<p>The variation in the Earth's rotation rate provides probably the biggest error for the eclipse prediction. Not only is the rotation rate slowing down (due to the interaction with the Moon) but it also varies irregularly due to other effects. The length of the day thus increases on average by about 1 milisecond per day, but this rate changes more or less irregularly by a similar amount over various time scales as shown in the following graph (taken from <a href="https://www.iers.org/IERS/EN/Science/EarthRotation/LODplot.html?nn=12932" rel="nofollow noreferrer">https://www.iers.org/IERS/EN/Science/EarthRotation/LODplot.html?nn=12932</a> )</p>
<p><a href="https://i.sstatic.net/vTQnAD1o.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vTQnAD1o.gif" alt="enter image description here" /></a></p>
<p>There is a long term component varying irregularly over a time span of a decade or so, and a more regular short term fluctuation over a period of a year or two (judging from the diagram). So if you assume an increased/decreased rate of 1ms/day on average, this would amount over a period of 20 years to about  <span class="math-container">$20\cdot 356 \cdot 10^{-3}$</span> sec = <strong>7 sec</strong>. As the eclipse shadow moves with about <strong>1 km/sec,</strong> this means the location of the shadow would be incorrect by about <strong>7 km</strong> in the direction of the shadow path  (much less so in the transverse direction). Now this error will to some extent be compensated by the introduction of leap seconds, so in the end you would probably end up with an error of <strong>1-2 sec</strong> in time and <strong>1-2 km</strong> in location for a 20 year in advance timing.</p>
<p>If you determine the correct timing just a year in advance, you would just have about an error of <span class="math-container">$365 \cdot 1ms = 365 ms$</span> due to changes in the Earth's rotation, so just a few tenths of a second.</p>

