Inclination: Wikis

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Encyclopedia

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

Orbits

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.[1]

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 plane containing Earth's orbital path.[2] 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. There are notable exceptions in the dwarf planets Pluto and Eris, which have inclinations to the ecliptic of 17 degrees and 44 degrees respectively, and the large asteroid Pallas, which is inclined at 34 degrees. Many of the currently known extrasolar planets are in multiple systems, and sometimes have high inclinations. However, the inclinations for most extrasolar planets were not measured, leaving only their minimum masses, which means that some of the extrasolar planets may actually be brown dwarfs or even dim red dwarf stars. So only transiting planets and planets detected by astrometry have known inclinations and hence true masses. Sometime in 2010s, the inclinations and hence true masses for almost all the exoplanets will be measured by the number of observatories in space, including the Gaia mission, Space Interferometry Mission, and James Webb Space Telescope.

Inclination
Name Inclination
to ecliptic (°)
Inclination
to Sun's equator
(°)
Inclination
to Invariable plane[3] (°)
Terrestrials Mercury 7.01 3.38 6.34
Venus 3.39 3.86 2.19
Earth N/A 7.155 1.57
Mars 1.85 5.65 1.67
Gas giants Jupiter 1.31 6.09 0.32
Saturn 2.49 5.51 0.93
Uranus 0.77 6.48 1.02
Neptune 1.77 6.43 0.72

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 greater than -90 and less than 90 degrees is a prograde orbit.
• an inclination greater than 90 and less than 270 degrees is a retrograde orbit.
• an inclination of exactly 90 degrees is a polar orbit, in which the spacecraft passes over the north and south poles of the planet; and
• an inclination of exactly 180 degrees is a retrograde equatorial orbit.
• an inclination of exactly 270 degrees is a polar orbit in the opposite direction to a 90 degree polar orbit.

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 (for slow-moving objects) with respect to the plane of the sky (see the definition given for binary stars, below).

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 (i.e. the plane of the orbit that Earth and Moon track together around the Sun), a fairly constant quantity.

File:Orbit1.svg

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 or axial inclination, but to avoid ambiguity can be called 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.
• Binary stars with inclinations close to 90 degrees (edge-on) are often eclipsing.
• In geology, the magnetic inclination is the angle made by a compass needle with respect to the horizontal surface of the Earth at a given latitude.

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.

References

1. ^ Chobotov, Vladimir A. (2002). Orbital Mechanics (3rd ed.). AIAA. pp. 28–30;. ISBN 1563475375.
2. ^ McBride, Neil; Bland, Philip A.; Gilmour, Iain (2004). An Introduction to the Solar System. Cambridge University Press. p. 248. ISBN 0521546206.
3. ^ "The MeanPlane (Invariable plane) of the Solar System passing through the barycenter". 2009-04-03. Retrieved 2009-04-10.   (produced with Solex 10 written by Aldo Vitagliano)