| z | |||
| The four laws of Cassini (celestial mechanics) | |||
| z
Having a body revolving, subject to tidal influence and "tidally despun": the above satisfies the generalized laws of Cassini, based on the hypothesis of a Newtonian orbit, with a constant precession of the nodes and of the pericenter. Cassini stated his laws taking into consideration
the Moon, but, "mutatis mutandis",
the same is also applicable to Mercury:
|
|||
| (1) | The Moon has uniform rotation about an axis fixed in the Moon, the period of rotation being equal to the mean sidereal period of its orbit about the Earth (resonance spin /orbit 1:1). The axis of rotation intersects the celestial sphere in C. | ||
| (2) | The inclination of the axis of rotation of the Moon vs the ecliptic is a constant angle, about 1° 35'. The pole of the ecliptic intersects the celestial sphere in Z. | ||
| (3) | While the line of the nodes regresses, its inclination remains constant, about 5° 9'. The pole of the lunar orbit intersects the celestial sphere in P. The arc of the great circle PC always includes Z. (see following figure) | ||
| (4) | Every time the body intersects the pericenter of its orbit, the axis of least equatorial inertia faces the pericenter. | ||
| z
With reference to Mercury the fourth law says: Every time Mercury intersects the perihelion, the equatorial axis of the least moment of inertia of Mercury points toward the centre of the Sun. (the side [facing the sun] is indifferent). At aphelion this axis is pointed toward the tangent of the elliptical orbit, and the axis of intermediate inertia is pointed toward the centre of the Sun.
|
|||