# Inclination

Inclination in general is the angle between an axis of direction or a plane, and a reference plane.

## Contents

### Orbits

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

In the solar system, the inclination (i in figure 1, below) 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. It could be measured with respect to another plane, such as the Sun's equator, Jupiter's orbital plane, or some such, but the ecliptic is more practical for Earth-bound observers.

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 in its equatorial plane, 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; and
• 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.

File:Orbit.png
Fig. 1: One view of inclination and other orbital parameters

### Other meanings

• For planets and other rotating celestial bodies, the angle of the axis of rotation on the plane of the orbit is also called inclination, or axial tilt.
• And in particular, for the Earth, the inclination or obliquity of the ecliptic is the angle between the plane of the ecliptic and the equator.
• The inclination of distant objects, such as a binary star, is defined as the angle between the normal to the orbital plane and the direction to the observer, since no other reference is available. Binary stars with inclination close to 90 degrees (edge-on) are often eclipsing.

## Calculation

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

$i=\arccos {h_{\mathrm {z} } \over \left|\mathbf {h} \right|}\,$ where:

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