Precession (redirected from Perihelion precession)

precession: see gyroscope.

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precession

Phenomenon associated with the action of a gyroscope or a spinning top and consisting of a comparatively slow rotation of the axis of rotation of a spinning body about a line intersecting the spin axis. It arises as a result of external torque acting on the body. One example of precession is the smooth, slow circling of a spinning top (the uneven wobbling is called nutation). Precession of the earth's axis of rotation is the reason that the positions of celestial bodies appear to drift systematically with the passage of time. See also precession of the equinoxes.

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Precession

The motion of an axis fixed in a body around a direction fixed in space. If the angle between the two is constant so that the axis sweeps out a circular cone, the motion is pure precession; oscillation of the angle is called nutation. An example of precession is the motion of the Earth's polar axis around the normal to the plane of the ecliptic; this is the precession of the equinoxes. A fast-spinning top, with nonvertical axis, which precesses slowly around the vertical direction, is another example. In both examples the precession is due to torque acting on the body. Another kind of precession, called free or fast precession, with a rate which is comparable to the rotation rate of the body, is seen, for instance, in a coin spun into the air.

As a simple example of gyroscopic motion, consider a rapidly spinning wheel with a horizontal axis supported at a distance d from the plane of the wheel (see illustration). The angular momentum is along the wheel symmetry axis and is approximately given by the angular momentum of the wheel about this axis; in the simple precession approximation to the motion, the angular momentum associated with precessional motion is neglected. The external torque due to the gravitational force is perpendicular to the wheel axis in the horizontal plane. The change in the angular momentum in an infinitesimal time interval dt is given by the rotational equation of motion in Eq. (1).

(1) 

See Rigid-body dynamics

Simple precession of a rapidly spinning wheel with a horizontal axis supported by a pivot

Since dand are perpendicular, the length is unchanged to first order in dt. The direction of is rotated counterclockwise in the horizontal plane. The angular velocity of precession &ohgr;_P about the vertical axis is then given by Eq. (2),

(2) 

where g is the gravitational acceleration, &ohgr; is the spin angular velocity, and a is the radius of the wheel. Thus &ohgr;_P is independent of the mass of the wheel and inversely proportional to &ohgr;. For &ohgr; very large, the precession rate &ohgr;_P is quite slow.