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arxiv: 2604.06705 · v1 · submitted 2026-04-08 · 🌌 astro-ph.EP · physics.geo-ph

Variable Earth's Rotation Speed in the 14th to 16th Centuries: New {Delta}T Constraints from Chinese Eclipse Records

Hisashi Hayakawa , Mitsuru S\^oma , Naiqi Li This is my paper

Pith reviewed 2026-05-10 18:40 UTC · model grok-4.3

classification 🌌 astro-ph.EP physics.geo-ph
keywords historical solar eclipsesEarth rotationDelta TMing DynastyChinese recordsephemeris
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The pith

Chinese eclipse records from Ming local treatises yield tighter bounds on Earth's rotation changes from 1361 to 1575.

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

This paper examines total solar eclipse accounts preserved in local Chinese treatises from the Ming Dynasty, focusing on those that explicitly note totality. It compares the reported dates and locations against modern ephemeris calculations to derive revised limits on ΔT, the cumulative offset between uniform time and observed solar time caused by variable Earth rotation. The new bounds are narrower than those from earlier spline fits and indicate that the slowdown was slightly steeper between 1514 and 1567. A sympathetic reader would care because these values help trace how tidal forces have gradually lengthened the day over the last several centuries.

Core claim

Using eclipse records that explicitly mentioned totality from (quasi-)contemporaneous local treatises compiled during the Ming Dynasty, and employing the NASA JPL DE 441 ephemeris, we revised the ΔT constraint in 1361 to -408 s ≤ ΔT ≤ 601 s and set new constraints of 277 s ≤ ΔT ≤ 890 s in 1514, -328 s ≤ ΔT ≤ 332 s in 1542, and -1762 s ≤ ΔT ≤ 1091 s in 1575. Overall, our ΔT constraints generally tighten the ΔT variations more than what prior fits produced for their ΔT spline curve, requiring downward modification around 1361 and upward modification around 1542, while suggesting that the ΔT decrease between 1514 and 1567 was slightly steeper than previously considered.

What carries the argument

ΔT constraints obtained by matching reported totality times and locations of historical solar eclipses against modern orbital predictions, which quantify the accumulated difference between Terrestrial Time and Universal Time.

Load-bearing premise

The local treatises accurately recorded the dates, locations, and occurrence of totality for the eclipses without significant errors that would prevent direct comparison to modern predictions.

What would settle it

Re-examination of the original local treatises revealing systematic errors in recorded eclipse dates, locations, or totality claims that shift the calculated ΔT bounds outside the reported ranges.

Figures

Figures reproduced from arXiv: 2604.06705 by Hisashi Hayakawa, Mitsuru S\^oma, Naiqi Li.

Figure 1
Figure 1. Figure 1: Our calculation of the totality path of the 1361 total solar eclipse in comparison with the location of Sōngjiāngfǔ, where we used M+21’s ΔT value (ΔT = 557 s) in 1361. We located Sìjīng at N31°07′, E121°16′ in the modern geographical coordinates. Using M+21’s ΔT spline curve (ΔT = 557 s in 1361), our calculation located Sìjīng outside the totality path ( [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Our calculation of the totality path of the 1514 total solar eclipse in comparison with the location of Jiǔjiāngfǔ and Dōngxiāngxiàn, where we used M+21’s ΔT value (ΔT = 264 s) in 1514. Combining X09 and Google Earth Pro, we located Jiǔjiāngfǔ at N29°42′, E115°59′ and Dōngxiāngxiàn at N28°14′, E116°36′ in the modern geographical coordinates, respectively. Using M+21’s ΔT spline curve (ΔT = 264 s in 1514), … view at source ↗
Figure 3
Figure 3. Figure 3: Our calculation of the totality path of the 1542 total solar eclipse in comparison with the location of Shūchéngxiàn, where we used M+21’s ΔT value (ΔT = 210 s) in 1542 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Our calculation of the totality path of the 1575 total solar eclipse in comparison with the location of Péngzéxiàn, Xiùshuǐxiàn, Hǎiyánxiàn, Sōngjiāngfǔ, and Běijīng, where we used M+21’s ΔT value (ΔT = 150 s) in 1575. Combining X09 and Google Earth Pro, we located Péngzéxiàn at N29°54′, E116°33′, Xiùshuǐxiàn at N30°45′, E120°47′, Hǎiyánxiàn at N30°32′, E120°57′, and Sōngjiāngfǔ at N31°07′, E121°16′, respe… view at source ↗
read the original abstract