CC BY-SA 4.0
2024-04-15T23:15:22.490Z
The predictions attempt to predict the variations in Earth's rotation (the previously discussed deltaT).  So, the the error is only as big as the error in predicting it, not the full effect.  Also, leap seconds do not help as the times are in TDT which does not have leap seconds, it is the deltaT parameter that accounts for leap seconds.
Greg Miller
CC BY-SA 4.0
2024-04-16T18:53:11.423Z
@GregMiller Publicly broadcast time signals are in UTC, and this certainly does include leap seconds. And as you can see from the top graph in the figure I posted, the random variation of the increase of the length of day is as big as the increase itself if you consider a time period of a few years. Essentially, this is an unmodelled variation, which is also expressed by the fact that the angular rotation rate of the Earth has a nominal relative undertainty  of about $10^{-8}$ (https://hpiers.obspm.fr/eop-pc/models/constants.html )
Thomas
CC BY-SA 4.0
2024-04-17T04:25:50.940Z
@Thomas A significant factor in the need for leap seconds is the fact that the SI second (defined in terms of caesium) is a bit short. It was defined to match the ephemeris second, which itself matched the mean solar second from ~1820, and of course the Earth's rotation speed has slowed somewhat in 200 years. Please see https://astronomy.stackexchange.com/a/40867/16685 https://physics.stackexchange.com/a/677946/123208 https://physics.stackexchange.com/a/402062/123208
PM 2Ring
CC BY-SA 4.0
2024-04-15T22:39:18.500Z
2024-04-16T20:56:19.400Z
2024-04-16T20:56:19.400Z
Thomas
<p>For the past few decades, the best eclipse data has been produced by Fred Espenak, aka Mr Eclipse. Fred is a former employee of <a href="https://www.nasa.gov/goddard/" rel="noreferrer">NASA's GSFC</a>. He's retired now, but he still maintains an excellent website devoted to eclipses, <a href="https://eclipsewise.com/eclipse.html" rel="noreferrer">EclipseWise.com</a>.</p>
<p>The most recent eclipse predictions on that site were produced using data from JPL's <a href="https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris" rel="noreferrer">Development Ephemeris</a>, <a href="https://eclipsewise.com/solar/SEhelp/de405-predictions.html" rel="noreferrer">DE 405</a>. The DE data is produced by integrating the equations of motion for the Solar System bodies, then fitting that data to ground- and space-based observations. It currently uses the masses and locations of all major Solar System bodies down to the 340 most significant asteroids.</p>
<p>To predict eclipses, you need to know the orbits of the Earth and Moon, and the JPL data for the Earth and Moon is excellent. There are several reflectors on the Moon that were placed there during the Apollo era. By shooting lasers at those reflectors for the past five decades, astronomers have gathered very high precision data of the Moon's orbit, so we can now predict the locations of those reflectors to precision better than one centimetre!</p>
<p>To predict eclipse tracks, you also need data regarding the Earth's rotation. The Earth's rotation speed is not quite perfectly uniform, and the Earth wobbles slightly on its axis. Some of these motions are predictable, but there are unpredictable components too.</p>
<p>The Earth's rotation is affected by motion in the atmosphere, oceans, and in the mantle. So predicting the exact rotation amounts to predicting the weather, and to predicting the &quot;weather&quot; in the mantle. The <a href="https://www.iers.org/IERS/EN/Science/EarthRotation/EarthRotation.html" rel="noreferrer">International Earth Rotation and Reference Systems Service</a> (IERS) coordinates the operations that gather the actual Earth rotation data. There is a wealth of information on their very extensive website. I have some info on this topic in <a href="https://astronomy.stackexchange.com/a/40867/16685">this answer</a>. The IERS publish Earth rotation data on a regular basis.</p>
<p>The unpredictable components of the direction of the Earth's wobble (<a href="https://en.wikipedia.org/wiki/Polar_motion" rel="noreferrer">polar motion</a>) amount to a few metres, so they have negligible effect on eclipse track predictions.</p>
<p>However, the unpredictable components of the rotation <em>rate</em> make it impossible to predict exactly how much the Earth has turned at the time of the eclipse. It also makes it impossible to know how many leapseconds will have been added to UTC time.</p>
<p>If you look closely at Fred's eclipse data, you will see that he gives times in the Terrestrial Dynamical Time (TD or TT) time scale. This is closely related to the timescale that JPL use to do the ephemeris calculations. Unlike UTC, it's a completely uniform scale, with no leapseconds.</p>
<p>So the UTC times given in those predictions are only provisional, but the TD times are much more reliable. To convert Terrestrial Time to UTC, you need to know the value of <a href="https://en.wikipedia.org/wiki/%CE%94T_(timekeeping)" rel="noreferrer">Delta T</a>, which is available from the IERS. Fred Espenak uses a <a href="https://www.eclipsewise.com/help/deltat.html" rel="noreferrer">pretty good estimate for Delta T</a>, but for the past few years the Earth rotation hasn't been slowing down at the expected rate. So we haven't had a leapsecond since December 2016, and the estimates Fred made several years ago for future UTC are high by a second or so.</p>
<p>The Earth's rotation speed at the equator is ~1,674.4 km/h or ~465 m/s. So an error of a couple of seconds can shift an eclipse track by a kilometre or so.</p>
<hr />
<p>For example, the data on the Eclipsewise page for the <a href="https://eclipsewise.com/solar/SEprime/2001-2100/SE2024Apr08Tprime.html" rel="noreferrer">2024 Apr 08 solar eclipse</a> was first published in 2014. It uses a Delta T value of 71.5 s, but the actual Delta T from the IERS for that date is ~69.2 s, so the predicted UT1 times are 2.3 seconds ahead of the true UT1 times. (UTC is kept within 0.9 s of UT1 via leapseconds).</p>
<p>In 2.3 seconds, the Earth rotates by ~0.00961°, so the actual eclipse track was shifted 0.00961° longitude east of the predicted track. Here's a table showing the corresponding distances in kilometres for several latitudes.</p>
<div class="s-table-container"><table class="s-table">
<thead>
<tr>
<th style="text-align: center;">Latitude</th>
<th style="text-align: center;">Distance</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: center;">0°</td>
<td style="text-align: center;">1.070</td>
</tr>
<tr>
<td style="text-align: center;">15°</td>
<td style="text-align: center;">1.034</td>
</tr>
<tr>
<td style="text-align: center;">30°</td>
<td style="text-align: center;">0.927</td>
</tr>
<tr>
<td style="text-align: center;">45°</td>
<td style="text-align: center;">0.758</td>
</tr>
</tbody>
</table></div>
<p>I calculated those values using this <a href="https://sagecell.sagemath.org/?z=eJxlkkFr3DAQhe%5F6FYN7sYPrXdsbr3eJSyk07SVQmpYcg9aS42lsyUgT2KX0v3ek7AZKfZKZ9755mlGSJHCLRoGWnsBZkoTWgEJP0vQaBmdnIJy1AP4eHBJpA4cTfLuD6juaJ6jW1aZYb4qyFEmSCBEds6QRcF6sI1gwBycVSuNzUPrJac0HjyaH3vJpPC2WhHgH96i003ICJU85oIGfP0rwurdGeeFRQQdtUzbcbdfu1nWzK4PrdpIhU4hiB6BRw8OX%2D3YDeppw8RaVGFjB3hJWUO3aorreVlV93dRsrsLN%2D14bctgjnYSuovI9BFPA38lf1oE8or%5Fg38Ax4%5FMsJFuaetsWZb2NFjRnizhwiZFXIEOBr3uBLNLJWYeuwI2QXpTO4aBJCqWHIHwMP%2DkyYraPo%2DeJHC8wnl2sxAHGU5Q4TS%5FOsGz1OtM0eDIhPqIh7WRPkf2Y0pG6rzRPn%2DwxTW7G%2DsNn6Xhd%5Fy3%5FZsW1JMsZzlvwXZmHrN36nGhiaQfV1YIhEgu4L28p1hbHPdMh%2DX3ed8ribF80w5%5FLC0jOmRkh2f924%5FNLSblT9irxLHEsYcS%5FbL8vagY%2Dz8z6C%2D0C1Hk=&amp;lang=python" rel="noreferrer">Python script</a>, running on the SageMathCell server. The script takes the flattening of the Earth into account. It uses a mean value for the rotation rate, which should be accurate to 8 digits or so.</p>

