Laplace plane

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The Laplace plane, named after Pierre-Simon Laplace, is defined as the mean plane occupied by the orbit of a satellite during a precession cycle.

In other words, this is the plane normal to the orbital precession pole of the satellite. It is a kind of "average orbit" of the satellite. This is not to be confused with the Laplacian plane, also named in honor of the French astronomer.

When satellites are near their primary, the main perturbations of the orbit come from the planets' oblateness so the satellite orbit precesses around the equator of the planet. So the Laplace plane is very near the equatorial plane of the planet. This is the case of the two Mars satellites and the four main moons of Jupiter.

With increasing distance to the planet, the oblateness perturbations drop sharply and the perturbations from the Sun increase, so the precession of the satellite orbit is dominated by the tidal forces from the Sun, and so the orbit precesses along the planet's ecliptic. This is the case of the Moon and of the outermost moons of Jupiter. In this case the Laplace plane nearly coincides with the ecliptic.

At intermediate distances, the Laplace plane has an intermediate position, in between the equator and the ecliptic of the planet. So this "plane" can be pictured as a non-planar surface, a series of concentric rings whose orientation in space is variable: the innermost rings are near plane of rotation of the planet, and the outermost rings near the its orbital plane. There are, however, some appreciable deviations from this rule. For example, the Laplace planes for the satellites of Neptune are strongly influenced by the largest moon Triton, while for the outer satellites of Jupiter (Ananke, Pasiphaë and the others), the perturbations induced by Saturn are sufficiently important to make the Laplace plane deviate from the orbital plane.