Total solar eclipses are not only astronomical spectacles but also great astrophysical laboratories. Their historical records are particularly helpful for assessing the past variability of the Earth's rotation speed. Chinese records played a key role for such analyses. However, Chinese eclipse records from the M\'ing period have not been used for {\Delta}T reconstructions, partially because most of the contemporaneous eclipse reports are found not in official histories but in local treatises. This study examines eclipse records in the (quasi-)contemporaneous local treatises, concentrating on what explicitly mentioned eclipse totality on the day of a total solar eclipse and what were compiled during the M\'ing Dynasty. On their basis, our study revised the {\Delta}T constraint in 1361 to -408 s =< {\Delta}T =< 601 s and set new {\Delta}T constraints of 277 s =< {\Delta}T =< 890 s in 1514, -328 s =< {\Delta}T =< 332 s in 1542, and -1762 s =< {\Delta}T =< 1091 s in 1575, respectively. We also revised most of the existing {\Delta}T constraints in the 14th to 16th centuries, using the ephemeris data of the NASA JPL DE 441. Overall, our {\Delta}T constraints generally tighten the {\Delta}T variations more than what M+21 fit for their {\Delta}T spline curve, requiring downward modification and upward modifications for the {\Delta}T reconstructions around 1361 and 1542, respectively. Our results suggest that the {\Delta}T decrease between 1514 and 1567 was slightly steeper than previously considered.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives revised and new constraints on the historical ΔT parameter (terrestrial time minus universal time) for the 14th–16th centuries by analyzing Chinese total solar eclipse records from (quasi-)contemporaneous Ming-dynasty local treatises that explicitly mention totality. Using the JPL DE441 ephemeris, it updates the 1361 bound to −408 s ≤ ΔT ≤ 601 s, introduces new bounds for 1514 (277 s ≤ ΔT ≤ 890 s), 1542 (−328 s ≤ ΔT ≤ 332 s), and 1575 (−1762 s ≤ ΔT ≤ 1091 s), revises most existing 14th–16th century constraints, and argues that these tighten ΔT variations relative to the M+21 spline fit, implying a steeper decrease between 1514 and 1567.

Significance. If the record interpretations hold, the tighter ΔT intervals would refine models of Earth's rotation variability in the late medieval period, with downstream value for geophysical studies of tidal friction and core-mantle coupling. The use of previously under-exploited local treatises expands the historical dataset beyond official histories, which is a constructive contribution provided the selection and error-handling steps are made fully transparent.

major comments (2)
  1. [record selection and results] The revised ΔT intervals (e.g., −408 s ≤ ΔT ≤ 601 s for 1361 and 277 s ≤ ΔT ≤ 890 s for 1514) are obtained by requiring that the DE441 umbral path passes over the reported observer location when the treatise states totality. This mapping is load-bearing for all new and revised bounds, yet the manuscript provides no quantitative assessment of possible dating, location, or totality-reporting errors in the local treatises, nor any cross-check against independent Ming sources (see the record-selection and results paragraphs).
  2. [comparison with M+21] The claim that the new constraints require downward modification around 1361 and upward modification around 1542 relative to the M+21 spline, and that the 1514–1567 decrease was slightly steeper, rests on direct comparison of the new intervals to the prior spline. Without an explicit overlay of the updated spline or a table quantifying the change in spline coefficients or knot values, the magnitude of the suggested revision cannot be evaluated.
minor comments (2)
  1. [references] The abstract and text repeatedly use the placeholder “M+21” without a full bibliographic entry; the reference list should supply the complete citation (presumably Morrison et al. 2021 or equivalent).
  2. [abstract and results] Notation for the inequality bounds is inconsistent (sometimes “=<”, sometimes “≤”); standardize to a single symbol throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address the major comments below and will incorporate revisions to enhance the clarity and robustness of our analysis.

read point-by-point responses

  1. Referee: The revised ΔT intervals (e.g., −408 s ≤ ΔT ≤ 601 s for 1361 and 277 s ≤ ΔT ≤ 890 s for 1514) are obtained by requiring that the DE441 umbral path passes over the reported observer location when the treatise states totality. This mapping is load-bearing for all new and revised bounds, yet the manuscript provides no quantitative assessment of possible dating, location, or totality-reporting errors in the local treatises, nor any cross-check against independent Ming sources (see the record-selection and results paragraphs).

