American Scientist

Whether apocryphal or purposefully fictional, doubtful stories about the timing of solar eclipses are sprinkled throughout history, such as in the story of "Ho and Hi, The Drunk Astronomers."

Here lie the bodies of Ho and Hi
Whose fate though sad was visible,
Being hanged because they could not spy
Th'eclipse which was invisible.
—Unknown Author (2137 B.C.E.)

Knowing what we know today about the movement of the Moon, Sun, and Earth, astronomers can pretty well validate which stories were at least coincidental with a solar eclipse. But even in NASA's table of Solar Eclipses of Historical Interest, "It is left to the reader to evaluate whether the eclipse association is valid or not."

In Western civilizations, the oldest known records of solar eclipses that consistently match up with today's calculations date back over 3,000 years to the Babylonians, who noticed three cycles of the Moon:

• Synodic month—new Moon to new Moon
• Anomalistic month—perigee to perigee (closest point between Earth and Moon)
• Draconic month—node to node (same point in celestial longitude)

With 900 years' worth of data, the Babylonians appear to have figured out that those three cycles line up every 6,585 days (about 18 years), meaning that they could predict a solar eclipse would repeat itself every 18 years (though today we know that it doesn't always happen for a variety of reasons, including that the cycles don't match up exactly:  they're off by a couple of hours).

Here's a modern-day (1955) representation of this 18-year cycle, which is called the Saros cycle, a term coined by Edmund Halley in 1691 after the Babylonian word sar. Today we know that sar refers to a period of 3,600 years (the Babylonians evidently thought in terms of long time scales). But in Halley's time (and for hundreds of years prior), it was thought to refer to this 18-year period.

Today, with modern computers, we can quickly and accurately compute the timing and viewing location of a solar eclipse (and know they happen a lot more often than once every 18 years). But the calculation isn't exact. Although the mathematical problem can be stated simply as a system of three ordinary differential equations, solving it exactly has eluded mathematicians for hundreds of years. The best we can do right now with such systems of equations is a numerical calculation, which, when tweaked to include everything that affects the motion of the Earth, Moon, and Sun, involves parameters such as the gravitational effects of Jupiter and Venus.

Mathematician Stephen Wolfram wrote about the "multimillenium tale of computation" of the solar eclipse prior to the August 21, 2017 eclipse and publicly analyzed his own data from his eclipse viewing in Jackson, Wyoming. As he told me in our phone conversation, solving the "Problem of the Moon," as it has been called historically, is a "big, complicated mess."

Still, Wolfram says he thinks with a little more data and a lot more computation, it'll be possible to compute the timing of the moment of totality to within 0.1 seconds. That's pretty accurate considering the Moon's shadow during this past eclipse was moving at a rate of about 1 kilometer/second. Here's a podcast I made from our conversation.