Can somebody explain how the moon stabilizes Earth's axis?

[Junghalli]

I know the moon is supposed to have a stabilizing effect on Earth's axis, preventing the planet from having big swings in polar inclination like Mars is thought to have and this is thought to have played a role in making the planet more habitable for life.

The problem is I haven't been able to find a really thorough explanation on the internet of how the mechanics of how this effect works. I've read that it has something to do with the Earth's equatorial bulge but I'd like to understand how it works. Is it a factor of how the moon's gravity pulls on different parts of the Earth at different strengths depending on how far away they are, like the tides? Or is it something else, maybe dependent on the general strength of the gravitational force of the moon on Earth (though I find that hard to believe, as IIRC the sun's gravity at Earth is stronger) or the ratio of the masses of Earth and the moon?

Part of the reason I ask this is because I'm working on a hypothetical Earthlike planet, and it orbits a dimmer star than our sun, making an Earthlike moon problematic because of the reduced Hill sphere. I figured a good solution might be to have a moon 1/8 the mass of ours at 1/2 the orbital distance - the planet should experience the same tides as Earth. But I read somewhere (it was on Google Books, I forget the book) that a moon 1/2 the mass of ours or less would not stabilize the Earth's axis - it didn't give any context for it though, like whether they were assuming this smaller moon was at the same distance as ours, or if it was some more absolute factor. So I want to understand exactly how the stabilization mechanism works, so I can figure this out.

Also, would a planet, say, twice the mass of Earth need a moon twice as big to stabilize its axis, or 1/2 as massive as Earth only need a moon 1/2 as massive?

Could someone explain exactly how the stabilization effect of the moon works to me?

Thanks, that would be really helpful.

[Spoonist]

Don't know the answer myself but a good bet would be to ask Phil Plait, depending on time he usually loves getting questions like that.
Here is his ooooooooold page on the earth-moon system;
http://www.badastronomy.com/bad/misc/tides.html

[Ryan Thunder]

Well, think of it kind of like this; say the Earth is a rod. You have a string attached to either end of the rod. Pulling on the middle of the string and holding the middle of the rod makes the rod stand up straight.

It's kind of like that, but over the whole planet.

[Simon_Jester]

My guess:

Look at it in terms of conservation of angular momentum. The Earth-Moon system gains a great deal of angular momentum from the orbiting moon. If the axis of the Earth's rotation shifts, what happens to the moon? You'll get an interchange of angular momentum between the two bodies, which will tend to reduce the change in the axis because a corresponding change in the Moon's plane of rotation is soaking up the change in momentum.

That's an intuitive answer, though; I may be wrong.

[Lord of the Abyss]

As I recall, a major reason why is the tidal bulge. It ensures that the Earth has extra mass aligned with the moon, which means any force tilting the Earth would have to be strong enough to move that mass against the centrifugal force produced by the Earth's spin as well as the pull of the Moon.

I recall reading that Mars lacking such a stabilizing effect apparently back in its prehistory when it was molten inside had its crust tilt due to volcanic action. Mass built up, and the crust slid over the molten interior until the more massive area ended up on the equator.

[Patrick Degan]

Essentially, imagine the Earth-Moon system as a gigantic gyroscope.