Apogee

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In Astronomy , an apsis (plural ''apsides'' "''ap-si-deez''") is the point of greatest or least distance of the Elliptical Orbit of a Celestial Body from its center of attraction, which is generally the Center Of Mass of the system.

The point of closest approach is called the periapsis or '''pericentre''' and the point of farthest excursion is the '''apoapsis''' (Greek απο, from), '''apocentre''' or '''apapsis''' (the latter term, although etymologically more correct, is much less used). A straight line drawn through the periapsis and apoapsis is the ''line of apsides''. This is the major axis of the Ellipse , the line through the longest part of the ellipse.

Related terms are used to identify the body being orbited. The most common are perigee and '''apogee''', referring to Earth orbits, and '''perihelion''' and '''aphelion''', referring to orbits around the Sun (Greek ἡλιος).

FORMULAE

There are Formula e used to derive apsis and periapsis:

Periapsis: maximum speed $v_\mathrm{per} = \sqrt{ rac{(1+e)\mu}{(1-e)a} } \,$ at minimum distance $r_\mathrm{per}=(1-e)a\!\,$ (periapsis distance)

Apoapsis: minimum speed $v_\mathrm{ap} = \sqrt{ rac{(1-e)\mu}{(1+e)a} } \,$ at maximum distance $r_\mathrm{ap}=(1+e)a\!\,$ (apoapsis distance)

where one easily verifies
:

h = \sqrt{(1-e^2)\mu a}

\epsilon=-rac{\mu}{2a}

(each the same for both points, like they are for the whole orbit, in accordance with Kepler's Laws Of Planetary Motion (conservation of Angular Momentum ) and the conservation of energy)

where:

$a\!\,$ is the Semi-major Axis

$e\!\,$ is the Eccentricity

$h\!\,$ is the Specific Relative Angular Momentum

$\epsilon\!\,$ is the Specific Orbital Energy

$\mu\!\,$ is the Standard Gravitational Parameter

Properties:

:

e=rac{r_\mathrm{ap}-r_\mathrm{per}}{r_\mathrm{ap}+r_\mathrm{per}}=1-rac{2}{rac{r_\mathrm{ap}}{r_\mathrm{per}}+1}

Note that for conversion from heights above the surface to distances, the radius of the central body has to be added, and conversely.

The Arithmetic Mean of the two distances is the semi-major axis

a\!\,

.
The Geometric Mean of the two distances is the Semi-minor Axis

b\!\,

.

The geometric mean of the two speeds is

\sqrt{-2\epsilon}

, the speed corresponding to a kinetic energy which, at any position of the orbit, added to the existing kinetic energy, would allow the orbiting body to escape (the square root of the sum of the squares of the two speeds is the local escape velocity).

TERMINOLOGY

Various related terms are used for other Celestial Objects . The '-gee', '-helion' and '-astron' and '-galacticon' forms are frequently used in the astronomical literature, while the other listed forms are occasionally used, although '-saturnium' has very rarely been used in the last 50 years. The '-gee' form is commonly (although incorrectly) used as a generic 'closest approach to planet' term instead of specifically applying to the Earth. The term ''peri/apomelasma'' was used by Geoffrey A. Landis in 1998 before ''peri/aponigricon'' appeared in the scientific literature in 2002 .

⁽¹⁾ Properly pronounced 'affelion', although 'ap-helion' is commonly heard.

Since "peri" and "apo" are Greek, it is considered by purists more correct to use the Greek form for the body, giving forms such as '-zene' for Jupiter and '-krone' for Saturn. For Venus, the alternate form '-krition' (from Kritias, an older name for Aphrodite ) has also been suggested. In the Moon's case, in practice all three forms are used, albeit very infrequently. The '-cynthion' form is, according to some, reserved for artificial bodies, whilst others reserve '-lune' for an object launched ''from'' the Moon and '-cynthion' for an object launched from elsewhere. For Jupiter, the '-jove' form is occasionally used by astronomers whilst the '-zene' form is never used, like the other pure Greek forms ('-cytherion' (Venus), '-areion' (Mars), '-hermion' (Mercury), '-krone' (Saturn), '-uranion' (Uranus), '-poseidion' (Neptune) and '-hadion' (Pluto)). The daunting prospect of having to maintain a different word for every orbitable body in the solar system (and beyond) is the main reason why the generic '-apsis' has become the almost universal norm.

SEE ALSO

Eccentric Anomaly

Elliptic Orbit

Apogee - Perigee Photographic Size Comparison

Aphelion - Perihelion Photographic Size Comparison

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Apogee