Solar eclipses on other planets

As seen in the Earth’s sky, the Moon and Sun are very close to the same size. I’ve seen it asserted a handful of times that this situation is unique in the Solar System (example). But is that actually true? It always sounded a little suspicious to me, so I decided to take a closer look.

[Note that I’m going to use the uncapitalized word “moon” to mean a natural satellite in general, not the Earth’s Moon in particular.]

The ambiguousness of “this situation” is a problem. I wonder if I might be reading an edited version of a statement that started out being perfectly accurate, but has since been simplified to the point where it is misleading or wrong. Perhaps the original statement required the moon to also appear similar in shape to the Sun (i.e. circular)? If so, the statement is certainly true. (And it should go without saying that for cloud-covered planets, the eclipse observer will be just above the clouds.) My less-than-rigorous research indicates that all the other round moons in the Solar System appear too large in their planet’s sky, except for Saturn’s moon Iapetus which appears too small. So if the moon has to be round, the statement is true.

What about non-round moons? In this article, researcher Bill Kramer claims that there are just two other known moons in the Solar System that can produce this sort of just-barely-total eclipse: Saturn’s moons Pandora and Epimetheus.

I did my some research of my own, and came up with three other candidates: Jupiter’s moon Amalthea, Saturn’s moon Prometheus, Uranus’s moon Perdita.

I’m pretty sure Amalthea is always too small to produce total eclipses on Jupiter. When it’s high overhead, its longest axis would appear longer than the Sun’s diameter. But its long axis is probably always pointed directly away from Jupiter, so you would never see it in that orientation. And even if you could change its orientation, it might still never be able to cover the whole Sun.

I guess Prometheus may have a similar problem. It’s highly elongated, and its shorter diameters might never be enough to cover the Sun.

Perdita is a tiny inner moon of Uranus, very roughly 30km in diameter. Not much is known about it, but by my calculations it’s about the right size and distance.

Something to keep in mind is that the giant planets are so large, and some of their moons so close, that the apparent size of a moon can vary significantly in different places on the planet’s surface. That is, a moon can appear quite a bit smaller as it gets closer to the horizon. This gives us a lot of wiggle room, though we do have to ensure that the moon would be visible above the horizon. A moon orbiting near the equator would likely not be visible all the way to the planet’s pole.

To show how I did my calculations, consider Epimetheus. It orbits 151410km from Saturn’s center. Saturn’s equatorial radius is 60268km, so the nearest point on Saturn’s surface is 151410km−60268km = 91142km away.

You cannot get as far away from Epimetheus as Saturn’s center, and still be on the surface of Saturn at a location where Epimetheus would be visible above the horizon. But my crude estimate is that you can get over 90% of the way there. 90% of 151410km is 136269km. (Note that the I’m talking about distance to the center of Saturn, not to its poles. The poles are farther away than the center. You can only get maybe 60–70% of the way from the equator to the north pole and still see Epimetheus.) So we have a range of 91142km to 136269km to work with.

Epimetheus’s size is around 130×114×106 km. The long diameter of a moon typically points away from the planet, so I’ll use 114×106 km as the relevant dimensions. The possible Saturn-Epimetheus distance/diameter ratios look like:

91142/114 = 799
91142/106 = 860
136269/114 = 1195
136269/106 = 1286

The Sun’s distance from Saturn ranges from 1,515,000,000 to 1,353,000,000 km. I’m not sure exactly what these distances represent, but it’s probably not worth worrying about the details.

The Sun’s diameter is about 1391400km. So the minimum and maximum Saturn-Sun distance/diameter ratios are:

1353000000/1391400 = 972
1515000000/1391400 = 1089

Note that the way I did these ratios, larger numbers mean the object looks smaller.

When Epimetheus is directly overhead, its smallest diameter is “860”, enough to cover the Sun (1089 to 927) at any time during Saturn’s year. So, total eclipses are possible.

When Epimetheus is near the horizon, its smallest diameter is “1286”, which is not enough to cover the Sun at any time during Saturn’s year. So, there must be in-between situations that are just barely enough to produce a total eclipse.

Reportedly, an eclipse by Epimetheus would last less than one second, so it wouldn’t be much of a spectacle.

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