"Frank" wrote in message
oups.com...
An article in the current Scientific American says that most regular
satelites in th solar system have orbits that are nearly equatorial and
nearly circular. "Equatorial" I can understand "circular" puzzles me.
Please tell me what is wrong with my reasoning.

First, an acceleration at perigee (in the direction of motion) will not
affect the distance at perigee but will increase the distance at
apogee. An acceleration at apogee, on the other hand, will increase the
distance at perigee.

Second, every satelite causes a tidal bulge on its primary, more
noticable on water, but still existant on land. The tidal bulge is
greatest on the spot which the satelite was directly above SHORTLY
BEFORE.

Isn't it the case that if the rotational period is
less than the orbital, the bulge will be carried
forward of the satellite as you say next?

(Also, there is another bulge on the opposite side of the
planet.) This bulge provides an acceleration eastward to the satelite
since the satelite (if it's not named "Phobos") has a sidereal period
greater than its primary's rotational period. The net accelleration is
the difference be tween the acceleration provided by the bulge directly
underneath and that provide by the bulge on the opposite side of the
planet. The size of the bulge is inversely proportional to the cube of
the distance from the satelite to teh planet, and the net acceleration
is proportional to the SIXTH power of the distance.

Hence the nearer one dominates. If the bulge is ahead
that would accelerate the satellite, as Earth does to
the Moon, hence by your argument tending to reduce the
eccentricity.

So, if the distnace at apogee is 1% greater than the distance a
perigee, the acceleration at perigee must be 6% greater. The increase
of distance at apogee must be (more than) 6 times teh increase at
perigee.This leads to the conclusion that any eccentricty should
increase over time.

But it hasn't. Why not? What is wrong with this chain of reaqsoning?

Any help greatly appreciated.

I think the general argument seems right but if the
rotation is faster, the bulge leads rather than
trails. I'm not a professional though so treat this
as a hint, not an answer.

George