standard deviations; a clearer caption stating that negative RF values mean earlier detection would help non-specialist readers.
  3. [Figures 2 and 4] Figure 2 versus Figure 4: the zero-point of Δt differs (first FF observation vs first of each series). A single sentence in each caption would prevent confusion when comparing slopes.
  4. [Tables 5–6] The weighted-average procedure that produces 267270 ± 870 km s⁻¹ (Table 5) and 298200 ± 1900 km s⁻¹ (Table 6) is not stated (inverse-variance?); one sentence would suffice.
  5. [References] Reference [24] citation form is incomplete (‘(n.d.)’); the Huygens Oeuvres volume and page already given earlier can be repeated for consistency.

Circularity Check

1 steps flagged

Headline c=(298200±1900) km/s is recovered only after defining Io’s synodic period by subtracting light-times that already use modern c; the uniform-circular ~10% result is not circular.

specific steps
  1. self definitional [§III “Calculation knowing the ‘exact’ value of the synodic period”; Table 4 tephemeris; Table 6; Abstract]
    "we now presume to know the speed of light and the exact positions of Jupiter (or Io) and Earth using the ephemeris given by Stellarium. In this way, observing and timing the ends of eclipses, we can calculate when Io emerged from Jupiter’s shadow by subtracting the times needed for light to travel from Io to Earth. These are the local (Jupiter) times of emersions. Using the first ... and last ... local times of emersions, and dividing this time interval by the 70 orbits ... we obtained for the synodic period of Io a value tephemeris=152917.1 s. We then used this tephemeris period to calculate"

    tephemeris is defined by removing light-travel delays computed with the known modern c (t_local=t_obs−d/c). The subsequent slope fit of modern Δx against delays measured relative to that same tephemeris therefore returns essentially the input c by construction (exactly at the endpoints; to within timing noise for intermediate points). The abstract’s c=(298200±1900) km/s is this consistency check renamed as a measurement, not an independent determination of c from the observations alone.

full rationale

The paper’s central non-circular claim holds: with adopted modern orbital radii/periods, a uniform-circular model, and purely observed emersion times, the slope of Δx vs light-delay yields c within ~10% (Table 5) without feeding modern c into the fit. The elliptical-orbit correction likewise does not use c. The load-bearing circular step is confined to §III “Calculation knowing the ‘exact’ value of the synodic period” and Table 6. There the authors explicitly presume modern c, subtract d/c from the observed Earth times to obtain local (Jupiter) emersion times, extract tephemeris=(t_local,last−t_local,first)/70=152917.1 s, then re-insert that period into the same slope procedure and recover c=298200±1900 km/s. For the endpoints this recovery is forced by construction: the period was defined by removing exactly the light-time delays that the slope is asked to measure. The abstract and conclusions still advertise this figure as a “noticeably accurate result” of Roemer’s method with modern ephemerides, without restating the presumption of c. No self-citation or uniqueness-theorem circularity is present; the historical GRS archival claim is independent. Overall: partial circularity on the headline high-precision number only.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The scientific claim rests on standard Newtonian/Keplerian orbital kinematics, published planetary and satellite periods/radii, and planetarium ephemerides, plus ordinary assumptions about visual detection and clock synchronization. No new physical entities are introduced. The load-bearing modelling choices are which synodic period to adopt and whether modern light-time may be used when constructing that period; free parameters are minimal beyond ordinary regression slopes and documented observation exclusions.

free parameters (3)
  • Regression slope for c (per observer series) = FF 258800; PG 261900; RF 267670 km/s (circular); weighted ephemeris average 298200±1900 km/s
    c is obtained as the slope of Δx versus light-delay Δt for each observer; the slope is fitted to the campaign data rather than predicted a priori.
  • Cloud-compromised timing exclusions = 2 of 18 listed timings excluded
    Two timings marked with asterisks were dropped because clouds delayed detection by >30 s relative to the series mean offset; exclusion is justified but post-selected on quality.
  • Mental-count stopwatch delay (eye runs) = 3–5 s procedural delay, not subtracted
    Observers waited 3–5 s after first hint before stopping the chronograph; they state subtracting this does not improve precision, so the raw stop time is used.
axioms (5)
  • domain assumption Earth and Jupiter may be modelled to first order as uniform circular orbits with modern semi-major axes and sidereal periods when estimating Δx and mean Io synodic period.
    §III Uniform circular model; Table 3 constants; used for the ~10% c results.
  • domain assumption Stellarium VSOP87 ephemerides supply sufficiently accurate Earth–Jupiter distances and reference emersion geometry for the campaign window.
    Used as the ‘real’ distance standard and for tephemeris (§III); modern planetary theory treated as external truth.
  • ad hoc to paper Io’s average synodic period over the observing span can be taken from ephemeris local emersion times after removing light travel time.
    §III ‘Calculation knowing the exact value of the synodic period’ explicitly subtracts light-time with known c to build tephemeris before refitting c.
  • domain assumption First unambiguous visual or first-frame CMOS detection is an adequate operational definition of emersion for differential timing across months.
    §II; authors prefer first-frame over half-max light curve after comparing scatter to Stellarium.
  • domain assumption Standard Euclidean light-time delay Δt = Δx/c with constant c in vacuum is the correct physical model for the observed schedule shifts.
    Core Roemer hypothesis retained throughout; no relativistic or medium corrections beyond brief penumbra/refraction remarks.

