WordNet

(geometry) the angle formed by the x-axis and a given line (measured counterclockwise from the positive half of the x-axis) (同)angle_of_inclination
(astronomy) the angle between the plane of the orbit and the plane of the ecliptic stated in degrees (同)inclination of an orbit
the act of inclining; bending forward; "an inclination of his head indicated his agreement" (同)inclining
an attitude of mind especially one that favors one alternative over others; "he had an inclination to give up too easily"; "a tendency to be too strict" (同)disposition, tendency
that toward which you are inclined to feel a liking; "her inclination is for classical music"
lower or bend (the head or upper body), as in a nod or bow; "She inclined her head to the student"
bend or turn (ones ear) towards a speaker in order to listen well; "He inclined his ear to the wise old man"
feel favorably disposed or willing; "She inclines to the view that people should be allowed to expres their religious beliefs"
charge with a tilt
the property possessed by a line or surface that departs from the vertical; "the tower had a pronounced tilt"; "the ship developed a list to starboard"; "he walked with a heavy inclination to the right" (同)list, inclination, lean, leaning
a slight but noticeable partiality; "the courts tilt toward conservative rulings"
slanting or inclined in direction or course or position--neither parallel nor perpendicular nor right-angled; "the oblique rays of the winter sun"; "acute and obtuse angles are oblique angles"; "the axis of an oblique cone is not perpendicular to its base"
any grammatical case other than the nominative (同)oblique case
that toward which you are inclined to feel dislike; "his disinclination for modesty is well known"

PrepTutorEJDIC

〈C〉《単数形で》『傾くこと』,傾けること;《an inclination》『傾き』,傾斜,斜面(slope) / 〈C〉〈U〉《文》(物事の)『傾向』 / 〈C〉〈U〉《しばしば複数形で》(人の)『好み』,意向
(…に)『心が傾く』,気が向く / 〈人・物が〉『傾向がある』(rend) / (…に)傾く,傾斜する;身をかがめる《+『to』(『toward』)+『名』》 / 〈物事が〉(…に)‘の'心を向けさせる / (…に)…‘を'傾ける,傾斜させる,かがめる《+『名』+『to』(『toward』)+『名』》 / 傾斜,こう配;斜面
…‘を'傾ける / (馬上槍試合で)〈槍〉‘を'突き出す,〈相手〉‘を'槍で突く / 傾く / 馬上槍試合をする / (相手を)槍で突く《+at+名》 / (文章・言葉で)(…を)攻撃する《+at+名》 / 傾き,傾斜(slope) / (中世騎士の)馬上槍試合 / (一般に)対決,試合
傾いた,斜めの / 間接の,遠回しの / 〈C〉〈U〉斜線(/)
気が進まないこと,いや気:《『disinclination』+『for』(『to』)+『名』(do『ing』)…に気が進まないこと》

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/09/22 02:04:17」(JST)

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

Orbital inclination is the angle between a reference plane and the orbital plane or axis of direction of an object in orbit around another object.

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 of the orbit of a planet is defined as the angle between the plane of the orbit of the planet and the ecliptic.^[2] Therefore Earth's inclination is, by definition, zero. Inclination could instead 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 the Solar System have relatively small inclinations, both in relation to each other and to the Sun's equator. On the other hand, the dwarf planets Pluto and Eris have inclinations to the ecliptic of 17 degrees and 44 degrees respectively, and the large asteroid Pallas is inclined at 34 degrees.

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	0	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°

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 do so close enough. The equatorial plane is the plane perpendicular to the axis of rotation of the central body.

an inclination of 0° means the orbiting body orbits the planet in its equatorial plane, in the same direction as the planet rotates;
an inclination greater than 0° and less than 90° is a prograde orbit.
an inclination greater than 90° and less than 180° is a retrograde orbit.
an inclination of exactly 90° is a polar orbit, in which the spacecraft passes over the north and south poles of the planet; and
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, it is expected that the orbital planes of moons will 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 will tend to be aligned with the giant planet's equator because these formed in circumplanetary disks.^[4]

The term "critical inclination" is often used when describing artificial satellites in orbit around Earth. This term refers to a satellite orbiting with an inclination of 63.4°. This inclination is described as critical as there is zero apogee drift for satellites in elliptical orbits at this inclination.^[5]

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 70% 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 M_J, corresponding to an M6V star, while its minimum mass was 9.28 M_J.

