Do you read other peoples' astronomy blogs? You should. You find all kinds of fun stuff that way... and you can also wind up with more ammo against creationists. Bear with me here. For example, Tom's Astronomy Blog has a post on Saturn's moon Epimetheus. A new picture from Cassini was just released showing the moon's shadow on Saturn's cloud tops, and it's very cool:
But then Tom noticed something interesting that I missed: the shadow is fairly sharp. When I read what he wrote, right away that triggered an instinct in my brain that I should check the apparent size of Epimetheus compared to the Sun as seen from Saturn. If the moon were much smaller than the Sun as seen from the cloud tops of Saturn, the shadow would be indistinct, because the moon wouldn't block enough of the Sun's disk to make an obvious shadow (I should note that the slight elongation of the shadow is probably due to the geometry of the positions of the moon, Sun, and Saturn's disk; if this is near the edge of the disk of the planet the shadow would get stretched out).
In other words, to see such a sharp shadow, the size of Epimetheus as seen from Saturn's cloud tops must be similar to or larger than the apparent size of the Sun. Well, that math isn't hard, so let's see. Epimetheus is roundish, but not a sphere. Its dimensions are 117 x 116 x 106 kilometers, so it's shaped roughly like a beachball someone is sitting on (note: these dimensions are approximate, because Epimetheus is actually pretty lumpy -- but they should be accurate to a few kilometers, which will suffice). Epimetheus has an orbit that is very circular, with a radius 151,410 km from the center of Saturn. We want the distance to the cloudtops, so subtract Saturn's equatorial radius of 60,268 km to get a distance from the tops of the clouds to Epimetheus of 91,142 km. An object 117 km across at a distance of 91,142 km would have an apparent size 265 arcseconds. That's 0.07 degrees. For comparison, from the Earth the Moon is about 2000 arcseconds (0.55 degrees) across. So Epimetheus looks pretty small from Saturn, about 1/8th the size of our own Moon as seen from Earth. But wait again! Saturn is a long way from the Sun, and so the Sun will look smaller, too. When that picture was taken, Saturn was about 1.39 billion km from the Sun. At that distance, the Sun would appear to be about 206 arcseconds across. That's smaller than Epimetheus! That's why the shadow is sharp. My instinct was right. If you were floating on Saturn's cloud tops and looking up at that moment, Epimetheus would be big enough to completely block the Sun. You'd be seeing a solar eclipse! In fact, Epimetheus is only about 30% bigger than the Sun, so it wouldn't be that much different than a solar eclipse on Earth, where the Moon and Sun are almost the same size in the sky. From the cloud top, you'd get an eclipse very much like you'd see on Earth. For us, the Moon can be as much as 5% bigger than the Sun in the sky if conditions are just so (we're as far from the Sun as possible to make it look small, and the Moon is as close as possible to make it look big). What I find irresistible about all this is that creationists love to point out that the apparent size of the Moon being roughly the same as that of the Sun makes the Earth unique in the solar system, because we are the only planet that can get total solar eclipses. We can see here that's not true! Shocking, that creationists might be wrong about something. Once again, we see that reality is far, far cooler than fantasy. Prettier, too.