pith-pipeline@v1.2.0-daily-grok45 · 19765 in / 3444 out tokens · 78928 ms · 2026-07-31T05:00:43.290242+00:00 · methodology

0 comments
read the original abstract

350 years from the 1676 announcement of the Roemer's discovery that light propagates with finite speed, we present our observations using eyes with telescopes having similar resolution compared to those in the late 17th century. We confirmed that Roemer's method is valid and gives reasonable values for the speed of light c, within about 10 per cent of the modern value for our measurements, even with the simplest modelling technique, using uniform circular motions. We found that increasing the complexity of the model, e.g., by taking into account the elliptical orbit of Jupiter, does not necessarily bring the results closer to the value of c due to the influence of other perturbations. Using modern ephemerides yields a noticeably accurate result of c=(298200+-1900) km/s. This experience can have great didactic value by showing the interconnections between formulation of hypotheses and the consequent predictions, making observations, reducing data, and searching for alternative explanations for the same phenomenon. Lastly, we also found, in the correspondence between Roemer and Huygens, that Roemer in 1677 searched for an independent confirmation of what he found during previous years observing Io's eclipses by making observations and reducing the data of the meridian transits of the Great Red Spot on Jupiter.

Figures

Figures reproduced from arXiv: 2607.28512 by Fabio Falchi, Maurizio Francesio, Paolo Gattillo, Riccardo Furgoni.

Figure 1
Figure 1. Figure 1: Panel a: Earth’s orbit and positions of our planet (in blue) on the given dates (opposition, first and last observation of Io’s eclipses) and Jupiter’s positions on the same [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The three series of observations where the symbols represent the increase in Jupiter-Earth distance from the first emersion in function of time delay in emersions. Blue [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Synodic period of Io variability during 23 opposition of Jupiter, from 2006 to 2030. The synodic period corresponding to our observations is that of number 17 in the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The three series of observations where the data-points represent the increase in Jupiter-Earth distance from the first emersion of each series in function of time delay D [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

18 extracted references

  1. [1]

    Demoraluminis,sivediffusionelu- minis successiva – Ricerca sulle prime misure della velocità della luce,

    M.Francesio,A.Lai,andG.Zanini,“Demoraluminis,sivediffusionelu- minis successiva – Ricerca sulle prime misure della velocità della luce,” La Fisica nella ScuolaXII(3), 68–82 (1979)

    1979

  2. [2]

    Galilei, Galileo, Discorsi e Dimostrazioni Matematiche, Intorno a Due Nuove Scienze(appresso gli Elsevirii, Leida, 1638)

  3. [3]

    Galileo,MeasurementoftheVelocityofLight, and the Reaction Times,

    R.Foschi,andM.Leone,“Galileo,MeasurementoftheVelocityofLight, and the Reaction Times,” Perception38(8), 1251–1259 (2009)

    2009

  4. [4]

    A demonstration concerning the motion of light, communicated from Paris, in the journal des scavans, and here made English,

    C. Huygens, Oeuvres Complètes. Tome VIII. Correspondance 1676-1684 , Jo- hannes Bosscha jr. ed. (Martinus Nijhoff, Den Haag, 1899), pp.30-31, let- ter n.2103, dated September 16, 1677. [5]“A demonstration concerning the motion of light, communicated from Paris, in the journal des scavans, and here made English,” Phil. Trans. R. Soc. 12(136), 893–894 (1677)

  5. [6]

    Lens Making for Scientific Instrumentation in the Seven- teenth Century,

    S.A. Bedini, “Lens Making for Scientific Instrumentation in the Seven- teenth Century,” Appl. Opt.5(5), 687 (1966)

    1966

  6. [7]

    Seventeenth- century telescope optics of Torricelli, Divini, and Campani,

    M. Miniati, A. Van Helden, V. Greco, and G. Molesini, “Seventeenth- century telescope optics of Torricelli, Divini, and Campani,” Appl. Opt. 41(4), 644 (2002). [8]J.D. Cassini, “An extract of Signor Cassini’s letter concerning a spot lately seen in the sun; together with a remarkable observation of Saturn, made by the same,” Phil. Trans. R. Soc.11(128), 6...