CC BY-SA 4.0
2024-04-10T12:01:26.430Z
Great answer. An example of a phenomenon that can (microscopically) alter the Earth's rotation is an earthquake. By rearranging the structure of the crust, it can change the Earth's moment of Inertia. Then, since angular momentum is conserved, the rotational period is altered. See https://www.jpl.nasa.gov/news/nasa-details-earthquake-effects-on-the-earth
Oscar Bravo
CC BY-SA 4.0
2024-04-10T15:27:58.443Z
Relevant to this, there was a lot of news coverage recently about an article in Nature (https://doi.org/10.1038/s41586-024-07170-0) that looked at the interaction of polar ice melt (leading to decreasing angular velocity for Earth) and changes in the planet's liquid core that have been increasing Earths's angular velocity. Here's an article covering it: https://www.scientificamerican.com/article/global-warming-is-slowing-the-earths-rotation/
anjama
CC BY-SA 4.0
2024-04-10T15:38:07.700Z
@anjama The rotation rate is still being affected by the slow rebound of the continental plates after the melting of the icesheets at the end of the last ice age. But at least that's one of the more predictable components.
PM 2Ring
CC BY-SA 4.0
2024-04-10T17:50:02.353Z
Excellent answer. As an aside, that ancient civilizations such as Babylonia and China recorded seeing total solar eclipses over specific ancient cities on specific dates, soon after writing began, gives scientists insight into how $\Delta T$ has changed over the last four thousand years, and thus how much the Earth's rotation has changed over that time.
David Hammen
CC BY-SA 4.0
2024-04-10T21:51:09.317Z
The precise path of the eclipse of two days ago was revised a few days before, bringing the northern limit of the path of totality south by about 1–2 km.
Pierre Paquette
CC BY-SA 4.0
2024-04-10T23:55:41.887Z
@pierre-paquette that means as it is 2044/2045, changes could occur
puzzled
CC BY-SA 4.0
2024-04-11T01:13:27.967Z
@puzzled: It’s not impossible, but it won’t be major; at most, a few kilometres. This mainly depends on a few factors such as the Earth’s rotation speed, which is ever-so-slightly variable in a not-quite-predictable way; the Moon’s precise orbit around the Earth; the Earth’s precise orbit around the Sun (both affected by the gravitational pull of other planets, asteroids, etc.); and—for eclipses that are in the very distant future—tectonic continental drift.
Pierre Paquette
CC BY-SA 4.0
2024-04-11T01:20:37.583Z
@puzzled Did you see the Delta T graphs on Wikipedia? https://upload.wikimedia.org/wikipedia/commons/3/3b/TT-UT1_2000%2B.svg That graph has predictions up to 2033, where the error range is around 1 second. So it's possible for the Delta T error to be around 2 seconds by 2044. That will only have a tiny effect on the *shape* of the eclipse shadow ground track, but it will rotate the location of the track east or west, by upto a kilometre, depending on latitude.
PM 2Ring
CC BY-SA 4.0
2024-04-11T01:29:28.540Z
@Pierre The Earth-Moon barycentre (EMB) orbit is very well-known, but admittedly the Moon's orbit around the EMB is a tiny bit less certain, although JPL have pretty good models dealing with the non-rigid dynamics of the Earth & Moon, as described in Park et al (2021) https://doi.org/10.3847/1538-3881/abd414
PM 2Ring
CC BY-SA 4.0
2024-04-11T01:33:23.070Z
JPL *need* to model the Moon's orbit to high precision, because it's needed to compute the Earth ephemeris from the EMB ephemeris.
PM 2Ring
CC BY-SA 4.0
2024-04-11T01:59:25.997Z
@PierrePaquette Oh, the path itself wasn't moved by 1-2 km a few days before the eclipse, only the much more sensitive "northern limit" along the path. *Interesting!* Is there any information about the path itself, did it move much?
uhoh
CC BY-SA 4.0
2024-04-11T11:07:04.850Z
@uhoh The time error has virtually no effect on the latitude, only the longitude. But by rotating the track to the east, it changes the northern limit of the track because the predicted northern limit got shifted into the Atlantic Ocean.
PM 2Ring
CC BY-SA 4.0
2024-04-11T14:29:43.483Z
@PM2Ring what I did not understand is that the correction made "a few days before the eclipse" was for a decade-old prediction. I assumed there were regular updates, say every year or so - just re-run some script. Now that I understand *how old the original prediction was* before the correction, a few km sounds ok.
uhoh
CC BY-SA 4.0
2024-04-11T14:48:53.403Z
@uhoh Updating a 5000 year collection of solar and lunar eclipses is a major task. ;) I suppose Fred *could* just update small batches, say, the next decade's worth. OTOH, for people doing eclipse research it's *very* useful to have large batches of eclipses that were all calculated with the same ephemeris parameters. Re-calculating the eclipses with the latest DE would only make a *tiny* difference to the fundamental eclipse geometry, the main difference is simply the longitude shift due to Delta T.
PM 2Ring
CC BY-SA 4.0
2024-04-11T14:49:26.477Z
I guess he *could* store the data in a way that makes it easy to re-generate the various tables, images, and anims with a different Delta T. But I don't know if he does that.
