Cassini's Laws
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Cassini's laws provide a compact description of the motion of the Moon. They were established in 1693 by Giovanni Domenico Cassini, a prominent scientist of his time.[1] Refinements of these laws to include physical librations have been made[1], and they have been generalized to treat other satellites and planets. For example, see Margot.[2][3]
The first law states that the Moon has 1:1 orbital resonance. This means that the rotation / orbit of the Moon is such that the same face is always facing the Earth.
The second law states that the Moon's rotational axis maintains the same angle of inclination from the ecliptic plane. In which case the Moon's axis forms a cone and this cone intersects the ecliptic plane as a circle.
The third law states that a plane formed from a normal to the ecliptic plane and a normal to the Moon's orbital plane will contain the Moon's rotational axis.
In the case of the Moon, its rotational axis always points some 1.5 degrees away from the North Ecliptic pole, and it precesses around that pole along a small circle with 1.5 degree radius with a period of some 18 years, the same period as the period of regression of the lunar nodes.
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.[2] [4] The Laplace plane is defined as the plane about which a planet's orbit precesses with constant inclination to the equatorial and ecliptic planes.[4]
[edit] References and notes
- ^ a b For the original statement of the laws, see V V Belet︠s︡kiĭ (2001). Essays on the Motion of Celestial Bodies. Birkhäuser. p. 181. ISBN 3764358661. http://books.google.com/books?id=byWZusmVSecC&pg=PA183&dq=%22Cassini%27s+laws%22&lr=&as_brr=0&sig=ACfU3U250Mi_F-U8qavV04MVL651tCMRkw#PPA181,M1.
- ^ a b Marie Yseboodt & Jean-Luc Margot Evolution of Mercury’s obliquity
- ^ V V Belet︠s︡kiĭ (2001). Essays on the Motion of Celestial Bodies. Birkhäuser. p. 179. ISBN 3764358661. http://books.google.com/books?id=byWZusmVSecC&pg=PA183&dq=%22Cassini%27s+laws%22&lr=&as_brr=0&sig=ACfU3U250Mi_F-U8qavV04MVL651tCMRkw#PPA179,M1.
- ^ a b Y. Calisesi (2007). Solar Variability and Planetary Climates. Springer. p. 34. ISBN 038748339X. http://books.google.com/books?id=QzXZs_xSLk4C&pg=PA36&dq=%22Cassini+state%22&lr=&as_brr=0&sig=ACfU3U3n_y74jM2muBFxR02g35SCGUP3qQ#PPA34,M1.
[edit] Further reading
- Cassini Laws -- from Eric Weisstein's World of Physics
- Eckhardt, Donald H. (1981). "Theory of the Libration of the Moon". Earth, Moon and Planets (Springer Netherlands) 25: 3–49. doi:.
- Cassini's 3 laws
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