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REVIEW 4 major objections 5 minor 1 references

Measuring Danjon index and umbral magnitude of a partial lunar eclipse (July 16, 2019)

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper reports that the July 16, 2019 partial lunar eclipse had an umbral visual magnitude of -0.42, a whole-disk equivalent of -0.65 ± 0.10, and Danjon index 1.

desk verdict A clever amateur method for comparing an eclipsed Moon to defocused planets gives a plausible raw visual magnitude, but the paper's whole-disk rescaling uses a 81% shadowed area that is geometrically wrong, shifting the final value by about 0.16 mag. read the letter →

arxiv 1910.09291 v1 pith:MSZRHBMF submitted 2019-08-16 physics.pop-ph

Costantino Sigismondi This is my paper · ORCID
classification physics.pop-ph
keywords partiallunareclipseDanjonindexvisualmagnitudeArgelandermethodPogsonlawumbralphotometrybrightnessstratosphericaerosols
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

This paper reports a way to put partial lunar eclipses on the same brightness scale as total ones. During the July 16, 2019 partial eclipse, the observer hid the still-illuminated part of the Moon behind distant buildings and compared the umbral region with defocused Jupiter and Saturn using the Argelander step method. The umbra was rated one step above Saturn, which converts to a visual magnitude of $-0.42$ with a $0.1$ magnitude uncertainty. Rescaling from the roughly $81\%$ shadowed area to the whole disk adds $0.23$ mag by Pogson's law, giving $-0.65 \pm 0.10$; the dark-brown umbra with silvery borders gives Danjon index 1. If the method holds, partial eclipses can be logged in the same database as total eclipses, which would sharpen the record of atmospheric and solar-cycle influences.

What carries the argument

The load-bearing device is the Argelander method, a visual step scale for estimating brightness differences, here applied to three extended objects rather than point stars. The observer placed the umbral Moon one step above Saturn on a five-step ladder ending at Jupiter; since Jupiter and Saturn differ by $2.6$ mag, each step carries $0.52$ mag, converting the rating into a physical magnitude. The second piece is a geometric rescaling: the shadowed area, taken as $81\%$ of the disk from the eclipse's geometric magnitude of $0.66$, defines a factor $1.2345$, which Pogson's law turns into a $0.23$ mag correction to a whole-disk value. The Danjon index, a subjective 0-to-4 classification of an eclipse's darkness and color, is the paper's third tool; here the dark-brown umbra with silvery borders reads as index 1.

What would settle it

Re-observe a partial lunar eclipse with geometric magnitude near $0.66$ and measure the umbral region with CCD aperture photometry relative to standard stars, or reduce archived images of the July 16, 2019 eclipse; if the integrated umbral brightness converted to a whole-disk value using the true shadowed-area fraction disagrees with $-0.65 \pm 0.10$ by more than $0.1$ mag, the uniform-brightness rescaling is refuted.

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Extended reading notes

Core claim

The central claim is that the umbral brightness of a partial lunar eclipse can be measured by adapting the standard comparison-star technique to extended objects, and that for July 16, 2019 the answer is $-0.42$ mag for the umbra alone and $-0.65 \pm 0.10$ mag for a whole-disk equivalent. From Padova at 21:40 UT, the brightness sequence Saturn, then the umbral Moon, then Jupiter was rated 0, 1, and 5 on the Argelander scale. With Jupiter at $-2.5$ and Saturn at $0.1$ mag from calsky.com ephemerides, one step is $2.6/5 = 0.52$ mag, so the umbra is $0.1 - 0.52 = -0.42$ mag. The eclipse's geometric magnitude of $0.66$ puts at most $81\%$ of the disk in shadow; scaling by $1/0.81 = 1.2345$ and applying Pogson's law adds $0.23$ mag. The observed color, dark brown with silver borders, is classified as Danjon index 1. The paper also tabulates several total eclipses and concludes that no clean 11-year solar-cycle period appears in the ephemerides because the geometric depth of the eclipse dominates the apparent brightness.

Load-bearing premise

The load-bearing assumption is that the umbra is uniformly bright across the $81\%$ shadowed disk, so a single geometric rescaling factor of $1.2345$ turns the observed umbral magnitude into a whole-disk magnitude; the paper does not carry the uncertainty of the area estimate into the final $\pm 0.10$.

Editorial extensions

If this is right

  • The July 16, 2019 partial eclipse is placed at Danjon index 1 and whole-disk equivalent magnitude $-0.65 \pm 0.10$, i.e. among the darker eclipses in the published sample.
  • Partial eclipses can be ranked on the same magnitude-and-Danjon scale as total eclipses, so every partial eclipse becomes a usable data point for eclipse-brightness statistics.
  • The historical table shows that apparent eclipse brightness is dominated by geometric magnitude, so searches for an 11-year solar-cycle signal in Danjon indices must first correct for eclipse depth.
  • Because Danjon index tracks stratospheric aerosol loading, systematic application of this method would turn eclipse watching into a climate-relevant atmospheric monitoring record.

