I'm working on creating a world with three moons, all with different sizes and different orbits. I'm wondering what effects this would have. How would the tides be affected, obviously, but also would anything else be obviously affected?
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2$\begingroup$ See in part worldbuilding.stackexchange.com/questions/71/…. $\endgroup$– HDE 226868 ♦Oct 17, 2015 at 0:19
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$\begingroup$ Right now both answers to this question deal only with the tides - if you want highly detailed answers about tides, maybe split this question: edit this one to be more specific, and add another one asking "How having 3 moons will affect a planet - aside from tides" to get quality general answers. If you care about only one of these, please say so specifically in the question. $\endgroup$– G0BLiNJul 1, 2018 at 18:46
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2 Answers
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The math
The effects of gravitation force scale linearly with the mass of the moons and inversely to the square of distance (double the distance and gravity is 1/4).
$$F_{\text{gravity}}=f\left(\frac{m_{\text{moon}}}{r_{\text{orbit}}^2}\right)$$
The effects of tidal force scale linearly with the mass of the moons and inversely to the cube of the distance (double the distance and tidal force is 1/8).
$$F_{\text{tidal}}=f\left(\frac{m_{\text{moon}}}{r_{\text{orbit}}^3}\right)$$
So the effects of the moons on the primary's tides depend very strongly upon where you place your moons and how big they are.
What it means
Assuming the moons have different orbits, the closest large moon's tides will swamp the tides of the other moons.
To give you an idea of the scale of effects. Terrestrial tides caused by our Sun are about 1/2 the size of Lunar tides. The Sun is about $2.7 \cdot 10^{8}$ times more massive than the Moon but is 372 times further away than the Moon.
$$F_{\text{Sun tide}} = f\left(\frac{2 \cdot 10^{30} kg}{\left(98 \cdot 10^{6} m\right)^3}\right) = 2.5 \cdot 10^{6} \frac{kg}{m^3}$$
$$F_{\text{Moon tide}} = f\left(\frac{7.3 \cdot 10^{22} kg}{\left(2.5 \cdot 10^{5} m\right)^3}\right) = 4.7 \cdot 10^{6} \frac{kg}{m^3}$$
And as expected, Moon exerts about 2x the tidal force of the Sun.
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$\begingroup$ Add the explanation of how to model multiple moons' tidal effects as the sum of sine waves (as done in this great answer to a similar question), and the math/astrophysics for how a sine's frequency is related to orbital distance, and a sine's amplitude to the moon's mass - and you'll turn this great answer to an amazingly useful one :) $\endgroup$– G0BLiNJul 1, 2018 at 19:00
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The biggest things are how big are the moons and how far away are they? The bigger each moon, the more direct affect it has on the planet it. The closer they are the more direct effect they have.
Each moon WILL be in a different orbit unless they happen to be in the Lagrange point of each other. And each distance of course affects how fast the moons orbits the planet.
Now if one moon is significantly larger than the other 2 it will have the most affect. The other two moons would tend to minimize the affect when both are on the opposite side as the large moon and maximize the tides when both are on the same side as the large one.
Now if all three were ruffly the same size then the tides will max when all three line up, but minimize when the three approximately equidistant apart. Tides would be much more tame in general until 2 or more of the moons align. I suspect the closest moon will have the most effect merely because of proximity.
This would also likely keep the plate tectonics and volcanoes a bit more active with all the pulling some times in opposite directions at the same time. Though the size of the moons will be the biggest piece of this puzzle.
3 small moons like Mars has really wouldn't affect the earth to greatly. Three the size of our moon might make it dangerous to live on this planet.
answered Oct 16, 2015 at 20:42
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$\begingroup$ What if the moons were large, but they were roughly identical and more than two were equally spaced around the same orbit? Would the tidal forces of some largely cancel out those of others? $\endgroup$– supercatJul 29, 2017 at 18:06
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$\begingroup$ @supercat - stable same orbit is possible only if one moon is significantly more massive, and the two others are at L4 and L5 Lagrange points of its orbit (60degs "ahead" and "behind" it) - in that case, the effect of the system will be pretty similar to that of a single moon, more massive than the largest of the trio. This is because part of the effect of the minor moons will amplify that of the main one, and the other part of each moon will cancel out its counter-part... $\endgroup$– G0BLiNJul 1, 2018 at 18:51