One of these things is not like the others:
The Cassini spacecraft took this lovely image in December 2011, during a close pass of Saturn’s moon Dione. Ignoring Saturn’s rings slashing through the picture, we see, from left to right, the moons Dione, Prometheus, and Epimetheus. Which is the odd moon out?
Here’s a hint: Dione is 1100 km (700 miles) across, Prometheus 86 km (53 miles) along its longest axis, and Epimetheus 113 km (70 miles). Got it now?
Yeah, sure, Dione is far larger than the other two! But that’s not my point: Dione is round, while the other, smaller moons are lumpy and rather potato-shaped. Why?
Size matters. In this case, a bigger moon means more mass, and that means more gravity. In general, the force of gravity points toward the center of an object. As you add more mass to an object, gravity gets stronger. On a small moon, a big lump of rock like a mountain feels very little force downward, while on a more massive moon the force would be larger. If the moon has enough mass, and enough gravity, the force will be more than the internal strength of the rock itself, and the mountain crumbles.
So moons that are big and massive enough will tend to flatten their surface, or, more accurately, shape them into spheres. Dione is big enough to do that. Prometheus and Epimetheus are not. Dione is a big ball, the other two are spuds.
Note that gravity’s not the only thing that can make objects spherical. Water has surface tension, for example, caused by the electrostatic attraction between water molecules. In space, without gravity, drops of water are spherical. Random processes can generate round objects too: I bet if we could get a super-duper close look at Saturn’s rings, we’d see the trillions of chunks of ice that make up the rings are round too. But that’s from collisions; there are enough of those bits of ice that they smack into each other. Since they spin and tumble, over time any part of a chunk will have gotten hit by some other chunk, and that will tend to make them round.
So how big does an object have to be before it starts to become round via gravity? That’s complicated, and depends on its composition – a ball of ice the same size as a ball of iron will have far less gravity since it’s so much less dense, and will have lower mass. But for a ball of ice and rock – like Dione – that size is clearly no bigger than 1100 km across. And if you’re wondering how this might play into our concept of what a planet is, then you might want to read this. I’m way ahead of you!