Preparing for August 21, 2017

On August 21, 2017, there's going to be a total eclipse of the Sun visible on a line across the US. But when exactly will the eclipse occur at a given location? Being able to predict astronomical events has historically been one of the great triumphs of exact science. But in 2017, how well can it actually be done?

The answer, I think, is well enough that even though the edge of totality moves at just over 1000 miles per hour it should be possible to predict when it will arrive at a given location to within perhaps a second. And as a demonstration of this, we've created a website to let anyone enter their geo location (or address) and then immediately compute when the eclipse will reach them—as well as generate many pages of other information.


It's an Old Business

These days it's easy to find out when the next solar eclipse will be; indeed built right into the Wolfram Language there's just a function that tells you (in this form the output is the "time of greatest eclipse"):

✕ SolarEclipse[]

It's also easy to find out, and plot, where the region of totality will be:

✕ GeoListPlot[SolarEclipse["TotalPhasePolygon"]]

Or to determine that the whole area of totality will be about 16% of the area of the US:

✕ GeoArea[SolarEclipse["TotalPhasePolygon"]]/GeoArea[Entity["Country", "UnitedStates"]]

But computing eclipses is not exactly a new business. In fact, the Antikythera device from 2000 years ago even tried to do it—using 37 metal gears to approximate the motion of the Sun and Moon (yes, with the Earth at the center). To me there's something unsettling—and cautionary—about the fact that the Antikythera device stands as such a solitary piece of technology, forgotten but not surpassed for more than 1600 years.

But right there on the bottom of the device there's an arm that moves around, and when it points to an Η or Σ marking, it indicates a possible Sun or Moon eclipse. The way of setting dates on the device is a bit funky (after all, the modern calendar wouldn't be invented for another 1500 years), but if one takes the simulation on the Wolfram Demonstrations Project (which was calibrated back in 2012 when the Demonstration was created), and turns the crank to set the device for August 21, 2017, here's what one gets:

And, yes, all those gears move so as to line the Moon indicator up with the Sun—and to make the arm on the bottom point right at an Η—just as it should for a solar eclipse. It's amazing to see this computation successfully happen on a device designed 2000 years ago.

Of course the results are a lot more accurate today. Though, strangely, despite all the theoretical science that's been done, the way we actually compute the position of the Sun and Moon is conceptually very much like the gears—and effectively epicycles—of the Antikythera device. It's just that now we have the digital equivalent of hundreds of thousands of gears.

Why Do Eclipses Happen?

A total solar eclipse occurs when the Moon gets in front of the Sun from the point of view of a particular location on the Earth. And it so happens that at this point in the Earth's history the Moon can just block the Sun because it has almost exactly the same angular diameter in the sky as the Sun (about 0.5° or 30 arc-minutes).

So when does the Moon get between the Sun and the Earth? Well, basically every time there's a new moon (i.e. once every lunar month). But we know there isn't an eclipse every month. So how come?

✕ Graphics[{Style[Disk[{0, 0}, .3/5], Yellow], Style[Disk[{.8, 0}, .1/5], Gray], Style[Disk[{1, 0}, .15/5], Blue]}]

Well, actually, in the analogous situation of Ganymede and Jupiter, there is an eclipse every time Ganymede goes around Jupiter (which happens to be about once per week). Like the Earth, Jupiter's orbit around the Sun lies in a particular plane (the "Plane of the Ecliptic"). And it turns out that Ganymede's orbit around Jupiter also lies in essentially the same plane. So every time Ganymede reaches the "new moon" position (or, in official astronomy parlance, when it's aligned "in syzygy"—pronounced sizz-ee-gee), it's in the right place to cast its shadow onto Jupiter, and to eclipse the Sun wherever that shadow