PM 2Ring
CC BY-SA 4.0
2024-04-11T18:49:41.743Z
The computations are done in two steps, first Besselian Elements are generated.  Then deltaT is combine to produce the paths and local circumstances on demand.  The code in the Github repo below shows how to perform the calculations, an an article on the example site shows how to generate the Besselian Elements. https://github.com/gmiller123456/solareclipseviewer/
Greg Miller
CC BY-SA 4.0
2024-04-16T18:56:52.523Z
The speed of the Moon's shadow is about 1 km/sec i.e. twice the Earth's rotation speed. On this basis, the distance error related to a given time error is twice the amount you gave.
Thomas
CC BY-SA 4.0
2024-04-16T19:05:18.707Z
@Thomas I didn't mention the speed of the Moon's shadow in my answer.
PM 2Ring
CC BY-SA 4.0
2024-04-16T19:15:54.650Z
@PM2Ring No, that's why I mentioned it. The 1 km/sec includes actually the Earths rotation speed already. Without it, it would be about 1.5 km/sec
Thomas
CC BY-SA 4.0
2024-04-16T19:22:59.297Z
@Thomas I'm only talking about the positioning of the entire track (as a static object), relative to the uncertainty in the axial rotation of the Earth. You are certainly welcome to talk about the speed of the Moon's shadow in your own answer.
PM 2Ring
CC BY-SA 4.0
2024-04-16T21:23:17.403Z
@PM2Ring I would not expect much of an effect of the Earth's rotation on the positioning of the track in the transverse direction. For one, its latitude is fairly constant over large sections of the path (corresponding to an hour or so of duration) and at medium to high latitude, the Earth's rotation speed is much smaller anyway.  For the 2044 and 2045 eclipses see  https://www.eclipsewise.com/solar/SEprime/2001-2100/SE2044Aug23Tprime.html    and  https://eclipse.gsfc.nasa.gov/SEpath/SEpath2001/SE2045Aug12Tpath.html
Thomas
CC BY-SA 4.0
2024-04-16T21:35:32.853Z
A kilometer seems like a pretty big distance to be off by, but given the path of totality was about 185 km across, that represents just about half a percent of the total width...
Darth Pseudonym
CC BY-SA 4.0
2024-04-17T03:06:32.490Z
@Thomas I agree
PM 2Ring
CC BY-SA 4.0
2024-04-17T07:15:32.750Z
@DarthPseudonym I wonder why you would choose an observation spot 1 km (or even within 10 km or so) from the edge of the path.
Thomas
CC BY-SA 4.0
2024-04-17T07:20:46.507Z
@Thomas From https://physics.stackexchange.com/a/806968/123208 "In 2017, the university where I was teaching hadn't considered holding an event on campus, even though we were in the path of totality, because we were only a mile from the edge of the path and it surely wouldn't be long enough to be interesting. WRONG. Just a mile from the edge of the path, we got about sixty seconds of total eclipse. We had about 5000 visitors for the event, perfect weather, an amazing experience".
PM 2Ring
CC BY-SA 4.0
2024-04-17T15:38:45.077Z
@Thomas I mean, I wouldn't personally. I was just saying a kilometer or two seems like a big distance on a human scale, but in context it's actually quite small.
Darth Pseudonym
CC BY-SA 4.0
2024-04-17T20:31:10.417Z
@DarthPseudonym On that note: I came across an official website of a town just outside the path of totality of last week's eclipse, advertising themselves as the ideal place to view the eclipse as it is less crowded than places in the path of totality. I wasn't quite sure whether they were serious or not. Having said this, I saw totality happen last week about 4-5 times live on TV. Most news channels had their cameras positioned  at several places along the path. This was a kind of nice experience as well.
Thomas
CC BY-SA 4.0
2024-04-17T20:41:51.937Z
@Thomas I can't be sure without seeing it, but the way I'd see it is a town just outside the path would be a pretty good staging site even if the viewing wouldn't be great from within the town proper. It's likely you could more easily get rooms and such, and you should be able to travel the short distance to get into range day-of without getting overly tangled in long-distance traffic.  That's basically what I did, except the 'staging site' was my house. We left mid-morning before the eclipse and drove just about an hour to get to a rural site near the center-line.
Darth Pseudonym
CC BY-SA 4.0
2024-04-10T11:08:32.550Z
2024-04-11T10:57:34.290Z
2024-04-11T10:57:34.290Z
PM 2Ring
<p>News says that next Solar eclipse in USA will be in <a href="https://en.wikipedia.org/wiki/Solar_eclipse_of_August_23,_2044" rel="noreferrer">2044</a> and <a href="https://www.timeanddate.com/eclipse/solar/2045-august-12" rel="noreferrer">2045</a> .</p>
<p>For 2045 eclipse eclipse begin time is calculated up to the seconds. Duration for USA is mentioned as 1h, 26m, 35s also.</p>
<p>I am not doubting these dates or path . My question is, is there any % change or statistically that could change or say that this is up-to 99% or 99.99% or some other number approximately to that is correct.</p>
<p>What about any unknown movement of Sun, Earth or moon, that could change the timing/path ?</p>

