Is there a way to measure how ocean currents would respond on a planet with three moons? It's a planet that's around twice the size of Earth and only one of its moons is large enough to have become spherical. The rest are small and shaped irregularly. I know the currents will be wonky, but I am curious to see if there would be a way to predict when they change course.
I got a very similar ask from an anon about basically this: How would having two moons affect an earth like planet?
so I’ll just answer them together. The main thing is going to be the tides. The time would also be affected as the moon actually affects our rotational speed. With multiple moons, the days would be longer and the months would be all irregular and wonky. A system of full and partial months would be needed.
now as far as the tides go, tides are extremely complex and have to do with a bunch of stuff, not just the moon. But a way to model how multiple moons would affect the earth or an earth like planet would be with sine waves.
If you map a sine wave for each moon based on how much gravitational pull they have (provided they are on the same orbital plane) then add all the sine waves together, you’ll get a rough graph of the tides
So here is the basic formula for each sine wave that you can plug into an online calculator f(x)=A*sin((1/(f/2pi))X) where A is the amplitude (how much force the moon is exerting) and F is frequency (the length of a lunar day divided by 2) and X is the variable. The period of a sine graph is inversely related to whatever is multiplied by X and because the period is already 2pi we have to compensate.
A lunar day is how long it takes for a spot on earth to rotate from an exact point under the moon to the same exact point. You cant just use the period of the moon because the planet rotates as well, so you’ll have to know the length of a lunar day. Also, when the moon is on one side of the earth, you also get a high tide on the opposite side of the earth. This is because the planet is closer to the moon than the water on the opposite side so the moon pulls the planet a bit, creating a second high tide. So while our moons lunar day is 24 hours (ish) we have a tidal period every 12 hours. As in, it takes 12 hours to go from high tide to low tide and back to high tide. Realistically, the tide when the moon is on the opposite side of the earth would be a bit lower and less drastic but thats complicated to graph.
so lets say we have 3 moons. Moon A, moon B, and moon C. I dont know how far away your smaller moons are so I’ll be making up distances and stuff for them but lets say moon A has a pull of 5. This is how many feet the tide will come up from the average, and drop from the average. It definitely changes based on where you are on the planet but the average difference between high and low tides on earth is about 10 feet of elevation, so 5+5 is ten. And for ease of visualization, lets say a solar day is 24 hours on this imaginary planet, and a lunar day of moon A is 24 hours as well. (our moons lunar day is 24 hours 50 minutes, I’m just going to use 24 hours though as its not our moon) Then we divide that by 2 to get 12 so moon A’s graph is A(x)=5*sin((1/(12/2pi)x)
let’s say moon B is 1/3 the size of moon A and halfway between the planet and moon A. So we divide 5 by 3 to get 1.66667 and then multiply that by 2 (because its twice as close) and get 3.3333. Then lets say its lunar day is…. 30 hours, and divide it by 2 to get 15 so its equation is B(x)=3.333*sin((1/(15/2pi)x)
Lets say moon C is ½ the size of moon A and ¼ the distance between the planet and moon A. So divide 5 by 2 to get 2.5. Then multiply it by 4 to get 10. And lets say the lunar day is 14 hours, and divide it to get 7 So the equation is C(x)=10*sin((1/(7/2pi)x)
here is the individual graphs of A B and C (A is red B is blue and C is green)
The y axis shows how high the tides are compared to the average in feet
and here’s all of the graphs added together
as you can see, it is all wonky and over the place, some high tides go up like 16 feet and some only go up 3 feet. But it gives you an estimation. You can use the same equations and just adjust for the lunar days that your moons have and how much pull they have compared to the main moon.
heres the site I used: https://www.desmos.com/calculator
and a better picture of the equations:
