## Tuesday, February 22, 2011

### Foreign Skies

Living on Earth, we are used to seeing the moon in the sky. Other planets, real or imagined, are unlikely to have moons identical to the Earth (well, ok, the imagined ones might). Other moons will look different and will take up different amounts of the sky. Today, I calculated how big various celestial bodies would appear from the surface of other celestial bodies and compared this with the size of the moon as seen from Earth.

In case you want to try this yourself, I will briefly explain how I did it. First I found the angular diameter of the object in the sky using the equation below. For objects that are much smaller than the distance they are away (so if radius divided by diameter is less than about 0.1), you can also use the small angle approximation, in which you can ignore the tan part and the angular diameter is approximately 2r/d.

 Here, r is the radius of the object in the sky and d is the distance it is away. Both r and d should be in the same units,  that is, both in km (or miles). If you have your calculator set to degrees, then α is the angular diameter of the object in the sky.
Now, because angular diameter doesn't really mean much on an intuitive level, I then divided this angle by the angular diameter of the full moon which is about 0.5 degrees. This gives me the number of full moons you could line up across the middle of the object. If you're interested in the area of sky covered by the object (in units of the full moon), then just square this number.

The Earth seen from the moon

The Earth is a lot bigger than the moon, so naturally it would look bigger if you were standing on the moon. In fact, the Earth seen from the moon is 3.6 times the size of the full moon. APOD have a nice photo for us of this scenario.

Living on Ganymede

Ganymede is the largest moon of Jupiter, and the third furthest away of the four Galilean moons. Ganymede is about three times as far from Jupiter as the moon is from Earth. However, Jupiter is very large (the largest planet in the solar system, in fact) and if visible from Ganymede's surface, would dominate the sky. As in happens, Ganymede is tidally locked with Jupiter, putting it in a synchronous orbit and meaning that the same face is always turned towards Jupiter. Unlike our moon rising and setting in the sky, it you stood on a part of Ganymede facing Jupiter, the gas giant planet would not move in the sky at all. Also, you could use Jupiter to navigate (even if it was directly above you, although it would be a bit trickier in that case) because the bands in its atmosphere run from east to west (here is another nice photo from APOD, which also shows Ganymede in the distance).

So, standing on the surface of Ganymede, how big would Jupiter look? Very big. Fifteen full moons across big. It's a bit hard to imagine and if I find a nice photo of a full moon above a city or other recognisable landmark, I will photoshop Jupiter in and post it here. Jupiter looks so big that you could spread 225 full moons over it and only just cover it up. Yeah. That big.

I also worked out how big Io, the closest Galilean moon to Jupiter, would look from Ganymede. Io is covered in volcanoes and sulfur and looks yellow. When Io is lined up between Ganymede and Jupiter, it will be 0.6 times the size of the full moon; a bit more than half. I initially decided that when Io was on the far side of Jupiter, even if it wasn't behind the parent planet, it would be too small to be very exciting, but doing a quick calculation I found that it would be about a third of the size of the full moon, so probably still big enough to be noticeable.

Phobos for a bit of fun

For a bit of fun, I also worked out how big Mars would look if you were standing on Phobos, one of its asteroid-like moons. Before doing this calculation, I never really appreciated how close in Mars' moons orbited. Firstly, Phobos is only about two Martian radii above the surface of Mars. This means that the small angle approximating definitely won't work when calculating Mars' apparent size. So how big does Mars look? Its angular diameter is a whopping 140º. That's the width of 280 full moons lined up next to each other. In fact, Mars would take up nearly the whole sky on Phobos. I think that's big enough to feel like you're falling towards it, particularly since Phobos has a very puny gravitational field. Scary.