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
Solar System
In the
Terminology and definition
This plane is sometimes called the "Laplacian" or "Laplace plane" or the "invariable plane of Laplace", though it should not be confused with the
Body | Inclination to | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Ecliptic | Sun's equator |
Invariable plane[1] | |||||||||
Terre- strials |
Mercury | 7.01° | 3.38° | 6.34° | |||||||
Venus | 3.39° | 3.86° | 2.19° | ||||||||
Earth | 0°
|
7.25°[6] | 1.57° | ||||||||
Mars | 1.85° | 5.65° | 1.67° | ||||||||
Gas & ice giants |
Jupiter | 1.31° | 6.09° | 0.32° | |||||||
Saturn | 2.49° | 5.51° | 0.93° | ||||||||
Uranus | 0.77° | 6.48° | 1.02° | ||||||||
Neptune | 1.77° | 6.43° | 0.72° | ||||||||
Minor planets |
Pluto | 17.14° | 11.88° | 15.55° | |||||||
Ceres | 10.59° | 9.20° | |||||||||
Pallas | 34.83° | 34.21° | |||||||||
Vesta | 5.58° | 7.13° |
Description
The magnitude of the orbital angular momentum vector of a planet is , where is the orbital radius of the planet (from the
If all Solar System bodies were point masses, or were rigid bodies having spherically symmetric mass distributions, and further if there were no external effects due to the uneven gravitation of the
Nevertheless, these changes are exceedingly small compared to the total angular momentum of the system, which is very nearly conserved despite these effects. For almost all purposes, the plane defined from the giant planets' orbits alone can be considered invariable when working in Newtonian dynamics, by also ignoring the even 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 passing nearby, Milky Way galactic tides, etc.
References
- ^ a b c Heider, K.P. (3 April 2009). "The mean plane (invariable plane) of the Solar System passing through the barycenter". Archived from the original on 3 June 2013. Retrieved 10 April 2009.
- produced using
- produced using
- ^ "MeanPlane (invariable plane) for 142400/01/01". 8 April 2009. Archived from the original on 3 June 2013. Retrieved 10 April 2009. (produced with Solex 10)
- ^ "MeanPlane (invariable plane) for 168000/01/01". 6 April 2009. Archived from the original on 3 June 2013. Retrieved 10 April 2009. (produced with Solex 10)
- ^
Tremaine, S.; Touma, J.; Namouni, F. (2009). "Satellite dynamics on the Laplace surface". S2CID 18901505.
- ^
La Place, P.-S., Marquis de (1829) [1799–1825]. Celestial Mechanics. Translated by Bowditch, Nathaniel. Boston, MA. volume I, chapter V, esp. page 121.
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: CS1 maint: multiple names: authors list (link) — English translation published in four volumes, 1829–1839;- originally published as
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- ^ Planetary Fact Sheets, at http://nssdc.gsfc.nasa.gov
Further reading
- Souami, D.; Souchay, J. (2012). "The solar system's invariable plane" (PDF). .