Ancient solar eclipse records reveal how Earth's rotation has changed

The ref paper is lengthy with some original language text too like koine Greek and other languages.

"Abstract
As one of the greatest astronomical spectacles, total solar eclipses have long been a subject of scientific interest and have been recorded by numerous civilizations over the millennia. These records are an essential reference for constraining and reconstructing Earth's variable rotation (ΔT) prior to the 17th century. However, ΔT reconstructions for the 4th–7th centuries have significant uncertainties, mainly owing to a data scarcity. Here, we analyze Byzantine historical sources with reports of total solar eclipses along the Eastern Mediterranean coasts and add probable ΔT constraints on their basis. We examined five cases of total solar eclipses in 346, 418, 484, 601, and 693 CE, identified times and locations of the observations, and compared them with the existing ΔT spline curve to derive new ΔT constraints. Our results probably tighten ΔT variability in 346 CE, show a larger ΔT range in 418 CE, and give smaller ΔT ranges in 484, 601, and 693 CE. Our study tightens the existing ΔT variations and occasionally support some ΔT constraints that slightly depart from the ΔT spline curve in the latest reconstructions. Our results are consistent with contemporary ΔT constraints from other studies and offer an improved understanding of Earth's variable rotation."

It would be interesting to convert deltaT into changing length of day or LOD. Other solar eclipse investigation using ancient records does show this.

Historical eclipses, Historical eclipses - NASA/ADS (harvard.edu)

"A historical overview of solar and lunar eclipses is presented in relation to calculating the change in diameter of the sun and the rate of spin of the earth. A 1979 estimate of change in the sun's diameter, based on daily observations since 1750, is calculated to be a 2 arcsec shrinkage, or about .1% per century. Based on solar eclipse timing in 1715 in England, it is concluded that the sun was 0.2 arcsec smaller in 1715 than it is now. Solar eclipse times, when compared with data on the transits of Mercury, reveal a .008 + or - .007 percentage decrease per century, but an 80 year oscillation period with a .025% amplitude may exist. To determine variations in the earth's rotation, only eclipse data from ancient and medieval times are of value. Perhaps the most reliable eclipse data is from observations of the Babylonian eclipse of 136 B.C. Calculations based on this and several other observations reveal an average rate of day lengthening since ancient times to be 1.78 + or - .11 milliseconds per century. To more accurately analyze eclipse observations, the celestial coordinates of the moon must be more precisely estimated."

My note. The Earth's LOD is slowing down and solar and lunar eclipse measurements supports this. The rate used in this report is 1.78E-3 s/100 years. That works out to be 1.78E-5 s/yr rate of slow down.

Reconstructing changes in Earth's LOD is painstaking and difficult. Some reports claim about an 18 hour day 1.4 Gyr ago.

Thank the moon for Earth's lengthening day, Thank the moon for Earth's lengthening day -- ScienceDaily
 
So long as the moon orbits the Earth more slowly than the Earth rotates, the tidal dynamic of Earth's oceans adds energy to the moon that is taken from Earth's rotational energy. So, the Earth is rotating slower and the moon is getting farther away (and is already tidally locked so that we only see one side of it from Earth).

Which raises the question in my mind whether the Earth's rotation will slow to the point that the Earth's rotation is also tidally locked to the moon. It seems to me that should be the final steady state. But, I have occassionally read elsewhere that the moon will eventually escape earth orbit. I am guessing that means there is enough rotational energy in Earth to accelerate the moon to escape velocity before Earth's rotation period equals the moons orbit period.

Does anybody know if that is correct?
 
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Using 3.82 cm/year rate of recession for the Moon and 100,000-year time period, the mean distance of the Moon from Earth could recede by some 3.82 km or more farther away than today. The Saros cycle will change and everything we have recorded about total solar eclipses changes too, going back to Babylonian and Assyrian eclipse records found dated some 3,000 to 4,000 years ago through the present. The Moon's angular size at about 60.27 earth radii distance is about 31 arcminutes. Going back to the time of the dinosaurs, say 70 million years ago, the Moon mean distance is about 2674 km closer than today or even closer with a larger angular size > 31 arcminutes. Everything changes in the Saros cycle just like extrapolations into the remote future.
 
Yes, the repeat period for solar eclipses, as measured by time, or numbers of moon orbits, or any measure, will change as the moon's orbital period increases as it recedes from Earth. And, Earth's rotation will be slowing at the same time, so counting the days will also change. Even "siderial" days, which measure our planet's rotation by looking at the "fixed" stars will probably change over such a long time period, because those stars are note even really "fixed", either.

