On Wed, Jan 11, 2006 at 11:44:13PM -0500, John Cowan wrote:
> I wouldn't be too quick to dismiss tidal braking from Phobos.  It's
> awfully close to Mars, and tidal braking is as you say an inverse-cube
> effect.  The formula (kai Wikipedia) is (2GMmr)/R^3, where M and m are
> the masses, r is the radius of the primary, and R is the orbital radius
> of the secondary.  The mass of the Earth-Moon system is eight orders of
> magnitude larger than the Mars-Phobos system, and the radius of Earth

I assume you mean the mass of phobos vs the mass of the moon, not the
systems, since that is what fits in the raw numbers and equations you
provide.  But that is less than 7 orders of magnitude different, as I
read your reference.

> is only twice the radius of Mars, but the ratio of the cubed orbital
> radii is five orders larger for Phobos than for the Moon.  So the tidal
> acceleration of the Moon toward the Earth is only some three orders larger
> than Phobos's toward Mars.  That puts the effect in the same ballpark.

But the tides from the sun are very significant on earth, and much
more pronounced on mars.

> (See http://www.madsci.org/posts/archives/oct98/908453811.As.r.html for
> the relevant masses and radii.)

A quick google search for   mars  tides  yields much more useful
and interesting answers.

 http://www.findarticles.com/p/articles/mi_m1134/is_5_112/ai_102275148

> the solid-body tides on Mars--caused by the Sun, not by a Martian
> satellite--are large enough to indicate that at least part of that
> planet's core is liquid.
> ...
> Early in the study, the investigators realized only a liquid core
> could give rise to a tidal bulge capable of having the observed
> gravitational effect on the spacecraft. And how much bulge is that?
> About a third of an inch.
> "Fluid core size of Mars from detection of the solar tide," Science
> 300:299-303, April 11,2003)

But of course we need to treat the web with some skepticism.  I doubt
this tidbit got it right about what causes the tides (Phobos vs the
sun):

http://ganymede.ipgp.jussieu.fr/GB/projets/netlander/
> Another way to proceed will be to measure tides produced by Phobos,
> one of Mars' moons. Those tides are 10 times lower than the tides
> produced by the Earth' Moon.

As for changes in the length of the day, we have to look at the
mechanism by which tides relate to the slowing of the day:

http://www.exo.net/~pauld/physics/tides/tidalevolution.htm

> There are also tides in the solid earth. The tidal bulge is about 1
> meter high. The moon pulls up this tidal bulge on the earth, there
> is a time delay between the pull of the moon and the time when the
> tidal bulge reaches its maximum height. During this time the
> rotation of the earth carries this tidal bulge around the planet in
> the direction of rotation.

> The moon then pulls on the mass of the tidal bulge and slows the
> rotation of the earth.

So the degree of slowing is affected by both the size of the bulge,
how delayed the bulge is, and the angular velocity of the body giving
rise to the tides, making it harder to compare the effects of the sun
with rapidly-moving phobos.

That is what would relate to this aspect of your question:

> How much difference in actual slowing can be attributed to Earth's ocean
> and Mars's lack of one I don't know.

I also note that the axial orientation of Mars changes widely back and
forth, which would clearly affect the long term effects due to the sun:

>  While Earth's tilt varies from 23 to 25 degrees, the Red Planet's
>  actually shifts from 15 to 40 degrees over a 100 million year
>  period

I don't see a handy reference to pull all that together right now....

Cheers,

Neal McBurnett                 http://bcn.boulder.co.us/~neal/

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