Orbital inclination

inclinationinclinedtiltedinclinationsiface-on orbitsincinclination angleinclination of the orbital planeinclination orbit
Orbital inclination measures the tilt of an object's orbit around a celestial body.wikipedia
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Plane of reference

reference planeplaneplanes
It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.
The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longitude of the ascending node.

Orbital elements

orbital parametersorbital elementKeplerian elements
The inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit.

Equator

equatorial planeThe Equator
For a satellite orbiting a planet, the plane of reference is usually the plane containing the planet's equator.
The added velocity reduces the fuel needed to launch spacecraft eastward (in the direction of Earth's rotation) to orbit, while simultaneously avoiding costly maneuvers to flatten inclination during missions such as the Apollo moon landings.

Natural satellite

moonmoonssatellite
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.
In contrast, irregular satellites (generally orbiting on distant, inclined, eccentric and/or retrograde orbits) are thought to be captured asteroids possibly further fragmented by collisions.

Orbit

orbitsorbital motionplanetary motion
The inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. Orbital inclination measures the tilt of an object's orbit around a celestial body.

Satellite

satellitesartificial satelliteartificial 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.
Geocentric orbits may be further classified by their altitude, inclination and eccentricity.

Retrograde and prograde motion

retrogradeprograderetrograde orbit
A celestial object's inclination indicates whether the object's orbit is prograde or retrograde.

Ecliptic

ecliptical orbitsecliptic planeplane of the ecliptic
For planets in the Solar System, the plane of reference is usually the ecliptic, the plane in which the Earth orbits the Sun. He showed that, for each planet, there is a distance such that moons closer to the planet than that distance maintain an almost constant orbital inclination with respect to the planet's equator (with an orbital precession mostly due to the tidal influence of the planet), whereas moons farther away maintain an almost constant orbital inclination with respect to the ecliptic (with precession due mostly to the tidal influence of the sun).
Ecliptic coordinates are convenient for specifying positions of Solar System objects, as most of the planets' orbits have small inclinations to the ecliptic, and therefore always appear relatively close to it on the sky.

Minimum mass

true massmassminimum
Consequently, most exoplanets found by radial velocity have true masses no more than 40% greater than their minimum masses.
This method reveals planets by measuring changes in the movement of stars in the line-of-sight, so the real orbital inclinations and true masses of the planets are generally unknown.

Planet

planetsFormer classification of planetsplanemo
For a satellite orbiting a planet, the plane of reference is usually the plane containing the planet's equator.
Planets also have varying degrees of axial tilt; they lie at an angle to the plane of their stars' equators.

Binary mass function

mass functiontrue masses
Consequently, most exoplanets found by radial velocity have true masses no more than 40% greater than their minimum masses.
The true mass and true orbital velocity cannot be determined from the radial velocity because the orbital inclination is generally unknown.

Orbital plane (astronomy)

orbital planeorbital planesplane of its orbit
It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.
The orbital plane is defined in relation to a reference plane by two parameters: inclination (i) and longitude of the ascending node .

Dwarf planet

dwarf planetsList of dwarf planetsplanet
On the other hand, the dwarf planets Pluto and Eris have inclinations to the ecliptic of 17° and 44° respectively, and the large asteroid Pallas is inclined at 34°.
Furthermore, having some unusual characteristics, such as large orbital eccentricity and a high orbital inclination, it became evident that it was a different kind of body from any of the other planets.

Orbit of the Moon

Moon's orbitits orbitorbit
In 1966, Peter Goldreich published a classic paper on the evolution of the moon's orbit and on the orbits of other moons in the solar system.
The Moon's orbital plane is inclined by about 5.1° with respect to the ecliptic plane, whereas the Moon's equatorial plane is tilted by only 1.5°.

Axial tilt

obliquityobliquity of the eclipticaxis
For planets and other rotating celestial bodies, the angle of the equatorial plane relative to the orbital plane — such as the tilt of the Earth's poles toward or away from the Sun — is sometimes also called inclination, but less ambiguous terms are axial tilt or obliquity.
It differs from orbital inclination.

Methods of detecting exoplanets

transit methodTransitdirect imaging
If the orbit is almost edge-on, then the planet can be seen transiting its star.
Unlike the majority of other methods, direct imaging works better with planets with face-on orbits rather than edge-on orbits, as a planet in a face-on orbit is observable during the entirety of the planet's orbit, while planets with edge-on orbits are most easily observable during their period of largest apparent separation from the parent star.

Doppler spectroscopy

radial velocity methodradial velocityradial-velocity method
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.
The observed Doppler velocity, where i is the inclination of the planet's orbit to the line perpendicular to the line-of-sight.

2 Pallas

Pallasasteroid Pallas(2) Pallas
On the other hand, the dwarf planets Pluto and Eris have inclinations to the ecliptic of 17° and 44° respectively, and the large asteroid Pallas is inclined at 34°.
Pallas has a relatively high orbital inclination to the plane of the ecliptic.

Orbital inclination change

inclination changeplane changechange inclination
Orbital inclination change is an orbital maneuver aimed at changing the inclination of an orbiting body's orbit.

Pluto

134340 Pluto(134340) Plutoescaped moon of Neptune
On the other hand, the dwarf planets Pluto and Eris have inclinations to the ecliptic of 17° and 44° respectively, and the large asteroid Pallas is inclined at 34°.
In contrast, Pluto's orbit is moderately inclined relative to the ecliptic (over 17°) and moderately eccentric (elliptical).

HD 33636

One particular example is HD 33636 B, which has true mass 142 M J, corresponding to an M6V star, while its minimum mass was 9.28 M J.
In 2007, Bean et al. used the Hubble Space Telescope (HST) and he found that this body has an inclination as little as 4.1 ± 0.1°, which yielded the true mass of 142 Jupiter masses.

Eris (dwarf planet)

Eris136199 Eris2003 UB313
On the other hand, the dwarf planets Pluto and Eris have inclinations to the ecliptic of 17° and 44° respectively, and the large asteroid Pallas is inclined at 34°.
Unlike the eight planets, whose orbits all lie roughly in the same plane as the Earth's, Eris's orbit is highly inclined: It is tilted at an angle of about 44 degrees to the ecliptic.

Nodal precession

precessnodes precessorbital precession
He showed that, for each planet, there is a distance such that moons closer to the planet than that distance maintain an almost constant orbital inclination with respect to the planet's equator (with an orbital precession mostly due to the tidal influence of the planet), whereas moons farther away maintain an almost constant orbital inclination with respect to the ecliptic (with precession due mostly to the tidal influence of the sun).
The rate of precession depends on the inclination of the orbital plane to the equatorial plane, as well as the orbital eccentricity.

Space Shuttle Columbia disaster

Space Shuttle ''Columbia'' disasterColumbia'' disasterColumbia
This would have to involve either rescue or repair – docking at the International Space Station for use as a haven while awaiting rescue (or to use the Soyuz to systematically ferry the crew to safety) would have been impossible due to the different orbital inclination of the vehicles.