This is fun: today’s BAN issue number is 777, but that’s in base 10, the number system we count in (called the decimal numeral system). In base 6, or the senary numeral system, that becomes 3333! If we had three fingers on each hand the issue number would still be repeating digits. Is this useful? Not really. I just like math and playing with numbers.

I’ve written about solar eclipse and given talks about them many dozens of times over the years. When I started, back in the 90s, eclipse maps were pretty good, and they’ve gotten better as tech has improved. You have to know things like the exact position of Earth and the Moon, the distance to the Sun, and some decent trig to map out the placement of the Moon’s shadow on Earth during the eclipse.

One thing I’ve often wondered is when we’d be able to take into account things like hills and valleys on Earth, which change the shadow geometry, and more importantly the topography of the Moon. A mountain on the Moon can block a lot of sunlight, and change the timing of the eclipse. Worse — far worse — a valley on the edge of the Moon might let enough sunlight through to change a total eclipse to a very slightly partial one. Any part of the Sun’s surface you can see during the eclipse will overwhelm the light from the corona, changing the eclipse from a life-changingly profound event to one that’s merely very cool.

The answer to my wondering is: now. We can do this now. A paper just published by a NASA solar astrophysicist and a NASA data visualizer goes into the details [link to journal paper]. They created software that will render maps of the eclipse path using topological data of the Earth to include the observer’s elevation, as well as topological data of the Moon from the Lunar Reconnaissance Orbiter, which uses a laser altimeter to measure the elevation of the lunar surface.

This makes the maps far more accurate than they were. Before, the Moon and Earth were both assumed to be smooth, and the Moon’s shadow therefore a smooth oval as it gets distorted by Earth’s curvature (think of how shadows get elongated when they’re cast on tilted surfaces). The new method includes mountains, valleys, crater walls, and more.

But accuracy isn’t the only outcome of the work. They found out the shadow of the Moon cast on Earth can be really bizarre. 

The Sun is what astronomers call an extended object, meaning it’s not a one-dimensional dot on the sky. Because of that, the Moon casts two shadows; both are long, narrow cones, with the darker shadow (the umbra) nested inside the larger, lighter shadow (the penumbra. Think of it this way: if the Moon only partially blocks the Sun, your light from the Sun is dimmed, but it’s still pretty bright; you’re in the penumbra. Only when the Moon completely blocks the Sun — the umbra — does it get dark.

But a valley between two mountains on the side of the Moon messes that neat picture up. The valley acts like a pinhole camera, letting light through and casting a narrow beam of sunlight down to Earth. Every dip in the Moon around its edge does this, creating a series of images of the Sun arrayed like petals of a flower, with a hole in the center where the umbra is.

The umbra is the tiny dark spot in the center. Every dip in the lunar surface around the edge as seen from Earth creates an image of the Sun centered around that dip, so you wind up getting a lot of big circles around the umbra, each tangent to it (meaning the edge of each circle just touches the edge of the umbra). I wouldn’t have thought of that, and it’s pretty cool. 

But depending on the Moon’s and Earth’s orientations, this can change the oval shape of the shadow on Earth’s surface to other, weirder shapes. This figure is from the paper:

How bizarre! Not only that but this overall distortion changes over time because we see the Moon from slightly different angles at different times; the elliptical orbit of the Moon means we sometimes can peak over the east and west edges, and the orbital tilt relative to Earth’s equator means we can see over the north and south poles a bit, too. The combined effect is called libration, and it looks like the Moon sways and nods a bit over the course of the month (and also changes size as it gets closer to us and recedes):

In that video the Moon’s motion is shown, and the blue line is the profile of the edge magnified by a factor of 20 to make it easier to see. How awesome is that? The Moon is far from a perfect sphere.

And because of the advances in mapping Earth and the Moon, and much faster computers, we can now use all this to make much better maps of future eclipses. So. Very. Cool.

I contacted the lead author of the paper, Ernie Wright, and asked him about the availability of the mapping software, and he said that for now you need to have familiarity with some advanced software like astropy, Mathematica or Matlab, which can then generate the numbers needed to plug into the equations in the journal paper, so it’s not like everyone can just make their own maps. However, he’s hoping to release the source code soon, and expects to be making maps for upcoming total solar eclipses like the ones over Spain and Iceland in 2026, and another over northern Africa in 2027.

I don’t have plans as yet to see those eclipses, but we’ll see. I missed the one earlier this year, and I’d really love to see another one. I wouldn’t mind visiting any of those places, so hopefully I can go. And if (when) I do, I’ll know with a lot more precision where exactly I want to be.

Correction: I originally wrote that the upcoming total eclipses are in 2025 and 2026, but they’re in 2026 and 2027 (there is none in 2025).

For Friday’s Scientific American article, I wrote about small asteroids with even smaller asteroidal moons — how these system form is a bit of a mystery, but scientists are getting closer to figuring it out. These binary asteroids are very common, so whatever forms them must be ubiquitous. Weirdly, the answer might be: sunlight!

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