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From: Neal McBurnett <neal_at_bcn.boulder.co.us>

Date: Thu, 12 Jan 2006 00:15:39 -0700

I referenced this page, but missed the most interesting part of it:

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

*> The height of a tidal bulge on a planet is proportional to the
*

*> inverse cube of the distance between the planet and the object
*

*> causing the tidal bulge. The torque which slows down the planet is
*

*> proportional to the inverse sixth power of the distance.
*

presumably because the the same third power works both on the size of

the bulge and the differential pull on the bulge. That suggests that

Phobos might raise a lower tide than the sun, but yet have a greater

tidal braking effect. But I expect the speed of response of the

planet to the tidal force could still play a role in comparing the

Phobos and solar effects.

Data on the speed of change of the orbit of Phobos combined with the

conservation of angular momentum should give a good handle on the size

of the effect from Phobox.

http://en.wikipedia.org/wiki/Phobos_%28moon%29

*> tidal forces are lowering its orbit, currently at the rate of about
*

*> 1.8 metres per century, and in about 50 million years it will
*

*> either impact the surface of Mars or (more likely) break up into a
*

*> planetary ring.
*

But its too late to do that math tonight....

-Neal

On Wed, Jan 11, 2006 at 11:41:27PM -0700, Neal McBurnett wrote:

*> 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/
*

Received on Wed Jan 11 2006 - 23:17:32 PST

Date: Thu, 12 Jan 2006 00:15:39 -0700

I referenced this page, but missed the most interesting part of it:

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

presumably because the the same third power works both on the size of

the bulge and the differential pull on the bulge. That suggests that

Phobos might raise a lower tide than the sun, but yet have a greater

tidal braking effect. But I expect the speed of response of the

planet to the tidal force could still play a role in comparing the

Phobos and solar effects.

Data on the speed of change of the orbit of Phobos combined with the

conservation of angular momentum should give a good handle on the size

of the effect from Phobox.

http://en.wikipedia.org/wiki/Phobos_%28moon%29

But its too late to do that math tonight....

-Neal

On Wed, Jan 11, 2006 at 11:41:27PM -0700, Neal McBurnett wrote:

Received on Wed Jan 11 2006 - 23:17:32 PST

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