Reading between the lines

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

  • An implicit limitation of the geometric rescaling is that real umbrae are brighter at the edge than at the center; a surface-brightness-weighted integration would give a more physical whole-disk equivalent, and could be tested by photometric imaging of the same eclipse.
  • The same visual-step procedure could be applied to penumbral or partly cloudy eclipses, extending the data set at no instrumental cost whenever Jupiter and Saturn are available as calibrators.
  • If the geometric-magnitude correction is applied retrospectively to the paper's total-eclipse table, the residual brightness differences might expose the solar-cycle and aerosol signals that the raw Danjon indices hide.
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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

4 major / 5 minor

Summary. The paper reports a visual photometric measurement of the partial lunar eclipse of 2019 July 16 made from Padova. By defocusing Jupiter and Saturn to the apparent diameter of the Moon and applying the Argelander step method, the author derives an umbral magnitude of -0.42 mag, rescales this to a whole-disk equivalent of -0.65 +/- 0.10 mag using a claimed shadowed area fraction of at most 81 percent, and assigns Danjon index 1. The paper also presents a table of other eclipse observations and ephemeris predictions and discusses the relation between the Danjon index and solar activity.

Significance. If the method were established, this would be a low-cost way to monitor lunar eclipse brightness and stratospheric aerosol content, and the idea of comparing the eclipsed Moon with defocused bright planets is simple and reproducible. The paper is transparent in reporting the raw step values and in comparing with existing ephemerides. However, the central numerical result is not yet supported: the uncertainty estimate is unjustified for a five-step visual scale, the area rescaling is geometrically inconsistent with the stated eclipse magnitude, and the extension of the Danjon index to partial eclipses lacks an operational definition. The contribution is therefore a useful observational report rather than a validated measurement.

major comments (4)
  1. [Method for the observations] The sentence 'An errorbar of 0.1 magnitudes is appropriate' is not justified. The Argelander step scale has five divisions between Saturn (magnitude 0.1) and Jupiter (magnitude -2.5), so one step corresponds to 2.6/5 = 0.52 mag. A single-step estimate on such a coarse scale carries a quantization uncertainty of at least a few tenths of a magnitude, and the defocusing comparison between point sources and an extended, nonuniform target adds further systematic uncertainty. The final +/- 0.10 mag quoted in the abstract and conclusions is therefore an underestimate unless an independent calibration is supplied.
  2. [Method for the observations] The statement 'Being the geometrical magnitude of the eclipse 0.66, the shadowed area is <= 81%' is unproven and, under the standard definition of eclipse magnitude, inconsistent. If M = 0.658 is the fraction of the lunar diameter immersed in the umbra, the unshadowed cap has height (1 - M) * 2R = 0.684R. The area of that cap is [arccos(1 - 0.684) - (1 - 0.684) * sqrt(2 * 0.684 - 0.684^2)] / pi, which is about 0.30 of the disk, so the shadowed fraction is about 0.70, not 0.81. The corresponding Pogson correction is 2.5 * log10(1 / 0.70) = 0.39 mag rather than the stated 0.23 mag, changing the rescaled whole-disk magnitude by about 0.16 mag to roughly -0.81. The 81 percent value would correspond to M near 0.75. The paper needs either a derivation of the 81 percent figure or a corrected rescaling, and the uncertainty in the area must be propagated.
  3. [Method for the observations] The rescaling from the umbral region to the whole disk assumes that the umbral surface brightness is uniform, so that the area ratio alone converts the measured surface brightness to a total-flux magnitude. The author's own description of the umbra as 'brown dark with silver borders' contradicts that assumption, especially for Danjon index 1, and no radial brightness model is provided. This is a systematic uncertainty that is not included in the quoted +/- 0.10 mag error bar.
  4. [Comparison with calsky.com ephemerides and Conclusions] The paper states that the Danjon index is calculated only for total eclipses, yet in the Conclusions it assigns 'Danjon index class 1' to the partial eclipse. Because the Danjon scale is defined by the appearance of totality, an extension to partial eclipses requires an explicit operational definition, for example which features of the umbra are used, or the claim should be downgraded to a qualitative description. As written, the Danjon-index part of the central claim is unsupported.
minor comments (5)
  1. [Abstract] The abstract lists 'July 27, 2019' as one of the total eclipses, while the body of the paper refers to the 'July 27 2018' eclipse; the date should be corrected.
  2. [Comparison with calsky.com ephemerides table] The table entry for 16 July 2019 appears garbled: '-9,0*' is likely a typo for '-0.9' or similar, and the asterisk does not have a matching footnote.
  3. [Table caption] The word 'brithness' appears in the table caption and should be 'brightness'.
  4. [Figures] The captions for Fig. 2 and for the January 2019 photograph mention labels and comparison stars, but no figures are visible in the text; if the figures are part of the submission, they should be included or explicitly referenced as supplementary material.
  5. [References] The references to Keen (2016) and Espenak (2014) consist only of URLs without titles, access dates, or page numbers; the reference list should be completed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central 2019 umbral magnitude is a direct photometric measurement, and the whole-disk rescaling is a geometric conversion rather than a fitted prediction.

