Laplace plane

In contrast, the Laplace plane may be different for different orbiting objects within a system.

Confusingly, a satellite's Laplace plane (as defined here) is also sometimes called its "invariable plane".

The Laplace plane is defined as the plane about which a planet's orbit precesses with constant inclination to the equatorial and ecliptic planes.

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.

Also, in some cases, larger satellites of a planet (such as Neptune's Triton) can affect the Laplace planes of smaller satellites orbiting the same planet.

The Laplace plane is a result of perturbational effects, which were discovered by Laplace while he was investigating the orbits of Jupiter's principal moons (the Galilean satellites of Jupiter).

The invariable plane is simply derived from the sum of angular momenta, and is "invariable" over the entire system, while the Laplace plane may be different for different orbiting objects within a system.

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.

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.

A system obeying these laws is said to be in a Cassini state, that is: an evolved rotational state where the spin axis, orbit normal, and normal to the Laplace plane are coplanar while the obliquity remains constant.

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.

It is to be distinguished from another and quite different plane, also discovered by Laplace, and which is also sometimes called the "Laplacian" or "Laplace plane", but more often the invariable plane (or the "invariable plane of Laplace").

This plane is sometimes called the "Laplacian" or "Laplace plane" or the "invariable plane of Laplace", though it should not be confused with the Laplace plane, which is the plane about which orbital planes precess.

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).