Inclination

Inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit and is the angular distance of the orbital plane from the plane of the reference (usually planet's equator or the ecliptic), stated in degrees.

In the solar system, the inclination of the orbit of a planet is defined as the angle between the plane of the orbit of the planet, and the ecliptic, which is the orbit of Earth.

The inclination of orbits of natural or artificial satellites is measured relative to the equatorial plane of the body they orbit (the equatorial plane is the plane perpendicular to the axis of rotation of the central body):

an inclination of 0 degrees means the orbiting body orbits the planet at its equator, and in the same direction as the planet rotates,
an inclination of 90 degrees indicates a polar orbit, in which the spacecraft passes over the north and south poles of the planet,
an inclination of 180 degrees indicates a retrograde equatorial orbit.

For the Moon however, this leads to a rapidly varying quantity and it makes more sense to measure it with respect to the ecliptic (i.e. the plane of the orbit that Earth and Moon track together around the Sun), a fairly constant quantity.

The inclination of a binary star is defined as the angle between the orbital plane and the direction to the observer. Binary stars with inclination close to 90 degrees are often eclipsing.

Inclination and other orbital parameters

Calculation

In astrodynamics inclination $i\,$ can be computed as follows:

$i=arccos{h_z\over\left|\mathbf{h}\right|}\,$

where:

$h_z\,$ is z-component of $\mathbf{h}\,$ ,
$\mathbf{h}\,$ is orbital momentum vector perpendicular to the orbital plane.

Inclination

Calculation

See also