full rationale

The paper's central measurement of the July 16, 2019 partial lunar eclipse is a direct visual photometric comparison of the umbral region with Jupiter and Saturn using the Argelander method. The planet magnitudes are taken from calsky.com ephemerides, and the umbral magnitude is computed from the reported step scale: 0.1 - (2.6/5) = -0.42 mag. This does not reduce to the target result by construction. The subsequent conversion to a whole-disk equivalent uses the eclipse's published geometric magnitude (0.66) to estimate a shadowed area and a Pogson scaling factor. Whether the area estimate of 81% is correct is a legitimate methodological and accuracy concern (a standard circular-segment calculation for umbral magnitude 0.658 gives roughly 70% shadowed area, which would shift the rescaled magnitude), but that is an error or model-assumption issue, not circularity: the observed umbral magnitude is not fitted to the final rescaled value. The paper also cites the author's own earlier 2018 eclipse observation as a validation of the method, but the 2019 measurement itself does not depend on that prior report; the self-citation is not load-bearing for the central result. No equation in the derivation is equivalent to its input by definition, and no fitted parameter is renamed as a prediction. The comparison with ephemerides is an external benchmark, even if imperfectly matched, and the Danjon index is assigned from the observed color description independently of the magnitude calculation.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper rests on a small set of observational assumptions: the reliability of the planet ephemerides, the validity of comparing defocused extended sources, and the extension of the Danjon scale to partial eclipses. The main free parameter is the shadowed-area fraction used for rescaling, which is not measured and carries no uncertainty.

free parameters (1)
  • shadowed area fraction = 0.81 (upper bound)
    The paper assumes the shadowed area of the lunar disk is at most 81 percent, which gives a scaling factor of 1.2345 for the whole-disk magnitude conversion. This value is stated without derivation and enters directly into the final magnitude.
assumptions (3)
  • domain assumption The catalog visual magnitudes of Jupiter and Saturn from calsky.com are accurate at the time of observation.
    The calibration of the Argelander step scale depends on Jupiter being -2.5 and Saturn being 0.1 magnitudes, so the final umbral magnitude shifts if these values are wrong.
  • domain assumption Defocused Jupiter and Saturn retain their effective point-source magnitudes for the eye when extended to the Moon's diameter.
    The comparison method assumes that blurring a planet's image to a larger disk does not change its perceived integrated brightness in a way that breaks the Argelander scale.
  • ad hoc to paper The Danjon index can be estimated from the umbral region of a partial eclipse even though it is formally defined only for total eclipses.
    The paper's own footnote states that the Danjon index is calculated only for total eclipses, yet the author assigns a Danjon index of 1 to this partial eclipse.

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Cite this review

Pith. "Pith review of Measuring Danjon index and umbral magnitude of a partial lunar eclipse (July 16, 2019)." pith.science (2026). https://pith.science/paper/MSZRHBMF

@misc{pith2026191009291,
  author       = {Pith},
  title        = {Pith review of: Measuring Danjon index and umbral magnitude of a partial lunar eclipse (July 16, 2019)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MSZRHBMF}},
  note         = {Machine review of arXiv:1910.09291}
}
read the original abstract

The partial lunar eclipse of July 16, 2019, left the lower part of the Moon illuminated at its maximum phase in Padova (Italy). Occulting it behind far buildings it was possible to compare the light of Jupiter and Saturn de-focused to the same diameter of the Moon with the light from the umbra. The luminosity of the eclipsed Moon as well as the Danjon index have been estimated and compared with ephemerides. January 21, 2019, July 27, 2019 and September 28, 2015 total lunar eclipses data are also published.

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

1 extracted references · 1 canonical work pages

  1. [1]

    S., Yendell, Journal: Popular Astronomy, 13, 453 (1905)

    P . S., Yendell, Journal: Popular Astronomy, 13, 453 (1905). S. Matsushima, Astronomical Journal, 71, 699 (1966) R. Keen (2016) https://www.esrl.noaa.gov/gmd/publications/annual_meetings/2016/ posters/P60-Keen.pdf F. Espenak, http://www.mreclipse.com/Special/danjon.html (2014) F. Espenak (2009) https://eclipse.gsfc.nasa.gov/LEplot/LEplot2001/LE2019Jul16P ...

    work page 1905

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