A lot of math.
No, seriously, astronomers do know the equations that model the motions of the Earth and Moon extraordinarily accurately. Eclipse predicting has been around for thousands of years, but with the computers we have now, those predictions are actually very quick and VERY accurate.
What is actually amazing is that the eclipse predicting techniques we use today were mathematically formalized way back 1824 by William Bessel – a mathematical genius who had NO University training – but did certainly change the way eclipses would forever be predicted. (With some modern refinements, Bessel’s technique is still used, and the specific numbers that are plugged into the algorithms for any given eclipse are in fact called that eclipse’s “Besselian Elements”!)
All great ideas are simple once you see them – but creating them from scratch is where the genius comes in. The first step is to know when an eclipse is “likely” to occur. Things called “eclipse seasons” were known to the ancient Greeks and Chinese, due to endless hours of observing and meticulous note-taking over generations. We also know that a solar eclipse can only occur during a period right around the time of New Moon – and that has been able to be predicted since antiquity. (So yes, the eclipse is going to happen on August 21! – not the 20th, and not the 22nd… just in case you were wondering about that!)
But when specifically will the eclipse happen? What time exactly? And in what locations on Earth?
Bessel’s simplification was to imagine the outline of the Moon’s shadow cone [the “umbra”] projected not onto a (somewhat) spherical Earth, but onto a “fundamental plane” through the Earth’s center which is normal (perpendicular) to the shadow’s central axis:
It is MUCH easier (read, it makes it possible) to calculate the intersection of the umbra with that plane rather than with the oblately spheroidal Earth. In fact, you can understand the math using no more than a bit of regular and spherical trigonometry. And, if you never studied spherical trig, if you know what sin, cos and tan mean from your high school days, there won’t be anything in the formulas that will look completely foreign to you. (Though before you start out, you should understand that the techniques are STILL pretty daunting!)
Once you know where that outline on the fundamental plane is, you use an iterative technique to bring up all the points on that outline onto the Earth’s surface. And now that you know where the shadow is going to be, and when, you figure out where the Earth will have rotated to at that time, and now you know what points on Earth will be eclipsed, and when.
Similar techniques exist for calculating things like:
- Duration of totality for a given point
- Northern/Southern limits of totality, and the path of the centerline
- The first points of contact for the umbra (and penumbra, for the points on Earth that will not experience totality).
Bessel’s genius was in devising the technique, but he worked under the confines of the highly manual nature of calculating in his day. His original papers are EXTREMELY difficult to follow, and they use many mathematical devices that are unnecessary when using computers to perform the plugging and chugging. But fortunately, refinements were devised by Chauvenet (1885), Comrie (1930s), and Meeus (1960s) which have made the methods more accessible to modern readers.
Using these methods, together with modern sophistications made possible by GPS, atomic clocks, lunar reconnaissance orbiters and HIGHLY accurate terrestrial mapping, we can generate incredibly accurate eclipse predictions. There are quite a few reference materials out there if you’d like to learn more! Here are a couple to get you started:
Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (1961). London: H.M. Stationery Office.
Chauvenet, W. (1960). A Manual of Spherical and Practical Astronomy. New York: Dover (reprint).
Meeus, J.; Grosjean, C.C.; Vanderleen, W. Canon of solar eclipses (1966). Oxford/New York: Pergamon Press.
Meeus, J. Elements of Solar Eclipses 1951-2200 (1989). Richmond, VA: Willman-Bell.
Comrie, L.J. The Computation of Total Solar Eclipses (1933). Monthly Notices of the Royal Astronomical Society, Vol. 93, p.175.
So, that’s how we can predict eclipses thousands of years from now with astounding accuracy – in fact, the only thing that prevents our long-range predictions from being perfect is that we don’t know exactly how much longer the day will get as the Earth’s spin gradually slows down over thousands and thousands of years!
Just little things like that…