CC BY-SA 4.0
2024-04-12T01:47:49.053Z
Thanks to @pm-2ring and all who have commented. I will end with https://www.brainyquote.com/quotes/isaac_newton_384639 that is **Isaac Newton** statement  **I can calculate the motion of heavenly bodies, but not the madness of people.**
puzzled
<solar-eclipse><future><prediction>
How precise are future Solar eclipse timing, path and dates, what could change timing/path?
puzzled
# How precise are future Solar eclipse timing, path and dates, what could change timing/path?

(Asked by: username_0 on 2024-04-10)

News says that next Solar eclipse in USA will be in [2044](https://en.wikipedia.org/wiki/Solar_eclipse_of_August_23,_2044) and [2045](https://www.timeanddate.com/eclipse/solar/2045-august-12) .

For 2045 eclipse eclipse begin time is calculated up to the seconds. Duration for USA is mentioned as 1h, 26m, 35s also.

I am not doubting these dates or path . My question is, is there any % change or statistically that could change or say that this is up-to 99% or 99.99% or some other number approximately to that is correct.

What about any unknown movement of Sun, Earth or moon, that could change the timing/path ?

**Tags:** solar-eclipse, future, prediction
> **Comments:**
> **username_0**: Thanks to @pm-2ring and all who have commented. I will end with https://www.brainyquote.com/quotes/isaac_newton_384639 that is **Isaac Newton** statement  **I can calculate the motion of heavenly bodies, but not the madness of people.**  

---

## 2 answers

### Answer by username_3 on 2024-04-10. Score: 51 | Accepted answer

For the past few decades, the best eclipse data has been produced by Fred Espenak, aka Mr Eclipse. Fred is a former employee of [NASA's GSFC](https://www.nasa.gov/goddard/). He's retired now, but he still maintains an excellent website devoted to eclipses, [EclipseWise.com](https://eclipsewise.com/eclipse.html).

The most recent eclipse predictions on that site were produced using data from JPL's [Development Ephemeris](https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris), [DE 405](https://eclipsewise.com/solar/SEhelp/de405-predictions.html). The DE data is produced by integrating the equations of motion for the Solar System bodies, then fitting that data to ground- and space-based observations. It currently uses the masses and locations of all major Solar System bodies down to the 340 most significant asteroids.

To predict eclipses, you need to know the orbits of the Earth and Moon, and the JPL data for the Earth and Moon is excellent. There are several reflectors on the Moon that were placed there during the Apollo era. By shooting lasers at those reflectors for the past five decades, astronomers have gathered very high precision data of the Moon's orbit, so we can now predict the locations of those reflectors to precision better than one centimetre!

To predict eclipse tracks, you also need data regarding the Earth's rotation. The Earth's rotation speed is not quite perfectly uniform, and the Earth wobbles slightly on its axis. Some of these motions are predictable, but there are unpredictable components too.

The Earth's rotation is affected by motion in the atmosphere, oceans, and in the mantle. So predicting the exact rotation amounts to predicting the weather, and to predicting the "weather" in the mantle. The [International Earth Rotation and Reference Systems Service](https://www.iers.org/IERS/EN/Science/EarthRotation/EarthRotation.html) (IERS) coordinates the operations that gather the actual Earth rotation data. There is a wealth of information on their very extensive website. I have some info on this topic in [this answer](https://astronomy.stackexchange.com/a/40867/16685). The IERS publish Earth rotation data on a regular basis.

