[net.space] oblate central masses and orbit precession

karn (08/06/82)

It is a well-known (and utilized) fact that a satellite in orbit about
an oblate central body does NOT follow classic two-body motion.
This is because the gravitational field around an oblate body is
dependent on position as well as radius distance from the body's
center.

For example, the earth's oblateness causes the "regression of nodes"
in which the plane of a satellite precesses (rotates) about the earth's
axis; the exact rate is a function of the orbital inclination
(angle with the equator) and the orbit period.  The so-called "sun
synchronous" orbit, in which the NOAA and LANDSAT satellites are
launched, along with amateur radio Oscars 6-9, consists of an
orbital inclination and period such that the plane precesses eastward
exactly once around the earth each year.  This compensates for the
earth's movement around the sun, hence the satellite's orbit plane
remains in a fixed angle with the day/night side terminator.
This means that the satellite cameras always see the same sun angle
on the earth below. ALL earth satellites except those in EXACTLY
polar orbits (inclination = 90 degrees) will precess in this manner.

In addition, the "line of apsides" (orientation of the semi-major
axis of the orbit ellipse WITHIN the orbit plane) rotates as a
function of inclination, orbital period and eccentricity.
The only way the line of apsides will remain fixed in earth orbit
(other than by using a perfectly circular orbit, in which case the "line of
apsides" is undefined) would be to set the inclination exactly equal
to 63.4+ degrees. This is used by the Russian Molniya satellite series,
in order to fix apogee at a high latitude over northern Siberia.

In the case of the planet Mercury, its line of apsides would also
rotate if the sun is indeed oblate, and I suspect that it is simply
due to its slow rotation (~25 day period.)

Phil Karn
Bell Labs Murray Hill