Perchance

This may not be the appropriate forum, but I couldn't think of a better one.

Can anyone tell me how high the tides or how catastrophic the ocean effects would be on a planet that had four moons? I'm thinking of three moons about the size of Earth's but placed at different distances, and one about half the size and very far away.

I realize it's a very precise (and strange) question. If anyone has a link to a mathematical formula or a table that could help me calculate this, it would be appreciated, and of a lot of help with a story I'm trying to write.

Thanks.

-Perchance.

Shadowy Man

I'd worry first about the orbits of these moons being stable. If they are in unstable orbits, the tides could be the least of your worries.

Coragyps

Not speaking as an expert....
I would think that you could make the tides do nearly anything you wanted by picking the periods of the large moons. If all three lined up, even on opposite sides of the planet, the tides would be additive and maybe huge, and when the three were (for instance) 120 degrees apart, tides would be hardly noticeable. I don't think you could have moons with integral ratios of periods, like moon A seven days, B 14, and C 21, as those resonances wouldn't give stable orbits. But 7, 13, and 19 or some such might be OK, and would still give alignments every so often.

The faraway moon could probably be ignored as far as tides go; I'll bet that the calculations with even three moons are the kind that mathematicians call "intractable."

And I want to read the story when it's finished!

Autonemesis

Well, let's see, there's <a href="http://www.ottisoft.com/orbit_x.htm" target="_blank">Orbit Explorer</a>, with a free trial version; a <a href="http://burtleburtle.net/bob/java/orbit/" target="_blank">java applet orbit simulator</a>, with examples - those should give you some ideas, even if you don't know how to use the applet to make your own orbits. Another porbit simulator program I found is called <a href="http://www.rcl-software.org.uk/gravel/" target="_blank">Gravel</a>, it appears to be free.

That should get you going towards a plausible planet-moon system.

Feather

Yeah, I'd worry more about stability of the orbits, first.

Newton solved the tides problem of earth with its one satellite using his calculus and model of gravitation (I like the treatment offered in <a href="http://search.barnesandnoble.com/textbooks/booksearch/isbninquiry.asp?userid=51GNIVX22L&isbn=0030973023" target="_blank">Marion and Thornton's "Classical Mechanics"</a> for a very basic approach).

The long and short of it is that the force causing the tides depends inversly on the cube of the distance between the planet and moon and directly on the masses of both bodies and also directly on the position on the surface of the planet where you wish to calculate the tide.

I'd start with a model that treats each moon's tidal effects as a separate problem (i.e. four one-moon tide problems) and using superposition "add" the effects.

That probably wouldn't be very accurate, though. I imagine the best approach would be to use a perturbation method instead (treat each of the moons' effects as perturbation of the others'). Which would lead to a lovely numerical solution at best, as I imagine a first- (or possibly even second) order correction would not be enough.

This looks like a fun problem, by the way. If I can get my other @#(*$)% homework done I think I will try it out. Thanks for the good idea.

Perchance

Thank you for the information, everyone.

And I agree, I need to worry about the stability of the orbits first . I downloaded Orbit Xplorer and managed to work a simulation where two bodies roughly the size of Earth's moon would orbit an Earth-like planet without crashing into each other, but when I add a third one it keeps colliding with one of the others- or taking off and not coming back.

Strangely, the distant, half-sized moon has actually worked with any simulation I've chosen, though it orbits the planet so fast I'm not sure it would be around long enough to have an effect.

Thanks again for the ideas.

-Perchance.

Undercurrent

Something to remember is that Earth's moon is abnormally large as moons go. Most terrestrial planets (of our large sample of 4 ) have no moons (Mercury, Venus) or small, asteroidal moons (Mars) which would not raise significant tides. Maybe a quartet of smaller moons would be in order.

Also note that the sun also has a tidal effect, hence the difference between spring and neap tides. The tidal displacement due to the Sun is about 1/2 of that of the moon.

One thing I could see is a planet with a large moon, and a much smaller moon at L4 or L5 (same orbit as the big moon, but 60 degrees ahead or behind it.) If the second moon is quite light, these orbits are stable.

Yet another thing is how, over time, resonances would form between the moons. I might expect a small farther-out moon to orbit the primary at near exactly 1/2 or 1/3 the angular velocity of a large, nearer moon.

m.

Perchance

Hey, Undercurrent, thanks for the suggestion! I made the moons smaller and got a stable four-moon system going. (At least, I think it's stable; the two outer moons have a tendency to dance around each other and come breathtakingly close to crashing, but they did manage one whole cycle without colliding).

-Perchance.

[ September 22, 2002: Message edited by: Perchance ]</p>

MattR

In the Jupiter system the four big moons Europa, Callisto, Ganymede and Io along with Jupiter are constantly pulling and pushing at each other causing the moons to distort their shape quite a lot. Io for instance is being pushed and pulled by Jupiter and Europa enough to casue massive volcanic eruptions covering the entire surface with molten sulfur.

Splat

Hellfire and brimstone---yum, yum!

Interesting side note, apropo of nothing: Newton's original tidal calculations were wrong, which cause him to wildly underestimate Earth's mass. Edmund Halley used that flawed estimate as the basis for his theory that Earth is hollow (actually a series of nested spheres). There are a surprising number of people today (hollow Earth cultists) who still believe versions of this wackadoodle theory.