The unpredictable components of the direction of the Earth's wobble ([polar motion](https://en.wikipedia.org/wiki/Polar_motion)) amount to a few metres, so they have negligible effect on eclipse track predictions.

However, the unpredictable components of the rotation *rate* make it impossible to predict exactly how much the Earth has turned at the time of the eclipse. It also makes it impossible to know how many leapseconds will have been added to UTC time.

If you look closely at Fred's eclipse data, you will see that he gives times in the Terrestrial Dynamical Time (TD or TT) time scale. This is closely related to the timescale that JPL use to do the ephemeris calculations. Unlike UTC, it's a completely uniform scale, with no leapseconds.

So the UTC times given in those predictions are only provisional, but the TD times are much more reliable. To convert Terrestrial Time to UTC, you need to know the value of [Delta T](https://en.wikipedia.org/wiki/%CE%94T_(timekeeping)), which is available from the IERS. Fred Espenak uses a [pretty good estimate for Delta T](https://www.eclipsewise.com/help/deltat.html), but for the past few years the Earth rotation hasn't been slowing down at the expected rate. So we haven't had a leapsecond since December 2016, and the estimates Fred made several years ago for future UTC are high by a second or so.

The Earth's rotation speed at the equator is ~1,674.4 km/h or ~465 m/s. So an error of a couple of seconds can shift an eclipse track by a kilometre or so.

---

For example, the data on the Eclipsewise page for the [2024 Apr 08 solar eclipse](https://eclipsewise.com/solar/SEprime/2001-2100/SE2024Apr08Tprime.html) was first published in 2014. It uses a Delta T value of 71.5 s, but the actual Delta T from the IERS for that date is ~69.2 s, so the predicted UT1 times are 2.3 seconds ahead of the true UT1 times. (UTC is kept within 0.9 s of UT1 via leapseconds).

In 2.3 seconds, the Earth rotates by ~0.00961°, so the actual eclipse track was shifted 0.00961° longitude east of the predicted track. Here's a table showing the corresponding distances in kilometres for several latitudes.

| Latitude | Distance |
| --- | --- |
| 0° | 1.070 |
| 15° | 1.034 |
| 30° | 0.927 |
| 45° | 0.758 |

I calculated those values using this [Python script](https://sagecell.sagemath.org/?z=eJxlkkFr3DAQhe%5F6FYN7sYPrXdsbr3eJSyk07SVQmpYcg9aS42lsyUgT2KX0v3ek7AZKfZKZ9755mlGSJHCLRoGWnsBZkoTWgEJP0vQaBmdnIJy1AP4eHBJpA4cTfLuD6juaJ6jW1aZYb4qyFEmSCBEds6QRcF6sI1gwBycVSuNzUPrJac0HjyaH3vJpPC2WhHgH96i003ICJU85oIGfP0rwurdGeeFRQQdtUzbcbdfu1nWzK4PrdpIhU4hiB6BRw8OX%2D3YDeppw8RaVGFjB3hJWUO3aorreVlV93dRsrsLN%2D14bctgjnYSuovI9BFPA38lf1oE8or%5Fg38Ax4%5FMsJFuaetsWZb2NFjRnizhwiZFXIEOBr3uBLNLJWYeuwI2QXpTO4aBJCqWHIHwMP%2DkyYraPo%2DeJHC8wnl2sxAHGU5Q4TS%5FOsGz1OtM0eDIhPqIh7WRPkf2Y0pG6rzRPn%2DwxTW7G%2DsNn6Xhd%5Fy3%5FZsW1JMsZzlvwXZmHrN36nGhiaQfV1YIhEgu4L28p1hbHPdMh%2DX3ed8ribF80w5%5FLC0jOmRkh2f924%5FNLSblT9irxLHEsYcS%5FbL8vagY%2Dz8z6C%2D0C1Hk=&lang=python), running on the SageMathCell server. The script takes the flattening of the Earth into account. It uses a mean value for the rotation rate, which should be accurate to 8 digits or so.

