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Concept
Invariable plane
Summary
The invariable plane of a planetary system, also called Laplace's invariable plane, is the plane passing through its barycenter (center of mass) perpendicular to its angular momentum vector. In the Solar System, about 98% of this effect is contributed by the orbital angular momenta of the four jovian planets (Jupiter, Saturn, Uranus, and Neptune). The invariable plane is within 0.5° of the orbital plane of Jupiter, and may be regarded as the weighted average of all planetary orbital and rotational planes.
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 the individual orbital planes of planetary satellites precess.
Both derive from the work of (and are at least sometimes named for) the French astronomer Pierre Simon Laplace. The two are equivalent only in the case where all perturbers and resonances are far from the precessing body. The invariable plane is derived from the sum of angular momenta, and is "invariable" over the entire system, while the Laplace plane for different orbiting objects within a system may be different. Laplace called the invariable plane the plane of maximum areas, where the "area" in this case is the product of the radius R and its time rate of change dR/dt, that is, its radial velocity, multiplied by the mass.
The magnitude of the orbital angular momentum vector of a planet is , where is the orbital radius of the planet (from the barycenter), is the mass of the planet, and is its orbital angular velocity. That of Jupiter contributes the bulk of the Solar System's angular momentum, 60.3%. Then comes Saturn at 24.5%, Neptune at 7.9%, and Uranus at 5.3%. The Sun forms a counterbalance to all of the planets, so it is near the barycenter when Jupiter is on one side and the other three jovian planets are diametrically opposite on the other side, but the Sun moves to 2.17 away from the barycenter when all jovian planets are in line on the other side.
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