When will the eclipse happen? A multimillennium tale of computation | Hacker News Reader

When will the eclipse happen? A multimillennium tale of computation

writings.stephenwolfram.com

140 pointsnsoonhui26 comments

The author does not give sufficient credit for a particular difficulty in calculating the location of a solar eclipse. He mentions in pathing that "the rotation of the Earth is gradually slowing down" and that "exactly when a new leap second will be needed is unpredictable". More precisely, he should have said that the Earth's rotation has a tendency to slow down - in contrast to today, it accelerated somewhat in the last third of the 19th century, for example. But more significant in this context, however, is the aspect that the estimation of the degree of change for a given period of time becomes quickly more and more inaccurate when we go forward or backward in time. In the case of ancient eclipses we cannot calculate their exact location from a prior knowledge of the Earth's rotational speed. It is the other way round: since we have historical reports from a particular region about an eclipse we can deduce the change in the Earth's rotational speed between now and then.

For more information about the change of Earth's rotational speed see the Wikipedia article on "ΔT (timekeeping)": https://en.wikipedia.org/wiki/%CE%94T_(timekeeping)

What if we could add giant engines to control the rotation speed and fix this leap day/second nonsense once and for all?

I guess you would have to anchor those engines pretty deep. I would assume that even anchoring them to bedrock would simply cause unscheduled continental drift, and possibly only mountainous relocations.

Goofing a bit, but couldn't you damn the Madeira river and then use the flow control to speed up/slow down the rotation of the earth[0]?

[0] https://en.wikipedia.org/wiki/Three_Gorges_Dam#Terrestrial_i...

Just walk down a hill to accelerate the rotation of the Earth a tiny bit. But when you need to walk up the hill again you decelerate it by the same amount. -- So building a dam preserves the rotational speed of the Earth with respect to the extent of the mass (or more exactly the angular momentum) of the retained water.

What a truly lovely piece of work. I'm so glad that Wolfram adores math and science, and history, so much and has the tools to craft an excellent precis like this. It's always good to go to original sources, and connect with the deep past of learning to which we are the grateful inheritors. Predicting eclipses, and the details of how it was and is done, is probably considered by many to be pointless, boring, or even harmful (stealing intelligent attention away from more pressing problems, or any number of other reasons). But I think it's beautiful to retell these stories and appreciate them and the minds behind them. There is something so entirely wholesome about a learned man appreciating the work of his forebears. Wonderful.

Agreed, it was a really nice read. Even simply in the role of an educator I've taken a liking to his blog posts. There is a certain combination of both breadth and depth that I've not found anywhere else. His overview of how LLMs work from last year was on of the first really good pieces describing them truly from first principles. And still shapes how I describe their workings to people outside of tech.

Wolfram’s Precision Eclipse website gives the wrong time for the eclipse at my location (23.7188, -105.6706).

It says, “Total Eclipse begins at 1:09:31 PM CST”: https://precisioneclipse.com/Results/46/b7/46b7ed589f764aec....

In fact, C2 will be at 18:09 UT, which is 12:09 CST (-0600): https://eclipsewise.com/solar/SEgmapx/2001-2100/SE2024Apr08T...

Can anyone confirm the correct time? I wonder if precisioneclipse.com isn't considering that Mexico abolished daylight savings since Oct 2022.

That’s almost certainly it - I don’t know they abolished it entirely; it used to be offset a few weeks.

The US Naval Observatory has an online calculator which is accurate and time zone agnostic:

https://aa.usno.navy.mil/data/SolarEclipses

That's a good one, thanks. It gives me `18:09 UT`, which is `12:09 CST`.

The Precision Eclipse calculator does seem to provide correct results in the US (e.g., 1:40 PM for Dallas TX). So, it must be a Mexico timezone calculation error.

Mathematica's SolarEclipse[] function, introduced in v10 and seriously updated in v14, is a gem.

https://reference.wolfram.com/language/ref/SolarEclipse

I wonder if he wrote it.

Incredibly esoteric functions, the hallmark of Mathematica!

Best website I've seen is this: https://eclipse2024.org/eclipse_cities/statemap.php

Click a location, then open the simulator for that location.

FYI, this site shows an nice plotted overview per region and period of time:

https://www.timeanddate.com/eclipse/list.html?region=europe

More specifically: https://www.timeanddate.com/eclipse/solar/2024-april-8

The Anticythera Mechanism was able to predict eclipses some 2000 years ago. Anyone know if its predictions would still be useful?

That is discussed extensively in the linked article.

I have the Classic Wolfram app on iOS. I asked it, “When is the next partial Solar eclipse in New Hampshire?” It missed the 2024 one and started giving details about a 2026 eclipse in Spain.

I'm a big fan of Mathematica even though all commercial software irritates me on some level (transparency, cost, and licensing annoyance).

As a result I follow Stephen's blog and sometimes they come off as a little self serving and grandiose, but this one was terrific to me as a non physicist in better learning the history and challenges of all of this. It's hard to understand sometimes that celestial mechanics is simply not a "solved" problem these days.

I can’t believe that when the last time this eclipse happened my friends had to twist my arm into pausing whatever important thing I was doing to go outside and see it because this wouldn’t happen again for thirty years, in 2024. I would be SO OLD then and probably not living there anyway so seize the day!

Fuuuuuuck.

Is there a closed form solution for this or is it an example of the three body problem?

See the "The Three-Body Problem" and several following sections. The fixed geometric approximations earlier in the article can have a closed form though.

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