Nodal Precession

Description

Nodal precession is the precession of an orbital plane around the rotation axis of an astronomical body such as Earth. This precession is due to the non-spherical nature of a spinning body, which creates a non-uniform gravitational field.

Around a spherical body, an orbital plane would remain fixed in space around the central body. However, most bodies rotate, which causes an equatorial bulge. This bulge creates a gravitational effect that causes orbits to precess around the rotational axis of the central body.

The direction of precession is opposite the direction of revolution. For a typical prograde (in the direction of central body rotation) orbit around Earth, the longitude of the ascending node decreases, i.e., node precesses westward. If the orbit is retrograde, this increases the longitude of the ascending node, i.e., node precesses eastward. This nodal progression enables Sun-synchronous orbits to maintain approximately constant angle relative to the Sun.precession of an orbital plane around the rotation axis of an astronomical body such as Earth. This precession iNodal precession is the precession of an orbital plane around the rotation axis of an astronomical body such as Earth. This precession is due to the non-spherical nature of a spinning body, which creates a non-uniform gravitational field.

Around a spherical body, an orbital plane would remain fixed in space around the central body. However, most bodies rotate, which causes an equatorial bulge. This bulge creates a gravitational effect that causes orbits to precess around the rotational axis of the central body.

The direction of precession is opposite the direction of revolution. For a typical prograde (in the direction of central body rotation) orbit around Earth, the longitude of the ascending node decreases, i.e., node precesses westward. If the orbit is retrograde, this increases the longitude of the ascending node, i.e., node precesses eastward. This nodal progression enables Sun-synchronous orbits to maintain approximately constant angle relative to the Sun.s due to the non-spherical nature of a spinning body, which creates a non-uniform gravitational field.

Around a spherical body, an orbital plane would remain fixed in space around the central body. However, most bodies rotate, which causes an equatorial bulge. This bulge creates a gravitational effect that causes orbits to precess around the rotational axis of the central body.

The direction of precession is opposite the direction of revolution. For a typical prograde (in the direction of central body rotation) orbit around Earth, the longitude of the ascending node decreases, i.e., node precesses westward. If the orbit is retrograde, this increases the longitude of the ascending node, i.e., node precesses eastward. This nodal progression enables Sun-synchronous orbits to maintain approximately constant angle relative to the Sun.

A non-rotating body of planetary scale or larger would be pulled by gravity into a sphere. Virtually all bodies rotate, however. The centrifugal force deforms the body so that it has an equatorial bulge. Because of the bulge the gravitational force on the satellite is not directly toward the center of the central body, but is offset toward the equator. Whichever hemisphere the satellite is in it is preferentially pulled slightly toward the equator. This creates a torque on the orbit. This torque does not reduce the inclination; rather, it causes a torque-induced gyroscopic precession, which causes the orbital nodes to drift with time.

The rate of precession depends on the inclination of the orbital plane to the equatorial plane, as well as the orbital eccentricity.

For a satellite in a prograde orbit around Earth, the precession is westward (nodal regression), the node and satellite move in opposite directions. A good approximation of the precession rate is shown here.

Related formulas

Variables

ωpprecession rate (rad/sec) (dimensionless)
REbody's equatorial radius (6 378 137 m for Earth) (m)
asemi-major axis of the satellite orbit (m)
eeccentricity of the satellite orbit (dimensionless)
J2ody's second dynamic form factor ( ody's second dynamic form factor (-1.08263*10^-3) for Earth.) (dimensionless)
ωangular frequency of the satellite's motion (rad/sec) - equals the mean motion for circular orbits (dimensionless)
iinclination (deg)