Lunisolar gravitational perturbations — the combined gravitational tug of the Sun and Moon — represent the most consequential force acting on a GEO orbit plane. Together, they torque the satellite’s orbital angular momentum vector, causing the orbit plane to tilt away from the equator. This manifests as a change in orbital inclination at a rate of approximately 0.85 degrees per year. A satellite launched into a perfect zero-inclination geostationary orbit would, if left unmanaged, see its inclination grow steadily, eventually reaching a maximum of roughly 15 degrees before cycling back down — a process that takes approximately 54 years to complete. As inclination grows, the satellite’s ground track traces an ever-larger figure-eight pattern centered on its assigned longitude, carrying it progressively further north and south of the equator each day. For missions requiring a fixed ground point — virtually all GEO communications and many intelligence missions — this is unacceptable. To stay in mission GEO satellites which require minimal inclination must perform North/South (N/S) Stationkeeping.

North/South stationkeeping: Expensive!

Satellite operators conduct N/S stationkeeping to maintain the orbit plane parallel to Earth’s equator — or equivalently, to keep the orbital inclination near zero — so the satellite remains geostationary rather than merely geosynchronous. And it is, by a wide margin, the most fuel-intensive component of GEO stationkeeping.

The challenge is the relentless lunisolar torque described above. At roughly 0.85 degrees per year of inclination change, a satellite that goes even a few years without N/S stationkeeping will develop a noticeable north-south excursion. For a satellite required to maintain an inclination below 0.05 degrees, maneuvers must be performed frequently — typically every one to two weeks.

The physics of N/S stationkeeping are demanding because changing an orbit’s plane requires a velocity change perpendicular to the orbit — essentially, the satellite must thrust “sideways” relative to its direction of travel. At GEO velocities of approximately 3,075 meters per second, even a one-degree change in the orbit plane requires a delta-V of roughly 54 meters per second. Annual N/S stationkeeping budgets for a tightly controlled geostationary satellite typically run 45 to 50 meters per second per year — roughly an order of magnitude more than East/West stationkeeping. Over a 15-year mission life, N/S stationkeeping alone can consume the vast majority of a satellite’s total propellant load. It is the single largest driver of GEO satellite mass, fuel capacity, and ultimately, mission lifetime.

The orbit pole and the Laplacian Plane

To understand N/S stationkeeping strategy — and to understand how China is exploiting the natural dynamics of the GEO environment — it is essential to understand the concept of the orbit pole and the Laplacian Plane.

An orbit’s orientation in space can be described by its angular momentum vector, which points perpendicular to the orbit plane. For a GEO satellite, this vector — often called the orbit pole — can be conveniently represented in a two-dimensional polar plot where the radial distance from the center represents orbital inclination and the angular position represents the Right Ascension of the Ascending Node (RAAN) (there was an example of this in the previous article and another one below). A satellite in a perfect geostationary orbit (zero inclination) sits at the origin of this plot. As the lunisolar perturbation increases the inclination, the orbit pole moves outward from the center.

Crucially, the orbit pole does not simply move radially outward. The Sun and Moon torque the orbit to precess in a clockwise rotation (as seen in the standard polar plot) around a specific point known as the Laplacian Pole (also called the Invariant Pole). The Laplacian Plane is the equilibrium plane of the Earth-Moon-Sun system — a plane perpendicular to the vector sum of all the angular momentum vectors of the relevant bodies. For GEO, the Laplacian Pole lies at approximately 7.3 degrees inclination and near 0 degrees RAAN — tilted toward the vernal equinox in the celestial sphere.

This means that the natural, unperturbed evolution of a GEO orbit pole is not a straight line but a circle centered on the Laplacian Pole. The radius of this circle depends on the satellite’s initial conditions at the time it reaches GEO. A satellite launched into zero inclination starts at the origin of the polar plot, approximately 7.3 degrees from the Laplace Pole, and will trace a circle of that radius over the full 54 year precession cycle. The inclination grows as the orbit pole swings away from the Earth’s equatorial pole, reaching a maximum of roughly 15 degrees when it passes through the far side of the circle, then decreasing as it swings back.

See below for a (hopefully) helpful graphic which depicts the epic journey of the Intelsat III F6 (04297) communications satellite. This particular satellite launched in 1970 and recently completed its Circumnavigation of the Laplacian Pole!