Inclination
Inclination in general is the
angle between a reference plane and another plane or
axis of direction.
Encyclopedia
Inclination in general is the
angle between a reference plane and another plane or
axis of direction.
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 , normally 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 plane containing
Earth's orbital path. It could be measured with respect to another plane, such as the
Sun's equator or even
Jupiter's orbital plane, but the ecliptic is more practical for Earth-bound observers. Most planetary orbits in our solar system have relatively small inclinations, both in relation to each other and to the Sun's equator, with the notable exception of the
dwarf planet Pluto, which has a 17 degree inclination to the
ecliptic. Many of the currently known
extrasolar planets are in multiple systems, and sometimes have high inclinations.
The inclination of orbits of
natural or
artificial satellites is measured relative to the equatorial plane of the body they orbit if they do so close enough. 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 objects farther away from the central body, another reference plane is often used: the Laplace plane. As one moves away from the primary, the Laplace plane starts off in its equatorial plane and then gradually tilts away from that plane until it merges with the primary's orbital plane at great distances.
For objects where the primary's axis of rotation is unknown or poorly known, a satellite's inclination will be given with respect to the ecliptic, or sometimes with respect to the plane of the sky .
For the
Moon, measuring its inclination with respect to Earth's equatorial plane leads to a rapidly varying quantity and it makes more sense to measure it with respect to the ecliptic , a fairly constant quantity.
Other meanings
- For planets and other rotating celestial bodies, the angle of the axis of rotation with respect to the normal to plane of the orbit is sometimes also called inclination, but is better referred to as the axial tilt or obliquity.
- In particular, for the Earth, the obliquity of the ecliptic is the angle between the plane of the ecliptic and the equator.
- The inclination of objects beyond the solar system, 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. Equivalently, this can be defined as the angle between the orbital plane and the plane of the sky. The latter depends on the direction in which an observer looks, so one has to be careful when comparing stars in different regions of the celestial sphere. Binary stars with inclinations close to 90 degrees are often eclipsing.
Calculation
In
astrodynamics, the
inclination can be computed as follows:
where:
- is z-component of ,
- is orbital momentum vector perpendicular to the orbital plane.
See also
