>> My greatest concern is whether/how long Cynthia might maintain a
>> stable, circular polar orbit.
[quoted text clipped - 3 lines]
> equator will tend to move the orbiting object into an equatoral orbit
> pretty fast. I could only guess at how long, though.
Sorry, no. The physical mechanism that "equatorializes" an orbit is the
slight transverse component of the tidal frictional torque created by
the rotation of the Earth, =NOT= its oblateness per se.
The tidal friction is approximately parallel to the _relative_ velocity of
the satellite w.r.t. the ground. Because the Earth is rotating, the "drag"
force on the satellite has a component in the direction of the Earth's
surface velocity, which is transverse to the satellite's orbital velocity.
This "drag" force exerts a torque that tips the satellite's angular momentum
vector over until eventually it would be aligned with the rotation axis of
the Earth (assuming it doesn't hit the ground first!).
If the Earth were =NOT= rotating, the tidal "drag" would have no transverse
component on a polar satellite, and no "tipping torque" on the satellite
would result.
> I believe that the only reason our moon is not exactly in an equatoral
> orbit is because of the gravitational effect of the sun pulling it out of
> plane.
In a certain technical sense, the Moon is _not_ orbiting the Earth, since
the force of the Sun's gravity on the Moon exceeds the force of the Earth's
gravity on the Moon, so that unlike every other natural satellite in the
solar system, the Moon's orbit is always "concave inward" and its velocity
never goes "retrograde" relative to its primary.
>From the Sun's point of view, the Moon and the Earth are in a rather
peculiar form of "1:1 orbital resonance," something like Saturn's
co-orbital satellites Janus and Epimethius --- the difference being
that the period of the "do-si-do" is only about 1/13th of their common
orbital period, instead of many times longer...
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Henry Spencer - 24 Oct 2003 02:47 GMT
>In a certain technical sense, the Moon is _not_ orbiting the Earth, since
>the force of the Sun's gravity on the Moon exceeds the force of the Earth's
>gravity on the Moon...
Not, however, in a very *useful* technical sense. What matters is not the
absolute force the Sun exerts on the Moon, but how the Moon's resulting
Sunward acceleration *differs* from the similar acceleration of the Earth.
A more sophisticated analysis shows that the Moon most definitely orbits
the Earth. When computing the Moon's motion, the errors introduced by
ignoring the Sun are much smaller than the errors introduced by ignoring
the Earth. (The surface where the two errors are equal is Earth's "sphere
of influence"; it is approximately spherical and its radius is more than
twice the average radius of the Moon's orbit.)
>...so that unlike every other natural satellite in the
>solar system, the Moon's orbit is always "concave inward" and its velocity
>never goes "retrograde" relative to its primary.
Both of which are mildly interesting facts which nobody considers to have
any real importance. (In particular, astronomers do not feel that they
make any fundamental difference to the status of the Moon.)

Signature
MOST launched 30 June; first light, 29 July; 5arcsec | Henry Spencer
pointing, 10 Sept; first science, early Oct; all well. | henry@spsystems.net