Re: Orbital precession

Leigh Palmer (
Wed, 2 Jul 1997 15:51:18 -0700

It is rarely that I can contribute to this group, but this is one of
those times. Orbital precession does not result from the application
of a force *per se* to a satellite; it is rather the result of a net
torque acting on the revolving satellite over an entire orbit.

Since these effects can be seen in the simplest of models*, circular
orbits about an oblate ellipsoidally symmetric Earth, we will discuss
that sort of orbit. The argument below depends strongly on appreciating
the symmetry of the problem.

First we must define the angular momentum of the orbit. It is a vector
quantity which can be considered as oriented perpendicularly to the
plane of the orbit and originating at the focus of the orbit, the
center of Earth. (Vector quantities are really not anchored to any
point in space, but it aids visualization to consider them in that way.)
Applied torque can change the direction of an angular momentum vector if
there is a component of that torque in a direction perpendicular to the
angular momentum vector. (There is a simple analog of Newton's second
law of motion which is the vector differential equation to which Bruno
is referring.)

If the gravitational force acting on the satellite always lies in the
plane of the satellite's orbit then when the net torque acting on the
satellite with respect to the center of its orbit is added up around a
complete orbit it will be found that there is no net torque acting on
the satellite. This condition holds only for two special cases of our
simple model, however: the equatorial and the polar orbits. For all
other orbits there is an out of plane force acting whenever the
satellite is located away from the Earth's equatorial plane. This out-
of-plane force is a tidal force due to the relative proximity of the
nearer bulge material. The torque due to this out-of-plane force adds
up constructively around each inclined orbit to yield a net torque
which is perpendicular to the angular momentum of the satellite orbit.
The consequence is a precession of the orbital plane.

Lacking graphical capability and the feedback from talking directly to
the student I can't really do better than that. I suspect that I have
said enough in words so that the original questioner will understand
my answer, but I'd be glad to answer questions.


*Yes, there is a very small general relativistic effect associated with
the rotation of the Earth. I believe it has never been detected and I
will certainly ignore it here.