# If Earth had a smaller second moon, what would the sky look like?

I am creating a fantasy world in which Earth has a second moon with an orbit between Earth and the current moon. The orbit of this new moon is faster because it's closer to earth. I'm not much concerned with realism, just how would it look from Earth: would the new moon be visible in the sky?

Would the new moon be tide locked or would it spin?

What information do I need to calculate when it would cross paths with the current moon. I've done some research on similar questions here on Worldbuilding.

I found this on one of the questions; it's a good example of what I have in mind for this alternate-earth Using something like this how can I chart when the moon cycles would align?

• The (assumed natural) smaller moon would quickly be perturbed out of a stable orbit, eventually crashing into a larger body or flung away into interplanetary space. Thus alignments would be difficult to predict far in advance. – user535733 Apr 3 at 14:12
• @user535733 Why do you assume that? The Sun has eight planets and thousands of other objects in stable orbits after billions of years. The gas giants in our solar system have no problem with having tens of moons left in stable orbits after billions of years. Mars has two moons. Pluto has five moons. What is specifically different about the Earth-Moon system that predicts that a second moon would quickly be perturbed out of orbit? – M. A. Golding Apr 3 at 16:01
• @M.A.Golding: What is specific to the Earth-Moon system is that our Moon is biggg, by far the most massive satellite with respect to its primary. – AlexP Apr 3 at 17:23
• @AlexP "Pluto has five moons" Pluto/Charon system is biggger than Earth/Moon system. – Alexander Apr 3 at 18:33
• @RobotPQ30 On your animated diagrams, the bottom left one shows that one moon is orbiting prograde and the other retrograde. Is that what you are intending with this question? That complicates the stability of the system. – Futoque Apr 3 at 18:45

## Need(ed) More Input (Second edit includes many more details)

Specific orbital behaviour would depend on a lot of factors, but some of your questions can be answered regardless.

You've not indicated whether the new moon is smaller than the existing one, but for the sake of argument we'll assume smaller because something as massive as the moon between the current moon and the Earth would definitely cause some interesting orbital perturbations that are potentially beyond the scope of the question. That said, even a small moon is going to be visible in the sky, probably during day and night, as with the current moon, while it's illuminated by the sun. (The ISS is visible from Earth and it's much smaller than the moon.)

Something the mass of the moon or smaller, orbiting inside the current moon's orbit, will definitely be tidally locked unless this moon is a recent acquisition. If it's been orbiting with its larger cousin this whole time, it will be tidally locked.

The place where this gets interesting is that our moon was formed by the collision of a third body with Earth, flinging the molten moon into space. We didn't have a substantial formation disc, as the gas giants did for their moons, so there's no reason to assume that two moons are necessarily coplanar. If they're not, the answer to "when would they align" might be "almost never". If they are, however, the answer is just "at common multiples of their orbit, on different points on the Earth's equator".

So to actually calculate when they would align, we'd need to know what InnerMoon's mass is, its orbital radius, and whether it's coplanar with OuterMoon.

Edit: It's also worth noting that the Moon's orbit started out ~20 000 km from Earth, so it's hard to imagine where this second moon might have slotted in without being torn apart by tidal forces, unless it arrived/was formed later.

Edit the second, in light of comments:

If the inner moon had half the radius of the outer moon, and we naively assume that the densities of the two moons are homogeneous and identical, the inner moon would be an eighth the mass of the outer moon.

If the inner moon's orbit is half that of the outer moon, e can then ignore moon-moon interactions (we shouldn't, but it's easier in the short term if we do), to calculate the orbital period:

$$T = 2\pi \sqrt{\frac{\alpha^3}{GM} }$$

the only significant changing value is alpha, the semi-major axis, so the inner moon's orbital period would be $$\sqrt{\frac{1}{8}}$$ that of the outer moon. So since the moon's orbit is once every 27.3 days, the inner moon would whip 'round every ~9.65 days. Assuming that they're coplanar and not retrograde to each other, they would appear aligned over some spot on the equator every 14.93 days.

Angular radius, when viewed from earth, is a straight ratio of orbital radius and orbiting body radius, so since the inner moon is half the size but twice as close, it would appear the same size as the outer moon.

Now, having an extra nine quintillion tonnes in orbit would not make things quite this straightforward, but we're assuming that the orbits, at the moment of your story, are in this state.

• Thanks for the reply. The new moon is smaller, lets say half the size of our current moon with half the mass with an orbital radius of about 653.9 which is somewhere around half way of the outer moon. as far as coplanar realistically it wouldn't be but for sake of simplicity the InnerMoon and OuterMoon are coplanar – RobotPQ30 Apr 3 at 18:42
• Edit now that I had more time to think actually noncoplanar might make more sense – RobotPQ30 Apr 3 at 19:09
• @RobotPQ30 - 653.9 of what unit? The orbital radius of the moon is (averaging) about 380 000 km, so I'm not sure what 653.9 is half of. Also, "half the size" and "half the mass" are two very different things. – jdunlop Apr 3 at 20:11
• I apologize! I had to do more research if you cut the current moon's mass in half it would be 20% smaller. I want the InnerMoon to be half the size of the current or OuterMoon. so the mass would be significantly less. I don't know exactly how to calculate the mass. 653.9 mi is around half the radius of the moon. if average orbital radius of the moon is about 380,000 km would it make sense that the InnerMoon would be average 190000 km ? – RobotPQ30 Apr 3 at 23:31
• @RobotPQ30 - updated with your values. – jdunlop Apr 4 at 0:27