REFERENCE: Inclination, the Z factor
Consider the Cartesian XYZ axis where XY is the traditional 2 dimensional (2 D) plane, and Z is a factor which adds elevation for a third dimension.
For convenience, Thought Experiment (TE) will assume Earth’s orbit to be exactly circular with constant Radius (R) of 1.0 AU. NOTE: Terran orbit is actually elliptic with small eccentricity of .0167.
In the highly unlikely event that an asteroid orbit resided completely in same plane as Earth’s Solar orbit; then, it would also have a zero Zfactor.
The orbital plane intersects a reference plane; for solar orbits, it is the ecliptic plane. The intersection is called the line of nodes, as it connects our sun, Solar System's center of mass, with the ascending and descending nodes.
Orbital inclination measures the tilt of an object's orbit. It is the angle between a reference plane and the object’s orbital plane or axis.
Components of the calculation of the orbital inclination from the momentum vector
Other
meaning
http://en.wikipedia.org/wiki/Orbital_inclination
Inclination is one of the six orbital parameters describing a celestial orbit.
Of these six parameters, two of them orient the plane of the object's orbit:
Longitude of the ascending node (Ω) horizontally orients the ascending node of the ellipse (where the orbit passes upward through the reference plane) with respect to the reference frame's vernal point.
Inclination (i) is the vertical tilt of the ellipse with respect to the reference plane. i is best displayed at the ascending node (where the orbit passes upward through the reference plane). Inclination is best measured by the orbital plane's angle (in degrees) to the plane of reference (usually the ecliptic).The ecliptic is the Earth's orbital path; thus, the plane containing the ecliptic is a very practical reference for Earthbound observers
Most planetary orbits in the Solar System have relatively small inclinations, both in relation to the ecliptic as well as to each other. However, inclinations of smaller bodies vary widely.EXAMPLES: Dwarf planets Pluto and Eris,have inclinations of 17° and 44° respectively. The large asteroid Pallas, is inclined at 34°.
Inclination of 0° means the orbiting body orbits Sol in same plane as Earth (ecliptic) in the same direction as Earth, counterclock wise (CCW) as observed from north of the ecliptic.
Inclination greater than 90° and less than 90° is a prograde orbit (CCW). Most solar objects orbit Sol in a prograde manner.
Inclination greater than 90° and less than 270° is a retrograde orbit (clockwise as observed from due north). Very few solar objects have such orbits.
Inclination of exactly 90° is a solar polar orbit, in which the object passes over the north and south poles of the Sun.
Inclination of exactly 180° is a retrograde ecliptic orbit (direction is exact opposite of Earth's orbit).
Calculation
In astrodynamics, inclination can be computed from the orbital momentum vector (or any vector perpendicular to the orbital plane) as , where is the zcomponent of .
Cross product is defined by the formula
Orbital Momentum
In an elliptical orbit, a specific relative angular momentum is twice the area per unit time swept out by a chord from the primary to the secondary: this is the area referred to by Kepler's second law of planetary motion. Since the entire orbital area is swept out in one orbital period, orbital momentum, h, equals twice the area of the ellipse divided by the orbital period, giving the equation:
is the semimajor axis.
is the semiminor axis.
G is the gravitational constant, 6.67 × 10^{ 20} km^{3}kg^{ 1}s^{ 2}.
For Solar orbiting objects M_{Sol} = mass of the Sun, 1.989 × 10^{30} kg
m is mass of solar orbiting object. Mass of m is relatively insignificant and can be disregarded.
Thus, it's more convenient to use, μ the standard gravitational parameter:
h = √( μ_{Sol} ×b^{2}/a)
h = √( μ_{Sol} × ℓ)
ℓis the semilatus rectum
Mutual inclination of two orbits may be also be calculated from their inclinations to another plane using cosine rule for angles.
Ecliptic contains Earth orbit.
Two dimensional Ecliptic is the plane of Earth's orbit around our sun, Sol. It could be described with Sol at origin (0,0) with X,Y coordinates given in Astronomical Units (AUs); an AU is the average distance from Sol to Terran orbit. As the reference plan, all Z coordinates are zero; thus, we might consider the Ecliptic as having a zero Zfactor.For convenience, Thought Experiment (TE) will assume Earth’s orbit to be exactly circular with constant Radius (R) of 1.0 AU. NOTE: Terran orbit is actually elliptic with small eccentricity of .0167.
In the highly unlikely event that an asteroid orbit resided completely in same plane as Earth’s Solar orbit; then, it would also have a zero Zfactor.
ω = 90⁰
Node of ascension coincides with a semilatus rectum. Line of nodes coincides with line connecting Sol with orbit's latus rectum. The argument of perihelion (ω) is an angle from Sol's ray to ascending node (☊) to Sol's ray to orbiting body's perihelion (q, closest point to Sol). This angle is measured in the asteroid's orbital plane and in the direction of motion.