    2002

  7. [12]

    Hultsch, Griechische und römische metrologie (Weidmann, Berlin, 1882), p.61

    F. Hultsch, Griechische und römische metrologie (Weidmann, Berlin, 1882), p.61

  8. [13]

    Ptolemy’s longitudes and Eratosthenes’ measurement of the earth’s circumference,

    L. Russo, “Ptolemy’s longitudes and Eratosthenes’ measurement of the earth’s circumference,” Math. Mech. Compl. Sys.1(1), 67–79 (2013)

    2013

  9. [14]

    Far-reaching Hellenistic geographical knowledge hidden in Ptolemy’s data,

    L. Russo, “Far-reaching Hellenistic geographical knowledge hidden in Ptolemy’s data,” Math. Mech. Compl. Sys.6(3), 181–200 (2018)

    2018

  10. [15]

    Favaro, Antonio,Le Opere Di Galileo Galilei (Barbera, Firenze, 1932), Vol. V, pp. 423-425

    1932

  11. [16]

    Favaro, Antonio,Le Opere Di Galileo Galilei (Barbera, Firenze, 1934), Vol. XII, p. 291-295. 10 DE MORA LUMINIS FALCHI ET AL

    1934

  12. [17]

    Favaro, Antonio,Le Opere Di Galileo Galilei (Barbera, Firenze, 1932), Vol. V, p. 415-418

    1932

  13. [18]

    Démonstration touchant le mouvement de la lumière trouvéparM.Roemerdel’Académiedessciences,

    O. Roemer, “Démonstration touchant le mouvement de la lumière trouvéparM.Roemerdel’Académiedessciences,”JournalDesSçavans, 233–236 (1676)

  14. [19]

    Cassini, Rømer, and the velocity of light,

    L. Bobis, and J. Lequeux, “Cassini, Rømer, and the velocity of light,” Journal of Astronomical History and Heritage11, 97–105 (2008). [20]J.-D. Cassini, Les Hypothèses et Les Tables Des Satellites de Jupiter , Réformées Sur de Nouvelles Observations (Imprimerie royale, Paris, 1693) p.52

    2008

  15. [21]

    Ole Rømer, the speed of light, the apparent period of Io, the Doppler effect, and the dynamics of Earth and Jupiter,

    C. Huygens, Oeuvres Complètes. Tome VIII. Correspondance 1676-1684 , Jo- hannes Bosscha jr. (Martinus Nijhoff, Den Haag, 1899) pp.33-35, Letter 2104, dated September 30, 1677. [22]J.H. Shea, “Ole Rømer, the speed of light, the apparent period of Io, the Doppler effect, and the dynamics of Earth and Jupiter,” American Jour- nal of Physics66(7), 561–569 (19...

    1998

  16. [24]

    Confirmatio doctrinae de Mora Luminis Ex novis Observa- tionibus anni 1677,

    O. Römer, “Confirmatio doctrinae de Mora Luminis Ex novis Observa- tionibus anni 1677,” C. Huygens, Oeuvres Complètes. Tome VIII. Corre- spondance 1676-1684, Johannes Bosscha Jr. Ed. (Martinus Nijhoff, Den Haag, 1899), Pp.56-58 (No 2116.), (n.d.). [25]A. Mallama, C. Stockdale, B.A. Krobusek, and P. Nelson, “Assessment of the resonant perturbation errors i...

    2010

  17. [26]

    Planetary Theories in rectangular and spherical variables: VSOP87 solution.,

    P. Bretagnon, and G. Francou, “Planetary Theories in rectangular and spherical variables: VSOP87 solution.,” Astronomy and Astrophysics 202, 309 (1988). [27]J. Taylor,Introduction to Error Analysis, the Study of Uncertainties in Physical Measurements, 2nd Edition (1997). [28]J. Appleton, “Rømer revisited: A modern estimation of the speed of light from obs...

    1988

  18. [29]

    Cassini,GiovanniDomenico, Ephemerides Bononienses Mediceorum syderum (Typis Emilij Mariae & fratrum de Manolessijs, Bologna, 1668). 11