> **Comments:**
> **username_4**: Great answer. An example of a phenomenon that can (microscopically) alter the Earth's rotation is an earthquake. By rearranging the structure of the crust, it can change the Earth's moment of Inertia. Then, since angular momentum is conserved, the rotational period is altered. See https://www.jpl.nasa.gov/news/nasa-details-earthquake-effects-on-the-earth  
> **username_5**: Relevant to this, there was a lot of news coverage recently about an article in Nature (https://doi.org/10.1038/s41586-024-07170-0) that looked at the interaction of polar ice melt (leading to decreasing angular velocity for Earth) and changes in the planet's liquid core that have been increasing Earths's angular velocity. Here's an article covering it: https://www.scientificamerican.com/article/global-warming-is-slowing-the-earths-rotation/  
> **username_3**: @anjama The rotation rate is still being affected by the slow rebound of the continental plates after the melting of the icesheets at the end of the last ice age. But at least that's one of the more predictable components.  
> **username_6**: Excellent answer. As an aside, that ancient civilizations such as Babylonia and China recorded seeing total solar eclipses over specific ancient cities on specific dates, soon after writing began, gives scientists insight into how $\Delta T$ has changed over the last four thousand years, and thus how much the Earth's rotation has changed over that time.  
> **username_7**: The precise path of the eclipse of two days ago was revised a few days before, bringing the northern limit of the path of totality south by about 1–2 km.  
> **username_0**: @pierre-paquette that means as it is 2044/2045, changes could occur  
> **username_7**: @puzzled: It’s not impossible, but it won’t be major; at most, a few kilometres. This mainly depends on a few factors such as the Earth’s rotation speed, which is ever-so-slightly variable in a not-quite-predictable way; the Moon’s precise orbit around the Earth; the Earth’s precise orbit around the Sun (both affected by the gravitational pull of other planets, asteroids, etc.); and—for eclipses that are in the very distant future—tectonic continental drift.  
> **username_3**: @puzzled Did you see the Delta T graphs on Wikipedia? https://upload.wikimedia.org/wikipedia/commons/3/3b/TT-UT1_2000%2B.svg That graph has predictions up to 2033, where the error range is around 1 second. So it's possible for the Delta T error to be around 2 seconds by 2044. That will only have a tiny effect on the *shape* of the eclipse shadow ground track, but it will rotate the location of the track east or west, by upto a kilometre, depending on latitude.  
> **username_3**: @Pierre The Earth-Moon barycentre (EMB) orbit is very well-known, but admittedly the Moon's orbit around the EMB is a tiny bit less certain, although JPL have pretty good models dealing with the non-rigid dynamics of the Earth & Moon, as described in Park et al (2021) https://doi.org/10.3847/1538-3881/abd414  
> **username_3**: JPL *need* to model the Moon's orbit to high precision, because it's needed to compute the Earth ephemeris from the EMB ephemeris.  
> **username_8**: @PierrePaquette Oh, the path itself wasn't moved by 1-2 km a few days before the eclipse, only the much more sensitive "northern limit" along the path. *Interesting!* Is there any information about the path itself, did it move much?  
> **username_3**: @uhoh The time error has virtually no effect on the latitude, only the longitude. But by rotating the track to the east, it changes the northern limit of the track because the predicted northern limit got shifted into the Atlantic Ocean.  
> **username_8**: @PM2Ring what I did not understand is that the correction made "a few days before the eclipse" was for a decade-old prediction. I assumed there were regular updates, say every year or so - just re-run some script. Now that I understand *how old the original prediction was* before the correction, a few km sounds ok.  
> **username_3**: @uhoh Updating a 5000 year collection of solar and lunar eclipses is a major task. ;) I suppose Fred *could* just update small batches, say, the next decade's worth. OTOH, for people doing eclipse research it's *very* useful to have large batches of eclipses that were all calculated with the same ephemeris parameters. Re-calculating the eclipses with the latest DE would only make a *tiny* difference to the fundamental eclipse geometry, the main difference is simply the longitude shift due to Delta T.  
> **username_3**: I guess he *could* store the data in a way that makes it easy to re-generate the various tables, images, and anims with a different Delta T. But I don't know if he does that.  
> **username_2**: The computations are done in two steps, first Besselian Elements are generated.  Then deltaT is combine to produce the paths and local circumstances on demand.  The code in the Github repo below shows how to perform the calculations, an an article on the example site shows how to generate the Besselian Elements. https://github.com/gmiller123456/solareclipseviewer/  
> **username_1**: The speed of the Moon's shadow is about 1 km/sec i.e. twice the Earth's rotation speed. On this basis, the distance error related to a given time error is twice the amount you gave.  
> **username_3**: @Thomas I didn't mention the speed of the Moon's shadow in my answer.  
> **username_1**: @PM2Ring No, that's why I mentioned it. The 1 km/sec includes actually the Earths rotation speed already. Without it, it would be about 1.5 km/sec  
> **username_3**: @Thomas I'm only talking about the positioning of the entire track (as a static object), relative to the uncertainty in the axial rotation of the Earth. You are certainly welcome to talk about the speed of the Moon's shadow in your own answer.  
> **username_1**: @PM2Ring I would not expect much of an effect of the Earth's rotation on the positioning of the track in the transverse direction. For one, its latitude is fairly constant over large sections of the path (corresponding to an hour or so of duration) and at medium to high latitude, the Earth's rotation speed is much smaller anyway.  For the 2044 and 2045 eclipses see  https://www.eclipsewise.com/solar/SEprime/2001-2100/SE2044Aug23Tprime.html    and  https://eclipse.gsfc.nasa.gov/SEpath/SEpath2001/SE2045Aug12Tpath.html  
> **username_9**: A kilometer seems like a pretty big distance to be off by, but given the path of totality was about 185 km across, that represents just about half a percent of the total width...  
> **username_3**: @Thomas I agree  
> **username_1**: @DarthPseudonym I wonder why you would choose an observation spot 1 km (or even within 10 km or so) from the edge of the path.  
> **username_3**: @Thomas From https://physics.stackexchange.com/a/806968/123208 "In 2017, the university where I was teaching hadn't considered holding an event on campus, even though we were in the path of totality, because we were only a mile from the edge of the path and it surely wouldn't be long enough to be interesting. WRONG. Just a mile from the edge of the path, we got about sixty seconds of total eclipse. We had about 5000 visitors for the event, perfect weather, an amazing experience".  
> **username_9**: @Thomas I mean, I wouldn't personally. I was just saying a kilometer or two seems like a big distance on a human scale, but in context it's actually quite small.  
> **username_1**: @DarthPseudonym On that note: I came across an official website of a town just outside the path of totality of last week's eclipse, advertising themselves as the ideal place to view the eclipse as it is less crowded than places in the path of totality. I wasn't quite sure whether they were serious or not. Having said this, I saw totality happen last week about 4-5 times live on TV. Most news channels had their cameras positioned  at several places along the path. This was a kind of nice experience as well.  
> **username_9**: @Thomas I can't be sure without seeing it, but the way I'd see it is a town just outside the path would be a pretty good staging site even if the viewing wouldn't be great from within the town proper. It's likely you could more easily get rooms and such, and you should be able to travel the short distance to get into range day-of without getting overly tangled in long-distance traffic.  That's basically what I did, except the 'staging site' was my house. We left mid-morning before the eclipse and drove just about an hour to get to a rural site near the center-line.  

