Laplace plane

The Laplace plane or Laplacian plane of a planetary satellite, named after its discoverer Pierre-Simon Laplace (1749–1827), is a mean or reference plane about whose axis the instantaneous orbital plane of a satellite precesses.

Laplace's name is sometimes applied to the invariable plane, which is the plane perpendicular to a system's mean angular momentum vector, but the two should not be confused. They are equivalent only in the case where all perturbers and resonances are far from the precessing body.

The axis of this Laplace plane is coplanar with, and between, (a) the polar axis of the parent planet's spin, and (b) the orbital axis of the parent planet's orbit around the Sun. The Laplace plane arises because the equatorial oblateness of the parent planet tends to cause the orbit of the satellite to precess around the polar axis of the parent planet's equatorial plane, while the solar perturbations tend to cause the orbit of the satellite to precess around the polar axis of the parent planet's orbital plane around the Sun. The two effects acting together result in an intermediate position for the reference axis for the satellite orbit's precession.

In effect, this is the plane normal to the orbital precession pole of the satellite. It is a kind of "average orbital plane" of the satellite, around which the instantaneous orbital plane of the satellite precesses, and to which it has a constant additional inclination.

In most cases, the Laplace plane is very close to the equatorial plane of its primary planet (if the satellite is very close to its planet) or to the plane of the primary planet's orbit around the Sun (if the satellite is far away from its planet). This is because the strength of the planet's perturbation on the satellite's orbit is much stronger for orbits close to the planet, but drops below the strength of the Sun's perturbation for orbits farther away. Examples of satellites whose Laplace plane is close to their planet's equatorial plane include the satellites of Mars and the inner satellites of the giant planets. Examples of satellites whose Laplace plane is close to their planet's orbital plane include Earth's Moon and the outer satellites of the giant planets. Some satellites, such as Saturn's Iapetus, are situated in the transitional zone and have Laplace planes that are midway between their planet's equatorial plane and the plane of its solar orbit.

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