    Authors: We agree that a quantitative assessment of potential errors would strengthen the manuscript. The selection of records was based on explicit mentions of totality in (quasi-)contemporaneous local treatises compiled during the Ming Dynasty, which we believe minimizes some uncertainties. However, in the revised version, we will add a new subsection under Methods or Results detailing possible sources of error in dating, location identification, and the interpretation of totality reports, including any available historical context for uncertainty estimates. We will also perform and report cross-checks against any independent Ming sources that mention the same events, noting limitations where such sources are unavailable or less detailed. revision: yes

  2. Referee: The claim that the new constraints require downward modification around 1361 and upward modification around 1542 relative to the M+21 spline, and that the 1514–1567 decrease was slightly steeper, rests on direct comparison of the new intervals to the prior spline. Without an explicit overlay of the updated spline or a table quantifying the change in spline coefficients or knot values, the magnitude of the suggested revision cannot be evaluated.

    Authors: We concur that an explicit comparison would better illustrate the implications of our new constraints. In the revised manuscript, we will add a figure showing the M+21 spline with our new ΔT bounds overlaid, and include a table that quantifies the differences at the relevant epochs (e.g., around 1361, 1514, 1542, 1567) and the change in the slope of the ΔT curve between 1514 and 1567. This will provide a clear, quantitative evaluation of how our results modify the previous fit. revision: yes

Circularity Check

0 steps flagged

No circularity: ΔT bounds from direct ephemeris comparison

full rationale

The paper's core derivation compares reported eclipse totality at specific locations and dates against predictions from the independent external ephemeris DE441. This produces numerical ΔT intervals (e.g., -408 s ≤ ΔT ≤ 601 s for 1361) without fitting any parameters to the historical data and then reusing those fits as predictions. No self-citations justify uniqueness theorems, ansatzes, or load-bearing premises; M+21 is cited only for prior spline context. The chain is self-contained against external benchmarks (ephemeris + records) and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the reliability of historical eclipse descriptions and the accuracy of the external ephemeris model. No new free parameters are fitted; ΔT ranges are derived constraints rather than ad-hoc adjustments.

axioms (2)
  • domain assumption The selected local treatises provide accurate, contemporaneous descriptions of eclipse totality at the reported locations and dates.
    Invoked when converting observed totality into ΔT bounds; appears in the description of record selection and analysis.
  • domain assumption NASA JPL DE 441 ephemeris provides sufficiently accurate Sun-Moon positions for the 14th-16th centuries to compute expected eclipse circumstances.
    Used to generate the predicted eclipse times against which historical records are compared.

pith-pipeline@v0.9.0 · 5641 in / 1443 out tokens · 50191 ms · 2026-05-10T18:40:19.586402+00:00 · methodology

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Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

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    Introduction Total solar eclipses have served human beings not only as one of the greatest astronomical spectacles, but also as one of the unique astrophysical laboratories (Orchiston et al., 2015; Littmann and Espenak, 2017; Pasachoff, 2017). Their long-term records have been used for multiple scientific measurements such as those for the solar coronal s...

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    and solar diameters (Fiala et al., 1994; Rozelot and Damiani, 2012). These records have also served as vital references to assessing and reconstructing the long-term variability of Earth’s rotation speed before the 1620s (Stephenson, 1997, hereafter S97; Sôma and Tanikawa, 2015; Orchiston et al., 2015; Stephenson et al., 2016, hereafter SMH16; Morrison et...

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    We then revise most of the ΔT constraints that M+21 used for their ΔT reconstructions in the 14th to 16th centuries (Section 8)

    and our methodology (Section 3), we develop case studies on the individual eclipses in 1361 (Section 4), 1514 (Section 5), 1542 (Section 6), and 1575 (Section 7), where Chinese local treatises explicitly mention the local total obscurations. We then revise most of the ΔT constraints that M+21 used for their ΔT reconstructions in the 14th to 16th centuries...

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    We agree with this interpretation, as this local treatise was compiled in Wànlì 24th year (≈

    Beijing Observatory (1988) omitted the 1542 entries and included only the 1575 entries for a good reason. We agree with this interpretation, as this local treatise was compiled in Wànlì 24th year (≈

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    Owing to their motivations, these local treatises generally describe the local events that occurred locally in the administrative units to which their contents were dedicated

    and the author has a higher probability of having an experience or a direct hearsay of the 1575 eclipse rather than the 1542 eclipse. Owing to their motivations, these local treatises generally describe the local events that occurred locally in the administrative units to which their contents were dedicated. S97 associated Sōngjiāngfǔzhì (松江府志) twice with...

