# Predicting lunar eclipses with multiple moons

I realize that creating worlds with multiple moons and/or suns is risky, but I'm toying with an idea to see where it goes. So, a planet has 3 moons. One is large like ours, the second is about half the first's diameter (and mass) and the third is about half of the second's diameter (and mass).

If all on the same plane, and having circular orbits, is there a way to calculate how often lunar eclipses would occur, and especially when all three align?

• Yes it is possible but it would require the distance between each moon and the planet to know their orbital period. and we need the mass of the planet. Commented Nov 11, 2014 at 22:01
• @Vincent Why mass? Commented Nov 11, 2014 at 22:34
• Tools like Space Engine or Universe Sandbox can be great for worldbuilders. Both allows you to create a planet, moons and stars and to simulate what would happens over a very long period. Commented Nov 11, 2014 at 23:22
• Halving the radius, diameter, or circumference reduces the volume to an 8th. An 8th of an 8th is a 256th. If the smallest moon has $\frac{1}{4}$ mass but $\frac{1}{256}$ the volume then it is 64 times denser. See worldbuilding.stackexchange.com/questions/493/… Commented Nov 11, 2014 at 23:58
• Mass becomes important for stability, if the moons get too close to each other they eventually get kicked in or out to a more stable setup. Commented Nov 13, 2014 at 0:51

I realize that creating worlds with multiple moons and/or suns is risky

I think I implied this is one of my answers. I suppose that this statement really comes down to opinion, but there's some rationale behind it. The point is this: Multiple stars can be risky; multiple moons generally aren't. So your idea is perfectly fine (I was going to talk about how Jupiter has so many moons, but I realized that you're probably not thinking about a gas giant!).

Is there a way to calculate how often lunar eclipses would occur?

The procedure for doing this wouldn't be any different from the way you would normally calculate when an eclipse would occur: Gather a lot of data and do a lot of calculations. This is actually really, really hard to do, as an explanation here says:

There is no simple formula to calculate what you are interested in. The calculation of eclipses is tedious work requiring many observations or calculations of the positions of the Moon and the Sun. The lunar orbit data must then be extrapolated to find the months when eclipses might occur and then the exact times determined to see where the eclipse will be visible. The eclipse path can then be projected into the Earth's surface to find if a total eclipse will be visible from a given location at a particular time. This work requires a lot of patience and an understanding of the geometry involved and cannot be reduced to a formula.

It kind of stinks, but it's the truth.

. . . especially when all three align?

Well, you really just have to do the calculations for each one, and figure out when they'll all meet up. It's helpful if they're in an orbital resonance, preferably something like $1:2:4$ or $2:6:7$.

By the way, you have to get the sizes and orbital radii of the moons just right. If they appear to small in the sky, you won't see solar eclipses - at least, not total solar eclipses.

• So just to verify, without a ton of dedicated work, theres not even a ballpark? From, every single night to only ever 100 years? Commented Sep 8, 2019 at 8:25

If you want to know when moons in different orbits line up, you want to calculate the synodic period. This tells when the Earth and a planet line up again, measured from the last time they lined up. If you substitute the two moons, this also gives the time for a eclipse when viewed from the primary. Assuming the orbits are not steeply inclined, the moons would eclipse each conjunction.

1/S = 1/P - 1/E

where: P - Nearer moon's sidereal period E - Farther's moon's sidereal period S - Time between conjunctions (synodic period)

So if moon 1 orbits in a week and moon 2 orbits in 1.5 weeks, then conjunctions will come every three weeks.

source: here

For additional moons, you could calculate the S period for one pair, then do the calculation again using S as one period and the third moon's period. This should give when a conjuction next lines up with an additional moon...or a triple conjunction.

You also have to consider how big the sun is, as well - if the sun is the same size as ours, then only the first moon in your scenario will eclipse it, as the others will be too small. They can still have "annular eclipses", though - where there is a ring of the sun visible around the moon, like a donut.