The orbital plane precesses about 6 degrees per day in geocentric reference because of Earth's equatorial oblateness. So the geocentric plane of the departure asymptote is sweeping across the celestial sphere at some combination of this rate, earth's axial tilt, and Earth's movement around the sun.
I'm afraid I'm not following. Do you know of any resources that explain this better? I tried sketching out some rough diagrams, but I don't really see what drives this precession, in particular how oblateness is relevant.
It's like gyroscopic precession. Think of it as the Earth as being a sphere (effectively a point mass) with a massive torus around the equator and the orbit as being the gyroscope. The torus tugs the gyroscope, changing the direction of its angular momentum vector, and it precesses.
https://en.wikipedia.org/wiki/Precession
Actually, I really don't like the gyroscope analogy because the physical effects are different, and they do not produce the same detailed motion -- it just LOOKS sort of the same.
I wrote a chapter on orbitology for my US Space command sponsored book on 'space power theory' [no, NOT the electrical kind]. Let me get a link.
Here's the specific passage where I explain the effect to pilots:
In practice, there are some other significant influences on the orbit
of a satellite. One of those is the influence of the equatorial
gravitational “bulge.” Since the Earth rotates, it flattens slightly at the
poles and bulges outward at the Equator. Probably the most
significant and mysterious impact of the equatorial bulge is how it
causes the path of an orbit to “twist” in space. Twist isn’t really the
right word; it’s more like a long, gentle “S” turn. However, “twist” is
the term used by most space operators. It’s as hard to understand and
as complicated as the not-right terminology indicates. But, orbital
twist is important enough to be explained. For better and more
detailed explanations, there are several good textbooks on orbital
mechanics.
Various analogies have been suggested in orbital mechanics
textbooks, having to do with right-angle forces on spinning wheels,
and other strained parallels with earthside experience. But the most
useful way to grasp the concept is to keep visualizing your space
vehicle moving under the influence of gravity and its own forward
speed—with extra localized gravitational pull as your satellite crosses
the equator. Think of Earth’s equatorial bulge as a ring around the
planet’s waist. It has its own mass, and will pull anything nearby
towards it.
Now imagine your satellite approaching Earth’s equator, say, from
the southwest, at an angle (remember that angle with which it crosses
the Equator is called the orbital inclination) greater than a few degrees.
It’s just been over a point well away and south of the Equator. It’s
aimed straight ahead for a spot above the Equator.
As it approaches the Equator, the nearest portion of the “bulge” is
also pulling on it, directly toward the Equator. Its path will veer
slightly toward the bulge, to the left. It will reach the Equator at a point
somewhat to the left of where it had originally been headed.
North of the Equator the process is symmetrical but in the opposite
direction. Now the nearest parts of this extra equatorial bulge are on
the right, and it is in this direction that the satellite veers. As it finally
distances itself from the Equator, the two effects—the veer to the left
(south of the Equator) and the veer to the right (north of the
Equator)—have balanced out to return the satellite to its original
direction.
However, the original swerve to the left (westwards) is NOT
counterbalanced, so the satellite’s orbital plane has been effectively
shifted a small amount. For a typical space shuttle flight from Florida,
this shift per Equator crossing amounts to about 20 to 25 km. That’s
not much on an orbit that is 40,000 km long per revolution, but it can
add up. For space shuttle flights, it can amount to a westwards plane
shift of about five to seven degrees per day.
Now, if we apply the principles of gravitation to this effect, we can
see how it works for different altitudes and inclinations. Since it is
caused by the extra gravity from the equatorial bulge, the closer you
are and the longer you stay close to this bulge, the bigger you should
expect the effect to be.
This is exactly the case. The lower the inclination of an orbit, the
longer it skirts “near” the Equator and the more it is twisted. The
higher the orbital altitude, altitude, the more distant its approach to the extra
mass, and so the less its orbital plane is twisted.
An interesting and very useful application of this orbital twisting
is connected with those orbits that are nearly perfectly north-south
(near-polar) orbits that are slightly “retrograde”—that is, they
approach the Equator from slightly east of south when northbound.
The twisting still occurs, but this time (think of where the extra mass
is closest), it is first to the right, towards the east and then to the left.
Sketch this out to convince yourself.
As Earth circles the Sun once per year, it moves in its orbit and the
Sun appears to move through the constellations. The rate is a little less
than one degree per day, which works out to be 360 degrees in 365
days plus some hours.
If a satellite is placed in a slightly retrograde near-polar orbit, the
equatorial bulge will twist the plane eastwards. The ideal situation is
that the orbital plane shifts (“twists”) eastward at the same rate as the
Sun appears to move against the background stars, and as a result, the
relationship of the orbital plane and the Earth-Sun line remains the
same. This means that as the satellite passes over ground locations, the
angle of sunlight—and the resulting shadows—remain fairly uniform,
no matter how much time, or how many orbits, have gone by.
This is called a “sun-synchronous” orbit. It has many obvious
applications to different types of observation platforms. The
applications are so obvious that any object in such an orbit is
presumed to be in some sort of Earth surface observation. There are a
few other satellites in the same type of orbit to remain in continuous
sunlight for reasons such as power, astronomical work, etc.
Recall that because the degree of orbital twisting depends on the
satellite’s altitude above the Earth, achieving the same amount of
orbital twisting (the technical term is “precession”) requires the
selection of different inclinations for different operational altitudes.
As the orbit gets higher (and farther from the Equatorial bulge), it
must have a lower inclination so as to spend a proportionately longer
time “close” to the bulge to accumulate the same amount of twisting.
As a result, it will pass over a lessened north to south range of the
Earth’s surface; therefore, sun synchronous orbits can’t be very high.