The orbital plane intersects a reference plane; for solar orbits, it is the ecliptic plane. The intersection is called the line of nodes, as it connects our sun, Solar System's center of mass, with the ascending and descending nodes.
Orbital inclination measures the tilt of an object's orbit. It is the angle between a reference plane and the object’s orbital plane or axis.
Precise observations of an asteroid’s orbit will determine:
 Perihelion, q, the closest distance to Sol, our sun.
 Aphelion, Q, the farthest distance from Sol.
This proves very practical for Earthbased observers; thus, Earth's orbital inclination is by definition zero (0°).
Inclination is one of the orbit’s six orbital elements which describe its shape and orientation compared to the ecliptic.
An inclination of 30° could also be described using an angle of 150°.
BY CONVENTION,
 the normal orbit is prograde, an orbit in the same direction as the planet rotates.
 Inclinations greater than 90° describe retrograde orbits.
Components of the calculation of the orbital inclination from the momentum vector
In astrodynamics, the inclination i can
be computed from the orbital momentum
vector h (or any vector perpendicular to the orbital plane)
as
While most planetary
orbits in the Solar System have relatively small inclinations, both in relation
to each other and to the Sun's equator.
However, there are notable exceptions. See following table:
17.14°

11.88°

15.55°


10.62°



9.20°


35.06°



34.43°


5.58°



7.13°


Asteroid

6.35°

Other
meaning
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.
Used in
sentence:
The
astronomer calculated the inclination of the orbital planes of each visible heavenly body.
References
^ McBride,
Neil; Bland, Philip A.; Gilmour, Iain (2004). An Introduction to the Solar
System. Cambridge
University Press. p. 248. ISBN 0521546206.
From Wikipediahttp://en.wikipedia.org/wiki/Orbital_inclination
Inclination is one of the six orbital parameters describing a celestial orbit.
Of these six parameters, two of them orient the plane of the object's orbit:
Calculation
In astrodynamics, inclination can be computed from the orbital momentum vector (or any vector perpendicular to the orbital plane) as , where is the zcomponent of .
Cross product is defined by the formula
Orbital Momentum
In an elliptical orbit, a specific relative angular momentum is twice the area per unit time swept out by a chord from the primary to the secondary: this is the area referred to by Kepler's second law of planetary motion. Since the entire orbital area is swept out in one orbital period, orbital momentum, h, equals twice the area of the ellipse divided by the orbital period, giving the equation:
h =  2πab 2π √(a^{3}/G(M+m) 

is the semiminor axis.
G is the gravitational constant, 6.67 × 10^{ 20} km^{3}kg^{ 1}s^{ 2}.
For Solar orbiting objects M_{Sol} = mass of the Sun, 1.989 × 10^{30} kg
m is mass of solar orbiting object. Mass of m is relatively insignificant and can be disregarded.
h =  2πab 2π √(a^{3}/μ_{Sol}) 

μ_{Sol} = G×M_{Sol}
For solar orbits, use μ_{Sol}, the heliocentric gravitational constant.
μ_{Sol} =1.327×10^{11} km^{3}s^{−2}
h = b × √(μ_{Sol}/a)h = √( μ_{Sol} ×b^{2}/a)
h = √( μ_{Sol} × ℓ)
ℓis the semilatus rectum
Mutual inclination of two orbits may be also be calculated from their inclinations to another plane using cosine rule for angles.
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