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.



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e-mail: pausch at stockholm dot bostream dot se
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"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.

"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

"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

"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

"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.