#21
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Uranus's axis
In article ,
Greg Neill wrote: "Paul Schlyter" wrote in message ... In article , Greg Neill wrote: It's a matter of torque and energy dissipation. In other words, inertia. Phobos and Deimos are mere specks of dirt compared with the Moon. So I'd say, yes, if they were in orbit about the Earth at a comparably close distance, then they would be tidally locked and orbiting very nearly in the plane of the equator by now. Yes they would, but the reason would be the proximity to the Earth, not their small sizes. Phobos and Deimos may be tiny specks compared to the Moon, but they're huge giants compared to the artificial satellites we've launched. And our artificial satellites don't move towards an equatorial orbit much faster because of their very low mass.... Suppose we could perform two trials. In one we put, say, Phobos in a given proximate orbit to the Earth and timed its orbit's relaxation to an equitorial one, and then did the same with a small satellite (after removing Phobos, of course). Would we see the same relaxation time? What factors might influence the results? Certainly the smaller satellite would present less volume for tidal action (inverse cube with distance) and dissipation of energy in its structure. The satellite would also be much more rigid. The small satellite would not raise measurable tides on the Earth, but then tides due to Phobos would be tiny, too. The larger size of Phobos would present a slightly larger "handle" for torques, due to the tidal bulge of the Earth, to act. In computing the gravitational parameter mu for the system, the satellite's mass would be totally negligible, and Phobos' nearly so. But the mutual gravitational force would be ever so slightly larger and the orbital period ever so slightly shorter. Have I missed anything? I think we would see very nearly the same relaxation time, since the difference in the parameter mu would be tiny. The greatest difference would be the tides upon the Earth, which of course would be proportional to the mass of the satellite. -- ---------------------------------------------------------------- Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN e-mail: pausch at stockholm dot bostream dot se WWW: http://www.stjarnhimlen.se/ http://home.tiscali.se/pausch/ |
#22
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Uranus's axis
"Paul Schlyter" wrote in message ...
I think we would see very nearly the same relaxation time, since the difference in the parameter mu would be tiny. The greatest difference would be the tides upon the Earth, which of course would be proportional to the mass of the satellite. You're probably right. I can't see in the usual equations anything that would lead directly to a change in the inclination of a satellite's orbit. Perhaps there's a dynamical friction element at work. Hmmm. |
#23
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Uranus's axis
"Greg Neill" wrote in message ...
"Paul Schlyter" wrote in message ... I think we would see very nearly the same relaxation time, since the difference in the parameter mu would be tiny. The greatest difference would be the tides upon the Earth, which of course would be proportional to the mass of the satellite. Isn't it the tides that causes the relaxation ? I thougth that was the mecanism, whereby the energy was removed. So the tiny satellites don't get moved towards an equatorial orbit because they don't cause tides ? Regards Carsten Nielsen Denmark |
#24
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Uranus's axis
"Carsten Nielsen" wrote in message
m... "Greg Neill" wrote in message ... "Paul Schlyter" wrote in message ... I think we would see very nearly the same relaxation time, since the difference in the parameter mu would be tiny. The greatest difference would be the tides upon the Earth, which of course would be proportional to the mass of the satellite. Isn't it the tides that causes the relaxation ? I thougth that was the mecanism, whereby the energy was removed. So the tiny satellites don't get moved towards an equatorial orbit because they don't cause tides ? The effects caused by the flattening of the Earth (equitorial bulge) are called the J2 effects, and include periodic orbit perturbations in the orbital elements which average out over one orbital revolution. So there's no overall change to the elements. What are called secular effects cause a slow rotation of the orbital plane around the polar axis, and a precessing of the orientation of the ellipse in the orbital plane. But there are no secular effects on semimajor axis, eccentricity, or inclination. So we're left with tides. Tides can transfer angular momentum, which is why the Earth is slowing and the Moon receding. So the question is, can this angular momentum transfer from the Earth's rotation to the Moon's orbit alter the direction of the Moon's inclination (it's angular momentum vector)? I suspect that a third body is needed to perform this feat, providing an angular momentum "handle" so to speak, and the likely culprit would be the Sun. Looks like I'll have to do some research. -Greg |
#25
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Uranus's axis
"Greg Neill" writes:
Tides can transfer angular momentum, which is why the Earth is slowing and the Moon receding. So the question is, can this angular momentum transfer from the Earth's rotation to the Moon's orbit alter the direction of the Moon's inclination (it's angular momentum vector)? I suspect that a third body is needed to perform this feat, providing an angular momentum "handle" so to speak, and the likely culprit would be the Sun. Well, the angular momentum from the Earth gained by the moon would have the same vector as the Earth's angular momentum had in the first place, this angular momentum by itself would cause an equatorially aligned lunar orbit. Of course the Moon's orbit still has whatever angular momentum it had in the first place so the gained angular momentum causes it to become more equatorially aligned but not completely so. Unless this momentum is also transferred back to Earth, changing its spin axis somewhat, which also causes the Moon to be more equatorially aligned. -- -Mike |
#26
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Uranus's axis
"Michael Moroney" wrote in message
... "Greg Neill" writes: Tides can transfer angular momentum, which is why the Earth is slowing and the Moon receding. So the question is, can this angular momentum transfer from the Earth's rotation to the Moon's orbit alter the direction of the Moon's inclination (it's angular momentum vector)? I suspect that a third body is needed to perform this feat, providing an angular momentum "handle" so to speak, and the likely culprit would be the Sun. Well, the angular momentum from the Earth gained by the moon would have the same vector as the Earth's angular momentum had in the first place, this angular momentum by itself would cause an equatorially aligned lunar orbit. Why so? The coupling is via the tidal bulge raised by the Moon on the Earth, which is aligned with the plane of the Moon's orbit. It could be that only the component of the Earth's angular momentum vector aligned with the Moon's is coupled. Of course the Moon's orbit still has whatever angular momentum it had in the first place so the gained angular momentum causes it to become more equatorially aligned but not completely so. Unless this momentum is also transferred back to Earth, changing its spin axis somewhat, which also causes the Moon to be more equatorially aligned. Yes, there's clearly a back-coupling too. I've seen references that say that the Moon helps to regulate the extent of the Earth's axis peregrinations, and that without it, our axis might be tipped a good deal more than what it is, and wander extensively. |
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