### precession

(periodic change in a body's rotation or orbit)

Precession is a cyclical change in an astronomical body's rotation or orbit. The Earth's rotation precesses the direction that the poles point, aligning most closely with different stars as the precession progresses (the precession of the equinoxes). In the case of planets or moons this type of precession is called axial precession. Earth's precession rate (precession constant) is about 1/26000 precession cycles per year. This is caused by the effect of the Sun's gravity on the Earth's tilted rotation axis as well as similar effects from the Moon and Jupiter, and from the Earth's orbital eccentricity.

Regarding an orbit's precession, an example of something other than axial precession, could be its apoapsis shifting to different directions over time. Other spinning objects besides astronomical bodies can precess, such as a spinning top's axis of rotation rotating so that its point at the top of the top moves in a circular path. Determining a planet's (axial) precession constant allows its moment of inertia to be calculated. For the effects of its star (much more massive than the planet), a formula is:

```Ω = (-3/2)((C-A)/C)(Gm/a3)(1/ω)cos β
```
• Ω - precession rate.
• C - planet's polar moment of inertia (i.e., due its equatorial bulge), essentially what we are after.
• A - planet's moment of inertia around any equatorial diameter, presumed to be well-estimated from mass and radius of a near-sphere.
• m - star's mass.
• G - gravitational constant.
• a - distance from star to planet.
• ω - planet's rotation rate (day).
• β - angle between planet's orbital plane and the plane of its equator.

(orbits,rotation,kinematics)