Orbital precession

Bruno Tilgner (Bruno_Tilgner@compuserve.com)
Wed, 2 Jul 1997 18:00:21 -0400


In the context of another mailing list on astronomy and satellites
I have come across the following problem:

we all know that the orbital plane of satellites performs a precession
in that for inclinations between 0 and 90 degrees it turns about the
Earth's axis in the direction east->west. For retrograde orbits the
precession is in the opposite direction.

The rate of precession is proportional to the cosine of the orbit's
inclination, i.e. it vanishes for a polar orbit and has a maximum
in the order of 10 degrees per day for near-equatorial orbits.
This is the rate integrated over one orbit, it is variable at different
points along the orbit. =

It is also well understood that this effect is due to the flattening of
the Earth (the J2 term in the Earth's potential). The mathematical
proof may be lenghty and cumbersome, but it is conclusive.

However, the result is not all intuitive. What exactly is the force
that makes the orbit precess, and why does this force depend on
inclination ? It is particularly intriguing that the rate of precession
increases as the orbital inclination decreases. In the limit, i.e. for
an equatorial orbit, there is a perfectly symmetrical and constant
situation with the attractive force all the time directed toward the
center of the Earth, and yet, this is when the precession is at its
maximum (to be entirely exact: for inclination zero precession is
not defined because there are no nodes, but at an infinitesimally small
inclination it is).

This is admittedly a theoretical question, not directly linked to the
observation of satellites but as I would like to understand (as opposed
to "being able to calculate") this phenomenon I thought that perhaps
someone on this list might have the answer.

To be clear: I am looking for an explanation which the moderately
educated layperson with a knowledge of the basic laws of physics can
understand but who cannot be bothered with partial differential
vector equations.

Thanks for any suggestions.

Bruno Tilgner