How many moons can form around this alternate Earth?

Say in an alternate timeline, Earth developed with more moons. Many, many many more moons. In fact, it developed with the absolute maximum amount of moons a planet of its size and mass can physically harbor without anything becoming unstable.

How many moons would there be? How big would they be? Would life be different if it developed on this alternate planet? How would our culture be different?

Please note that nothing changes on Earth. The landmasses and oceans are the exact same, as well as the makeup of its crust, mantle and core.

• In future, wait before accepting an answer. Stack Exchange has global reach, yet people in other time zones didn't even get a chance to write an answer. – M i ech Aug 13 '17 at 16:49

The number of moons

Sean Raymond wrote a great answer to a similar question, and I'd like to base my answer on his. He used the following technique to estimate the total number of moons orbiting a planet, assuming all the moons are in mean motion orbital resonances with one another.

1. Calculate the outer edge of the region of stable orbits, which is one half of the Hill radius. For Earth, this distance is $$\sim0.005\text{ AU}$$. For comparison, the Moon's semi-major axis is $$\sim0.0025\text{ AU}$$.
2. Estimate the inner edge of the region. I'll guess that it's 1/20th of the Moon's semi-major axis, or $$\sim0.000125\text{ AU}$$. The very inner limit is the Roche limit. However, that depends on the mass of the orbiting body. Without knowing what the moons would be like, I'm not inclined to speculate on what the Roche limit would be (we're probably safe, though, with this as our inner bound).
3. Divide the outer radius by the inner one. That gets you $$40$$.
4. Kepler's third law relates semi-major axis $$a$$ to period $$P$$ by $$a^3\propto P^2$$ Raise your previous result to the $$3/2$$ power. This gets us a factor of $$252$$, which is close to $$256=2^8$$. This implies that we could fit $$8+1=9$$ moons comfortably in orbit, if we bend the limits a bit.

Some extra thoughts on stability:

• The masses of the moons would need to be adjusted so as to not perturb one another too much. I'd guess they would all have very little mass, but I don't know for sure. It's actually an interesting question, come to think of it: how small can you make a moon that will clear its orbit in a debris disk? I'll update this if I find a good answer.
• The formation of the system would be difficult to explain. Stable resonances can of course arise - and we do see this in the Jovian and Saturnian moon systems, specifically, some of the Galilean moons - but this many moons would be a bit much. You'd also need a rather large debris disk around Earth. I don't think the Giant Impact Hypothesis could work here!
• The system would likely be stable if it was isolated, but if an outside body came by, things would go wrong rather rapidly.

The effects

Whenever you create a system of moons, tides tend to come to mind. The site has covered the tidal patterns from multiple moons in some depth (see How would having multiple moons affect tides?), although never with 9 moons, I believe. The method to model tides would be to simple treat the cycles as the sum of 9 sine waves, one for each moon, and look at the patterns that arise.

Culture is always an interesting one to think about. Many civilizations had deities for the Sun and the Moon; maybe you'd have something similar here. 9 moon deities give you fodder for plenty of interesting stories. For me, the myths centered on the Pleiades comes to mind. Calendars might also be different; more complicated timekeeping systems would certainly be possible. You might want to explore that angle a little.

• This was extremely well explained and interesting. Thanks so much for your help – LargeDan69 Aug 13 '17 at 18:50

You can have as many "moons" as you like, provided they're small enough (think Saturn's rings, which are actually composed by zillions little "moons").

OTOH many large moons (compared to planet size) are unlikely. Most likely our Moon wouldn't be able to cohabit with another moon about its size.

Having many moons would "even-out" tides which may or may not have an influence to life and culture.

Ditto for night illumination which has some influence on agriculture and plants (at least).

• Well, not on plant life. The light coming from the Moon is a tiny tiny fraction of the light coming from the Sun. And regarding the tides, the classical civilization developed around the Mediterranean which has very small tides. – AlexP Aug 13 '17 at 16:00
• @ZioByte I appreciate your response! I have another question, though. If it had many little moons orbiting it, there would have to be some distance away where earth's gravity could no longer effect any celestial bodies. Do you know how far this is, and how far away each moon would have to be from each other? – LargeDan69 Aug 13 '17 at 16:08
• @KingMagmaBlock: I'm not sure I follow You. Gravity pull force decreases with square of distance, but never goes to zero, so it will "affect celestial bodies" in the whole universe. Of course the magnitude of this interaction will rapidly become negligible when larger/nearer bodies are present. Please rephrase. – ZioByte Aug 13 '17 at 16:38
• @AlexP: ask any farmer; there's a lot of difference planting with rising or falling moon and that is attributed to fact during full moon certain processes aren't stopped completely by darkness and thus don't need to be restarted next morning. I'm not an expert so I cannot be more precise, but effect surely exists. – ZioByte Aug 13 '17 at 16:42
• @KingMagmaBlock: it is a question od relative distance. Two bodies alone in space will orbit around their common center of mass at whatever distance. Presence of a third (or more) body if $\frac{mass}{distance^2}$ for the bodies becomes comparable with that of "planet". – ZioByte Aug 13 '17 at 17:57