Orbital inclination

Fig. 1: One view of inclination i (green) and other orbital parameters

Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.

For a satellite orbiting the Earth directly above the equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular orbit is that it is tilted, spending half an orbit over the northern hemisphere and half over the southern. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°.

Orbits

The inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the orbital plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planet's equator. For planets in the Solar System, the plane of reference is usually the ecliptic, the plane in which the Earth orbits the Sun.[1][2] This reference plane is most practical for Earth-based observers. Therefore, Earth's inclination is, by definition, zero.

Inclination can instead be measured with respect to another plane, such as the Sun's equator or the invariable plane (the plane that represents the angular momentum of the Solar System, approximately the orbital plane of Jupiter).

Natural and artificial satellites

The inclination of orbits of natural or artificial satellites is measured relative to the equatorial plane of the body they orbit, if they orbit sufficiently closely. The equatorial plane is the plane perpendicular to the axis of rotation of the central body.

An inclination of 30° could also be described using an angle of 150°. The convention is that the normal orbit is prograde, an orbit in the same direction as the planet rotates. Inclinations greater than 90° describe retrograde orbits. Thus:

  • An inclination of 0° means the orbiting body has a prograde orbit in the planet's equatorial plane.
  • An inclination greater than 0° and less than 90° also describe prograde orbits.
  • An inclination of 63.4° is often called a critical inclination, when describing artificial satellites orbiting the Earth, because they have zero apogee drift.[3]
  • An inclination of exactly 90° is a polar orbit, in which the spacecraft passes over the north and south poles of the planet.
  • An inclination greater than 90° and less than 180° is a retrograde orbit.
  • An inclination of exactly 180° is a retrograde equatorial orbit.

For impact-generated moons of terrestrial planets not too far from their star, with a large planet–moon distance, the orbital planes of moons tend to be aligned with the planet's orbit around the star due to tides from the star, but if the planet–moon distance is small, it may be inclined. For gas giants, the orbits of moons tend to be aligned with the giant planet's equator, because these formed in circumplanetary disks.[4]

Exoplanets and multiple star systems

The inclination of exoplanets or members of multiple stars is the angle of the plane of the orbit relative to the plane perpendicular to the line-of-sight from Earth to the object.

  • An inclination of 0° is a face-on orbit, meaning the plane of its orbit is parallel to the sky.
  • An inclination of 90° is an edge-on orbit, meaning the plane of its orbit is perpendicular to the sky.

Since the word 'inclination' is used in exoplanet studies for this line-of-sight inclination then the angle between the planet's orbit and the star's rotation must use a different word and is termed the spin-orbit angle or spin-orbit alignment. In most cases the orientation of the star's rotational axis is unknown.

Because the radial-velocity method more easily finds planets with orbits closer to edge-on, most exoplanets found by this method have inclinations between 45° and 135°, although in most cases the inclination is not known. Consequently, most exoplanets found by radial velocity have true masses no more than 40% greater than their minimum masses.[citation needed] If the orbit is almost face-on, especially for superjovians detected by radial velocity, then those objects may actually be brown dwarfs or even red dwarfs. One particular example is HD 33636 B, which has true mass 142 MJ, corresponding to an M6V star, while its minimum mass was 9.28 MJ.

If the orbit is almost edge-on, then the planet can be seen transiting its star.

Other Languages
Afrikaans: Baanhelling
Alemannisch: Bahnneigung
العربية: زاوية ميلان
asturianu: Enclín orbital
български: Инклинация
català: Inclinació
čeština: Sklon dráhy
Deutsch: Bahnneigung
Ελληνικά: Κλίση τροχιάς
Esperanto: Orbita klineco
Gaelg: Cleayn
한국어: 궤도 경사
hrvatski: Inklinacija
Bahasa Indonesia: Inklinasi
magyar: Inklináció
македонски: Наклон (орбита)
Bahasa Melayu: Kecondongan
Nederlands: Glooiingshoek
日本語: 軌道傾斜角
norsk nynorsk: Banehelling
Plattdüütsch: Bahnnegen
polski: Inklinacja
português: Inclinação
Simple English: Orbital inclination
slovenčina: Uhol sklonu dráhy
slovenščina: Naklon tira
српски / srpski: Инклинација
srpskohrvatski / српскохрватски: Inklinacija
svenska: Banlutning
українська: Нахил орбіти
中文: 軌道傾角