Inclination maneuvers for GEO satellites

Question

I was wondering about the orbital location to perform inclination nulling maneuvers for GEO satellites.

I know from basic astrodynamics that the best place to perform inclination correction is at the line of nodes.

However, for GEO satellites, according to the Handbook for Geostationary Orbits by E. M. Soop, (google books) the best place to perform those maneuvers is around the inertial +/- Y axis (90 and 270 deg from vernal equinox). I read his explanation but still cannot understand why there is better than the LON.

In the book circa chapter 6, page 147, Soop mentions that:

... the perturbing forces act on the orbit inclination with a north acceleration when the spacecraft is near the +y axis and a south acceleration near the -y axis. The mean direction of the drift vector di/dt is then approximately in the +x direction... To compensate for the perturbations, the inclination station keeping maneuvers then have to be given as south thrusts near the +y axis i.e. a sidereal angle of 90 deg or as north thrusts when the spacecraft is near a sidereal angle of 270 deg. Since the sidereal angle of the thrust is approximately given, the time of day of the thrust must be selected according to the time of year. The local time, at the spacecraft longitude, is given by the following table.

            North Thrust         South Thrust
Spring      Morning              Evening
Summer      Midnight             Noon
Autumn      Evening              Morning
Winter      Noon                 Midnight

To clarify, I'm talking about practical cases in which there is a Line Of Nodes since there is a small inclination to the satellite. I don't talk about the academic ideal case where the GEO inclination is zero.

Answer 1

If i read your quote correctly, it doesn't state that a burn at the inertial y-axis is cheaper than a burn at the LON, but it explains that your satellite will encounter an acceleration towards north at +y and south at -y, so your LON will in fact line up with the y-axis after a while because of the inclination change due to this perturbation, so it's still cheapest to correct your inclination at the LON but your LON will be at 90/270 degrees.

Answer 2

To answer your question, both conditions are satisfied. Yes it is best (most efficient delta-v wise) to perform a maneuver at the line of nodes (at the equator).

It is also a characteristic of GEO orbits that the solar gravity interacts with a equatorial (GEO) orbit to drive the line of nodes to the 90/270 line in the inertial frame. (the tilt of the earth creates a condition where the sun always exerts an imbalance of gravity on the orbit, which results in a torque, which acts on the orbit's angular momentum vector to turn the orbit, like the old bicycle wheel physics demo).

Answer 3

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