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

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.^{[citation needed]}
In geology, the magnetic inclination is the angle made by a compass needle with respect to the horizontal surface of Earth at a given latitude.^{[citation needed]}

Calculation

components of the calculation of the orbital inclination from the momentum vector

In astrodynamics, the inclination can be computed from the orbital momentum vector (or any vector perpendicular to the orbital plane) as , where is the z-component of .

Mutual inclination of two orbits may be calculated from their inclinations to another plane using cosine rule for angles.

References

^ Chobotov, Vladimir A. (2002). Orbital Mechanics (3rd ed.). AIAA. pp. 28–30;. ISBN 1-56347-537-5.
^ McBride, Neil; Bland, Philip A.; Gilmour, Iain (2004). An Introduction to the Solar System. Cambridge University Press. p. 248. ISBN 0-521-54620-6.
^ "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)
^ Moon formation and orbital evolution in extrasolar planetary systems-A literature review, K Lewis – EPJ Web of Conferences, 2011 – epj-conferences.org
^ Arctic Communications System Utilizing Satellites in Highly Elliptical Orbits, Lars Løge – Section 3.1, Page 17

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Numerical Simulation of Natural Convection of a Nanofluid in an Inclined Heated Enclosure Using Two-Phase Lattice Boltzmann Method: Accurate Effects of Thermophoresis and Brownian Forces.

Ahmed M1, Eslamian M.
Nanoscale research letters.Nanoscale Res Lett.2015 Dec;10(1):1006. doi: 10.1186/s11671-015-1006-0. Epub 2015 Jul 16.
Laminar natural convection in differentially heated (β = 0°, where β is the inclination angle), inclined (β = 30° and 60°), and bottom-heated (β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the incli
PMID 26183389

Decay characteristics and erosion-related transport of glyphosate in Chinese loess soil under field conditions.

Yang X1, Wang F2, Bento CP3, Meng L4, van Dam R5, Mol H5, Liu G6, Ritsema CJ3, Geissen V7.
The Science of the total environment.Sci Total Environ.2015 Oct 15;530-531:87-95. doi: 10.1016/j.scitotenv.2015.05.082. Epub 2015 May 28.
The decay characteristics and erosion-related transport of glyphosate and aminomethylphosphonic acid (AMPA) were monitored for 35d at different slope gradients and rates of application in plots with loess soil on the Loess Plateau, China. The initial glyphosate decayed rapidly (half-life of 3.5d) in
PMID 26026412

Association of sagittal spinal alignment with thickness and echo intensity of lumbar back muscles in middle-aged and elderly women.

Masaki M1, Ikezoe T2, Fukumoto Y3, Minami S4, Tsukagoshi R5, Sakuma K6, Ibuki S2, Yamada Y7, Kimura M8, Ichihashi N2.
Archives of gerontology and geriatrics.Arch Gerontol Geriatr.2015 Sep-Oct;61(2):197-201. doi: 10.1016/j.archger.2015.05.010. Epub 2015 May 28.
OBJECTIVE: Quantitative changes, such as a decrease in muscle mass, and qualitative changes, such as an increase in the amount of intramuscular non-contractile tissue, occur with aging. However, it is unclear whether quantitative or qualitative changes in back muscles are associated with spinal alig
PMID 26058723

Lateral forces exerted through ball or bar attachments in relation to the inclination of mini-implant underneath overdentures: in vitro study.

Takagaki K1, Gonda T1, Maeda Y1.
Clinical oral implants research.Clin Oral Implants Res.2015 Sep;26(9):1060-3. doi: 10.1111/clr.12400. Epub 2014 Apr 15.
OBJECTIVE: Lateral force to mini-implants should be avoided because mini-implants are weak mechanically because of its small diameter. Overdentures retained by mini-implants are usually formed using ball attachments. However, bar attachments can offer the advantage of splinting the mini-implants. Th
PMID 24730651