# What if our moon had a moon?

lxXTaCoXxl
This is a question I have been pondering for quite some time. I haven't done much research on the matter but I can't find any theories, hypotheses, or explanations of this matter. So I calculate that the best route to take would be to ask those who know about the topic better than myself. I am a student a Full Sail University and I'm getting a degree in Game Design; knowing that 99% of all games do not use true physical systems, I am wanting to keep my game as realistic as possible. I'm developing a game that takes place in outer space in a parallel universe to our own, where our Earth is instead orbiting our moon. Now I know this doesn't seem practical in any way because the Earth's mass relative to the moon's would not allow it to orbit the moon. This is just a big what if type thing and I have made it work by creating a new Earth with the same size but with less density. My question is, what would happen to the Earth in our present universe if our Earth was to switch places with the moon. What would happen if our moon had a moon 1/8 it's size? 1/4 it's size?

Thanks,
Taco

When dealing with two bodies, the orbits of both are around the center of mass. Earth-moon center of mass is well inside the earth, so that having the moon orbiting the earth makes sense. If the two bodies are about the same size, the center of mass would be about halfway in between. You can work out the cases you are interested in.

Mentor
In its orbit, moon accelerates with ~0.0027m/s^2 towards earth. Without precision experiments, you do not notice the orbit at all (even if you stand on the moon) - the other object appears to move around you, unless the rotation is tidally locked (as it is for the moon - if you stand on moon, you always see earth at a fixed position in the sky).

I am wanting to keep my game as realistic as possible.
In this case, you cannot let earth orbit the moon. You can adjust masses a bit, to give some more movement of earth itself, but you would not notice the effect in everyday life.

Earth with a significantly reduced mass would be:
- a big ball of water (reduces mass by a factor of ~4 with the same radius)
- significantly smaller

My question is, what would happen to the Earth in our present universe if our Earth was to switch places with the moon.
This does not work. Can you describe which visual effects you want to get? Maybe there is a physical solution.

lxXTaCoXxl
Well I was more of wanting to know the effects on Earth if our moon had a moon about 1/8 it's size, or to go a little bigger; to be about 1/4 it's size. It's an interesting notion to me. As far as the Earth orbiting the moon, I realize that the theory is not even plausible in current physics however, it sounded like a good idea for my game so I made adjustments to make it work. Granted it's not true physics that powers it because the math doesn't allow it. So what would the Earth be like if our moon had a moon? I would like to create a possible scenario to suit this theory for my game.

Thanks,
Taco

Gold Member
A body of that mass would have an unstable orbit due to earth gravity.

Mentor
Moon's Lagrange points are ~60000 km away from moon. Stable orbits around the moon have to be smaller, with ~20000km radius as maximum for long-term stability. At the lower side, we have the Roche limit - for a moon-like moon of moon, this is ~2.5 times the radius of moon or ~4300km

Somewhere between those values, moons are possible, I would keep away from the limits to be safe. 1/4 of its size corresponds to 1/64 of its mass, the influence on our tides and so on would be negligible. It would probably be tidally locked to moon: it would always show the same side for moon, similar to our own moon, where we can see one side only.