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[FearfulJesuit]

Hey all,

I do world-building, and I'm currently modifying my conworld. The idea is that my conworld, where my cultures will be, will have a radius that's 1.2 that of Earth's, and be accompanied by a moon/smaller planet with a radius that's 0.8 that of Earth's. (The moon also has life on it.)

What I need is this: a formula where, given a planet/moon A, a planet/moon B, and the distance between them, some number that's directly proportional to tide strength. (I don't need a number that means anything- I just need to compare to Earth's tides.) Does anybody know how to calculate that?

[MonkeyHead]

At its most basic level, tides are an application of Newtonian Gravitation (F_net = (GM_planetm_moon)/(r²)). Here is some suggested Wikipedia reading:

http://en.wikipedia.org/wiki/Tidal_force
http://en.wikipedia.org/wiki/Theory_of_tides

What I think you are looking for are the Laplace equations, which appear all over those pages.

Edit: fixed the links.

[Normandy]

Messed up a bit on those links

http://en.wikipedia.org/wiki/Theory_of_tides actually has the exact formula you're looking for:


Just follow the symbol definitions through the page and you can simply plug in all of the required values.

If you're not familiar with vector math or error notation, the letters in bold are vectors. x_m is a unit vector pointing from the mass of water being considered to the moon and x is a unit vector pointing from the center of the earth to the mass of water being considered. Since you're only interested in relative total strength, just assume they're pointing in opposite directions (that is, you're experiencing full tides).

The O(epsilon^4) simply gives how fast the error grows relative to epsilon. Don't worry about it.

It should be noted though that the specific topography of different bays and such often have a much bigger impact on how powerful the tides are than celestial mechanics. The strength of riptides and the height of tides depend a lot on currents and underwater surface features. If you want some sort of "average" tide height compared to earth then you're prolly best off just using the ratio of the tidal force on your planet to the tidal force on earth, as long as the tidal forces are comparable to each other (i.e. in the same order of magnitude). That should give you an okay estimate.