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    We then compared their dates to the union catalog of Chinese astronomical records (中國古代天象記錄總集; Beijing Observatory,

    Materials and Methods In order to satisfy the said purpose, we first picked up the dates for total solar eclipses that were viewed in China during the reigns of the Yuán and Míng Dynasties, using the NASA Five Millennium Catalog of Solar Eclipses (Espenak and Meeus, 2009). We then compared their dates to the union catalog of Chinese astronomical records (...

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    The source report is acquired from Chronicon Aulae Regiae, by hand of local Cistercian abbots (Antonín, 2019)

    For the 1330 ΔT constraint, M+21 used a Zbraslav report of a partial eclipse on 16 July 1330, rejecting other records of Tüngedaer Schloß and Constantinople. The source report is acquired from Chronicon Aulae Regiae, by hand of local Cistercian abbots (Antonín, 2019). This monastery was located in the old town area of Zbraslav (N49°58.5' E014°23.5'). In o...

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    For the 1406 ΔT constraint, M+21 used a Bordeaux report and a Liege report for a total solar eclipse on 16 June 1406 and rejected a Hamburg report that S97 and Tanikawa et al. (2023, hereafter T+23) used. However, M+21 located Hamburg to N53°33', E007°38', near modern Wittmundhafen Air Base of Lower Saxony. This is some 160 km westward from Hamburg (N53°3...

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    SMH16 and M+21 commonly use this eclipse for one of their ΔT constraints. In order to locate Augsburg (N48°22', E010°54') and Karlštejn (N49°56', E014°11') in the totality path, we need to set ΔT constraints of −995 s ≤ ΔT ≤ 575 s and 413 s ≤ ΔT ≤ 2034 s, respectively. In combination, we need to set a ΔT constraint of 413 s ≤ ΔT ≤ 575 s in 1433 to satisfy...

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    In combination, we need to set a ΔT constraint of −227 s ≤ ΔT ≤ 497 s in 1485 to satisfy these reports

    In order to locate Bourges (N47°05', E002°24') and Fribourg (N46°48', E007°10') in the totality path, we need to set ΔT constraints of −1867 s ≤ ΔT ≤ 497 s and −227 s ≤ ΔT ≤ 1955 s, respectively. In combination, we need to set a ΔT constraint of −227 s ≤ ΔT ≤ 497 s in 1485 to satisfy these reports. This result slightly improves M+21’s existing ΔT constrai...

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    into M+21’s existing ΔT constraints and ΔT spline curve, revising one ΔT constraint (1361) and adding three new ΔT constraints (1514, 1542, and 1575). Our revision of the 1361 eclipse reports requires us to either revise M+21's ΔT spline curve upward (from ΔT = 557 s to 602 s ≤ ΔT ≤ 1864 s) or change the interpretation for the local eclipse visibility fro...

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    In combination, these data allow us to tentatively set the actual ΔT values in 1542 as 277 s ≤ ΔT ≤ 332 s. These constraints are compared with the ΔT constraint of 145 s ≤ ΔT ≤ 165 s in 1567 (Stephenson et al., 1997; M+21). This study allows us to detect short-term ΔT fluctuations that SMH16 and M+21’s ΔT spline curves have missed so far. It is desired to...

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    DOI: 10.1088/0004-637X/802/2/105 Rozelot, J. P., Damiani, C. 2012, Rights and Wrongs of the Temporal Solar Radius Variability, The European Physical Journal H, 37, 709-743. DOI: 10.1140/epjh/e2012-20030-4 Stephenson, F. R. 1997, Historical Eclipses and Earth's Rotation, Cambridge, Cambridge University Press (S97) Stephenson, F. R., Morrison, L. V., Hohenk...

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    Their copies are also found elsewhere

    DOI: 10.1007/s00190-021-01513-9 Appendix: Source Documents They are shown in their original languages with a reference ID in the National Central Library of Hayakawa, Sôma, and Li (2026) Monthly Notices of the Royal Astronomical Society, DOI: 10.1093/mnras/stag656 26 Taipei (NCL). Their copies are also found elsewhere. See Kanseki Database5 to locate thei...

    work page doi:10.1007/s00190-021-01513-9 2026