Cassini's laws

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.

Refinements of these laws to include physical librations have been made, and they have been generalized to treat other satellites and planets.

In the case of the Moon, its rotational axis always points some 1.5 degrees away from the North ecliptic pole. The normals to the orbital plane and the rotational axis are always in opposite sides of the normal to the ecliptic.

Therefore, both the normal to the orbital plane and the Moon's rotational axis precess around the ecliptic pole with the same period. The period is about 18.6 years and the motion is retrograde.

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 is defined as the plane about which a planet or satellite orbit precesses with constant inclination.

Cassini state 1 is defined as the situation in which both the spin axis and the orbit normal axis are on the same side of the normal to the Laplace plane. Cassini state 2 is defined as the case in which the spin axis and the orbit normal axis are on opposite sides of the normal to the Laplace plane. Earth's moon is in Cassini state 2.

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