What if we had two moons?

Suppose the earth had two moons instead of one. Let’s say the second moon having the same density but half the size of the moon we have now. How would things be different? I expect it would do something to the tides at the very least, but what exactly? Would it have any other significant effect on the earth? Or would it just change how our sky looks?

How far away do you want to assume the second moon is?

I was thinking about roughly the same distance as the real moon. I’m woefully ignorant as to how orbits work though, I don’t suppose that it would result in a collision with the other moon at some point, would it?

Technically we already have a second moon, and perhaps more:

The term “once in a blue moon” might have to be altered to um. . . something different.

There would be a never ending war between the Skeksis and the Urus.

OK, with the second moon at the same distance as the first one, the most likely orbital configuration would probably be something like that of Saturn’s moons Janus and Epimetheus. The two moons are in nearly the same orbit, but at slightly different distances (less difference than the diameter of either). Whichever one is closer moves slightly faster in its orbit, until eventually it almost completely “laps” the other. When they get close enough, the gravitational interaction between the two slightly raises the orbit of the low one, and slightly lowers the orbit of the higher one, such that the one that was closer becomes the further one. At this point, the one that’s in front is now the low one, and so goes faster, eventually lapping the other one, and the process repeats.

All of that is to say that the two moons will mostly move together, but would gradually get closer together or farther apart in the sky. So if, on one day, they rise an hour apart, the next day they’ll rise very close to an hour apart as well.

As for what effect the smaller moon would have, it would have 1/4 the cross sectional area, and hence 1/4 the brightness, of the larger moon, and 1/8 the volume (and hence mass, given the same density), so 1/8 as much of an effect on the tides. For comparison, the Sun has about half the effect on the tides that the Moon does, so the second moon’s tidal effects would still be smaller than the Sun’s.