News says that next Solar eclipse in USA will be in 2044 and 2045 .
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 ?
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. He's retired now, but he still maintains an excellent website devoted to eclipses, EclipseWise.com.
The most recent eclipse predictions on that site were produced using data from JPL's Development Ephemeris, DE 405. 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 (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. The IERS publish Earth rotation data on a regular basis.
The unpredictable components of the direction of the Earth's wobble (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, which is available from the IERS. Fred Espenak uses a pretty good estimate for Delta T, 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 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, 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.
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 )
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.
