## Invariable plane |

Year | Jupiter | Saturn | Uranus | Neptune |
---|---|---|---|---|

2009^{[1]} | 0.32° | 0.93° | 1.02° | 0.72° |

142400^{[2]} | 0.48° | 0.79° | 1.04° | 0.55° |

168000^{[3]} | 0.23° | 1.01° | 1.12° | 0.55° |

The **invariable plane** of a **Laplace's invariable plane**, is the plane passing through its ^{[1]} 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 ^{[4]} Both derive from the work of (and are at least sometimes named for) the ^{[5]} The two are equivalent only in the case where all *plane of maximum areas*, where the area is the product of the radius and its differential time change dR/dt, that is, its velocity, multiplied by the mass.

Inclination | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Name | Inclination to | to Sun's equator | Inclination to invariable plane ^{[1]} | ||||||||

7.01° | 3.38° | 6.34° | |||||||||

3.39° | 3.86° | 2.19° | |||||||||

0 | 7.155° | 1.57° | |||||||||

1.85° | 5.65° | 1.67° | |||||||||

1.31° | 6.09° | 0.32° | |||||||||

2.49° | 5.51° | 0.93° | |||||||||

0.77° | 6.48° | 1.02° | |||||||||

1.77° | 6.43° | 0.72° | |||||||||

17.14° | 11.88° | 15.55° | |||||||||

10.62° | -- | 9.20° | |||||||||

35.06° | -- | 34.43° | |||||||||

5.58° | -- | 7.13° |

- description
- references

The magnitude of the orbital

If all Solar System bodies were point masses, or were rigid bodies having spherically symmetric mass distributions, then an invariable plane defined on orbits alone would be truly invariable and would constitute an inertial frame of reference. But almost all are not, allowing the transfer of a very small amount of momenta from axial rotations to orbital revolutions due to tidal friction and to bodies being non-spherical. This causes a change in the magnitude of the orbital angular momentum, as well as a change in its direction (precession) because the rotational axes are not parallel to the orbital axes. Nevertheless, these changes are exceedingly small compared to the total angular momenta of the system (which is conserved despite these effects, ignoring the even much tinier amounts of angular momentum ejected in material and gravitational waves leaving the Solar System, and the extremely tiny torques exerted on the Solar System by other stars, etc.), and for almost all purposes the plane defined on orbits alone can be considered invariable when working in

Other Languages

català: Pla invariable

español: Plano invariable

euskara: Plano inbariante

français: Plan invariable

Bahasa Indonesia: Bidang invariabel

italiano: Piano invariabile

Bahasa Melayu: Satah tak beraneka

polski: Płaszczyzna niezmienna Laplace’a

português: Plano invariável

Simple English: Invariable plane

українська: Незмінна площина