While watching the shadow of Io cross Jupiter last night, I got to thinking: What would it look like if I were standing on the surface of Jupiter while Io's shadow passed over me?
From that location, how large is Io in Jupiter's sky? How large is the Sun? How about the other Galilean moons?
Io is about 3,600 km across, and is about 422,000 km from Jupiter. At that distance, it extends a little less than half a degree. Very close to the way that the Moon appears from the Earth, which shouldn't surprise anyone, since the Moon is about 3,500 km across and lies around 385,000 km from the Earth.
However, that would be the view for a hypothetical observer at the center of Jupiter. Since no one could observe from there (or indeed survive to observe from there, even if Jupiter were transparent), it makes more sense to consider the view of Io from the surface of Jupiter, right under where Io is at that point. In that case, we have to subtract half the width of Jupiter from the distance. Jupiter is about 143,000 km across, and 422,000 km minus 71,500 km is just over 350,000 km. From that distance, Io extends across about 35 arcminutes, or just a bit more than the width of the Moon as seen from the Earth.
There is another difference. Io is reasonably reflective; its albedo, or the fraction of light which it reflects back, is about 0.6, as compared with the Moon's 0.12. Square foot for square foot, it reflects about five times as much of whatever light hits it. However, much less light hits Io than hits the Moon. The Sun is about 5.2 times further from Jupiter than it is from the Earth, and the same ratio applies to the satellites. Therefore, the Moon is illuminated about 5.2 squared or 27 times more brightly than Io, so that although its albedo is much lower, it still has a surface brightness 5.4 times greater.
All this has little to do with Io's appearance during a solar eclipse, during which time the side that faces Jupiter is almost completely unilluminated. Since Io's apparent size is very close to that of the Moon as we see it, and even a little larger, shouldn't the solar eclipses be that much better?
Unfortunately not. Part of the beauty of a total solar eclipse on the Earth is that the Moon just barely fits over the disc of the Sun—both have an apparent size of about half a degree. Now, Io as seen from Jupiter's "surface" would also have that size, or a little bigger. But the Sun as seen from Jupiter is 5.2 times smaller, by diameter, than it seems from the Earth—just about 1/10 of a degree. So Io is too large. We want a satellite that looks close to 1/10 of a degree across as seen from Jupiter.
What about Europa? At a diameter of 3,100 km, it's smaller than Io, and it's further away from Jupiter, too. The distance from it to the center of Jupiter is 671,000 km, meaning that the distance to the cloudtops of Jupiter is about 600,000 km. At that distance, Europa will look about 18 arcminutes across—about 3/10 of a degree. Smaller, but not smaller enough.
Similarly, Ganymede and Callisto will look about 18 and 9 arcminutes across, respectively. So Callisto comes closest, but it's still too big. The other satellites of Jupiter are too small, or too irregular in shape, or something.
Still, Ganymede and Europa are both in the vicinity of 18 arcminutes in width as seen from just underneath on the Jovian cloudtops. Might it not be a tremendous sight just to see Europa occult and almost cover up Ganymede? They would both be about 60 percent the apparent size of the Moon as we see it, so it would not be a bland case of unresolved dot covering up unresolved dot. That could really be something!
Copyright (c) 2003 Brian Tung