---

### Answer by username_1 on 2024-04-15. Score: 1

The variation in the Earth's rotation rate provides probably the biggest error for the eclipse prediction. Not only is the rotation rate slowing down (due to the interaction with the Moon) but it also varies irregularly due to other effects. The length of the day thus increases on average by about 1 milisecond per day, but this rate changes more or less irregularly by a similar amount over various time scales as shown in the following graph (taken from <https://www.iers.org/IERS/EN/Science/EarthRotation/LODplot.html?nn=12932> )

[![enter image description here](https://i.sstatic.net/vTQnAD1o.gif)](https://i.sstatic.net/vTQnAD1o.gif)

There is a long term component varying irregularly over a time span of a decade or so, and a more regular short term fluctuation over a period of a year or two (judging from the diagram). So if you assume an increased/decreased rate of 1ms/day on average, this would amount over a period of 20 years to about $20\cdot 356 \cdot 10^{-3}$ sec = **7 sec**. As the eclipse shadow moves with about **1 km/sec,** this means the location of the shadow would be incorrect by about **7 km** in the direction of the shadow path (much less so in the transverse direction). Now this error will to some extent be compensated by the introduction of leap seconds, so in the end you would probably end up with an error of **1-2 sec** in time and **1-2 km** in location for a 20 year in advance timing.

If you determine the correct timing just a year in advance, you would just have about an error of $365 \cdot 1ms = 365 ms$ due to changes in the Earth's rotation, so just a few tenths of a second.

> **Comments:**
> **username_2**: The predictions attempt to predict the variations in Earth's rotation (the previously discussed deltaT).  So, the the error is only as big as the error in predicting it, not the full effect.  Also, leap seconds do not help as the times are in TDT which does not have leap seconds, it is the deltaT parameter that accounts for leap seconds.  
> **username_1**: @GregMiller Publicly broadcast time signals are in UTC, and this certainly does include leap seconds. And as you can see from the top graph in the figure I posted, the random variation of the increase of the length of day is as big as the increase itself if you consider a time period of a few years. Essentially, this is an unmodelled variation, which is also expressed by the fact that the angular rotation rate of the Earth has a nominal relative undertainty  of about $10^{-8}$ (https://hpiers.obspm.fr/eop-pc/models/constants.html )  
> **username_3**: @Thomas A significant factor in the need for leap seconds is the fact that the SI second (defined in terms of caesium) is a bit short. It was defined to match the ephemeris second, which itself matched the mean solar second from ~1820, and of course the Earth's rotation speed has slowed somewhat in 200 years. Please see https://astronomy.stackexchange.com/a/40867/16685 https://physics.stackexchange.com/a/677946/123208 https://physics.stackexchange.com/a/402062/123208  

---

