Precession

In astronomy, precession refers to any of several slow changes in an astronomical body's rotational or orbital parameters.

An important example is the steady change in the orientation of the axis of rotation of the Earth, known as the precession of the equinoxes.

Torque-free precession implies that no external moment (torque) is applied to the body.

If an object is asymmetric about its principal axis of rotation, the moment of inertia with respect to each coordinate direction will change with time, while preserving angular momentum.

where ωp is the precession rate, ωs is the spin rate about the axis of symmetry, Is is the moment of inertia about the axis of symmetry, Ip is moment of inertia about either of the other two equal perpendicular principal axes, and α is the angle between the moment of inertia direction and the symmetry axis.

[2] When an object is not perfectly rigid, inelastic dissipation will tend to damp torque-free precession,[3] and the rotation axis will align itself with one of the inertia axes of the body.

The errors induced by finite time steps tend to increase the rotational kinetic energy:

this unphysical tendency can be counteracted by repeatedly applying a small rotation vector v perpendicular to both ω and L, noting that

The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession.

In the case of a toy top, its weight is acting downwards from its center of mass and the normal force (reaction) of the ground is pushing up on it at the point of contact with the support.

From inside to outside there are three axes of rotation: the hub of the wheel, the gimbal axis, and the vertical pivot.

At the depicted moment in time, section dm1 is at the perimeter of the rotating motion around the (vertical) pivot axis.

It is important to note that the torque around the gimbal axis arises without any delay; the response is instantaneous.

This pitching motion reorients the spinning top with respect to the torque that is being exerted.

Precession or gyroscopic considerations have an effect on bicycle performance at high speed.

The general equation that relates the torque to the rate of change of angular momentum is:

Under these circumstances the angular velocity of precession is given by: [5] where Is is the moment of inertia, ωs is the angular velocity of spin about the spin axis, m is the mass, g is the acceleration due to gravity, θ is the angle between the spin axis and the axis of precession and r is the distance between the center of mass and the pivot.

The special and general theories of relativity give three types of corrections to the Newtonian precession, of a gyroscope near a large mass such as Earth, described above.

In astronomy, precession refers to any of several gravity-induced, slow and continuous changes in an astronomical body's rotational axis or orbital path.

Precession of the equinoxes, perihelion precession, changes in the tilt of Earth's axis to its orbit, and the eccentricity of its orbit over tens of thousands of years are all important parts of the astronomical theory of ice ages.

The ancient Greek astronomer Hipparchus (c. 190–120 BC) is generally accepted to be the earliest known astronomer to recognize and assess the precession of the equinoxes at about 1° per century (which is not far from the actual value for antiquity, 1.38°),[7] although there is some minor dispute about whether he was.

307–345 AD) made a similar discovery centuries later, noting that the position of the Sun during the winter solstice had drifted roughly one degree over the course of fifty years relative to the position of the stars.

Being an oblate spheroid, Earth has a non-spherical shape, bulging outward at the equator.

The gravitational tidal forces of the Moon and Sun apply torque to the equator, attempting to pull the equatorial bulge into the plane of the ecliptic, but instead causing it to precess.

[10] The orbits of planets around the Sun do not really follow an identical ellipse each time, but actually trace out a flower-petal shape because the major axis of each planet's elliptical orbit also precesses within its orbital plane, partly in response to perturbations in the form of the changing gravitational forces exerted by other planets.

As the Earth travels around the Sun, its elliptical orbit rotates gradually over time.

The eccentricity of its ellipse and the precession rate of its orbit are exaggerated for visualization.

Most orbits in the Solar System have a much smaller eccentricity and precess at a much slower rate, making them nearly circular and nearly stationary.

Discrepancies between the observed perihelion precession rate of the planet Mercury and that predicted by classical mechanics were prominent among the forms of experimental evidence leading to the acceptance of Einstein's Theory of Relativity (in particular, his General Theory of Relativity), which accurately predicted the anomalies.

[11][12] Deviating from Newton's law, Einstein's theory of gravitation predicts an extra term of ⁠A/r4⁠, which accurately gives the observed excess turning rate of 43 arcseconds every 100 years.