Nodal regression
Encyclopedia
Nodal precession is the precession of an orbital plane around the rotation axis of an astronomical body such as the Earth. This precession is due to the non spherical nature of a spinning body which creates a non spherical gravitational field.
Around a spherical body, an orbital plane would remain fixed in space around the central body. However, because most bodies are non spherical due to their rotation, this causes an equatorial bulge. Equatorial bulges have a gravitational effect that causes orbits to precess around the rotational axis of the central body.
For a satellite in a retrograde orbit about the Earth, the longitude of the ascending node
increases and the node precesses eastward. This nodal progression allows sun-synchronous orbit
s to maintain a constant angle relative to the Sun
.
of the orbital plane to the equatorial plane, as well as the orbital eccentricity.
For a satellite in a prograde orbit about the Earth, the precession is westward (nodal regression), the node and satellite move in opposite directions. A good approximation of the precession rate is
where
is the precession rate (rad
/s)
is the Earth's equatorial radius (6 378 137 m)
is the semi-major axis of the satellite orbit
is the eccentricity of the satellite orbit
is its angular frequency (
radians divided by its period)
its inclination
is the Earth's second dynamic form factor 
.
This last quantity is related to the oblateness as follows:
where
is the Earth's oblateness
is Earth's equatorial radius
is the Earth's rotation rate (7.292115×10−5 rad/s)
is the product of the universal constant of gravitation
and the Earth's mass (3.986004418×1014 m3/s2)
Around a spherical body, an orbital plane would remain fixed in space around the central body. However, because most bodies are non spherical due to their rotation, this causes an equatorial bulge. Equatorial bulges have a gravitational effect that causes orbits to precess around the rotational axis of the central body.
For a satellite in a retrograde orbit about the Earth, the longitude of the ascending node
Longitude of the ascending node
The longitude of the ascending node is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a reference direction, called the origin of longitude, to the direction of the ascending node, measured in a reference plane...
increases and the node precesses eastward. This nodal progression allows sun-synchronous orbit
Sun-synchronous orbit
A Sun-synchronous orbit is a geocentric orbit which combines altitude and inclination in such a way that an object on that orbit ascends or descends over any given point of the Earth's surface at the same local mean solar time. The surface illumination angle will be nearly the same every time...
s to maintain a constant angle relative to the Sun
Beta angle
The beta angle is a value that is used most notably in spaceflight. The beta angle determines the percentage of time an object such as a spacecraft in low Earth orbit spends in direct sunlight, absorbing solar energy. Beta angle is defined as the angle between the orbit plane and the vector from...
.
Equation
The rate of precession depends on the inclinationInclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...
of the orbital plane to the equatorial plane, as well as the orbital eccentricity.
For a satellite in a prograde orbit about the Earth, the precession is westward (nodal regression), the node and satellite move in opposite directions. A good approximation of the precession rate is
where
is the precession rate (radRadian
Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...
/s)
is the Earth's equatorial radius (6 378 137 m) is the semi-major axis of the satellite orbit is the eccentricity of the satellite orbit is its angular frequency ( radians divided by its period) its inclination is the Earth's second dynamic form factor .This last quantity is related to the oblateness as follows:
where
is the Earth's oblateness is Earth's equatorial radius is the Earth's rotation rate (7.292115×10−5 rad/s) is the product of the universal constant of gravitationGravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
and the Earth's mass (3.986004418×1014 m3/s2)