It is an odd coincidence that civilization arose at the same time that the moon's apparent size from the Earth's surface is just a tad smaller than the sun's apparent size, making for a period of eclipse darkness with a ring of "fire" visible around the edge of the otherwise "invisible" moon.

That awe-inspiring sight is probably one of the things that drove humans to try to understand the stars and ultimately the universe. If our planet had perpetually cloudy skies, I wonder if we would know anything about the universe beyond our atmosphere at this point in our development.
 
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Here is some more info on attempts to trace the changing Earth-Moon distance and Earth's LOD back through geologic time, some tables go to 3.2 Gyr in Precambrian strata. However, the introduction does indicate that geologic strata used to interpret and reconstruct this past orbital history, is difficult to validate.

The Resonant Tidal Evolution of the Earth-Moon Distance, https://arxiv.org/abs/2207.00438

Ref - https://arxiv.org/pdf/2207.00438.pdf, 04-July-2022, 20-page PDF report, see attached. “1. Introduction Due to the tidal interplay in the Earth-Moon system, the spin of the Earth brakes with time and the Earth-Moon distance increases (Darwin 1879) at a present rate of 3.830 +/-0.008 cm/year that is measured using Lunar Laser Ranging (LLR) (Williams & Boggs 2016). There exists a rich narrative exploring the long term evolution of the system (Goldreich 1966; Mignard 1979; Touma&Wisdom 1994; Neron de Surgy& Laskar 1997) and the dynamical constraints on the origin of the Moon (Touma &Wisdom 1998; C´ uk et al. 2019). Among all, it has been established that simple tidal models starting with the present recession rate and integrated backward in time predict a close encounter in the Earth-Moon system within less than 1.6 billion years (Ga) (Gerstenkorn 1967; MacDonald 1967). This is clearly not compatible with the estimated age of the Moon of 4.425 +/- 0.025 Ga (Maurice et al. 2020), which suggests that the present rate of rotational energy dissipation is much larger than it has typically been over the Earth’s history. To bypass this difficulty, empirical models have been fitted to the available geological evidences of the past rotational state of the Earth (Walker & Zahnle 1986; Waltham 2015), acquired through the analysis of paleontological data (e.g. (Williams 2000)), sedimentary records of tidal rhythmites (Williams 1997; Sonett & Chan 1998; Williams 2000; Eriksson & Simpson 2000; de Azarevich & Azarevich 2017), or Milankovitch cyclostratigraphic sequences (Meyers & Malinverno 2018; Huang et al. 2020; Sørensen et al. 2020; Lantink et al. 2021). However, such models bring very little physical insight, and the remaining uncertainty of the geological data itself does not prevent circular arguments”.

My observation. This is refreshing to read and indicates the geologic record used to argue for the rate of change in Earth's rotation, lunar distance, etc. is difficult to use at best and we have an age for the Earth-Moon system < 1.6 Gyr old if current lunar recession rate or tidal dissipation rate used throughout geologic time. There are good tables in the PDF report like Table D.1. and Table D.2. Extrapolations for Earth-Moon distance and LOD for Earth too. 2.46 Gyr the distance is 50.24 earth radii and Earth LOD 16.98-hour day. Another value is 3.2 Gyr with Earth-Moon distance 46.45 earth radii compared to mean today about 60.27 earth radii with Earth LOD 15.17-hour day. At 46.45 earth radii, the Moon's angular size is larger than 40 arcminutes.

I searched the 20-page PDF for Theia and giant impact model, did not find references. The giant impact model takes place with a proto-earth and Theia, resulting in a proto-Earth with proto-Moon forming, both continue to accrete and grow :) Some reports I have indicate the early Moon formed some 4-6 earth radii distance in the giant impact model compared to mean today near 60.27 earth radii. Such a distance would provide an angular size for the early Moon, assuming same diameter as today about 5.18 degrees across.

However, using my telescopes today, I cannot verify these orbital changes in the Earth-Moon system extrapolated back through geologic time :). Such orbital changes and LOD for Earth are significant.
 
Interesting looking at the flow diagrams for the various Eigen values for the tidal effects. Of course, those don't seem to take into account the effects of the continents. But, I had never thought about the tidal effects being an Eigen function problem, before.

It makes me wonder how much of the plate tectonic process is affected/caused by the moon.
 

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