Apsis

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For Edenbridge's album, see Aphelion (album).
For the literary journal Perigee, see Perigee: Publication for the Arts.

In celestial mechanics, an apsis, plural apsides (pronounced /ˈæpsɨdiːz/) is the point of greatest or least distance of the elliptical orbit of an object from its center of attraction, which is generally the center of mass of the system.

The point of closest approach (the point at which two bodies are the closest) is called the periapsis or pericentre, from Greek περὶ, peri, around. The point of farthest excursion is called the apoapsis (ἀπό, apó, "from", which becomes ἀπ-, ap- or ἀφ-, aph- before an unaspirated or aspirated vowel, respectively), 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.

Derivative terms are used to identify the body being orbited. The most common are perigee and apogee, referring to orbits around the Earth (Greek γῆ, , "earth"), and perihelion and aphelion, referring to orbits around the Sun (Greek ἥλιος, hēlios, "sun"). During the Apollo program, the terms pericynthion and apocynthion were used when referring to the moon.

## Formula

 A diagram of Keplerian orbital elements. F Periaps, H Apoapsis and the red line between them is the line of apsides

These formulae characterize the periapsis and apoapsis of an orbit:

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

while, in accordance with Kepler's laws of planetary motion (conservation of angular momentum) and the conservation of energy, these quantities are constant for a given orbit:

where:

• $a\!\,$ is the semi-major axis
• $\mu\!\,$ is the standard gravitational parameter
• $e\!\,$ is the eccentricity, defined as $e=\frac{r_\mathrm{ap}-r_\mathrm{per}}{r_\mathrm{ap}+r_\mathrm{per}}=1-\frac{2}{\frac{r_\mathrm{ap}}{r_\mathrm{per}}+1}$

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

The arithmetic mean of the two limiting distances is the length of the semi-major axis $a\!\,$. The geometric mean of the two distances is the length of the semi-minor axis $b\!\,$.

The geometric means of the two limiting 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 product of the two speeds is the local escape velocity).

## Terminology

The words "pericenter" and "apocenter" are occasionally seen, although periapsis/apoapsis are preferred in technical usage.

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 (from the Greek root) was used by physicist Geoffrey A. Landis in 1998 before peri/aponigricon (from the Latin) appeared in the scientific literature in 2002 .

Body Closest approach Farthest approach
Galaxy Perigalacticon Apogalacticon
Star Periastron Apastron
Black hole Perimelasma/Peribothra/Perinigricon Apomelasma/Apobothra/Aponigricon
Sun Perihelion Aphelion[2]
Mercury Perihermion Apohermion
Venus Pericytherion/Pericytherean/Perikrition Apocytherion/Apocytherean/Apokrition
Earth Perigee Apogee
Moon Periselene/Pericynthion/Perilune Aposelene/Apocynthion/Apolune
Mars Periareion Apoareion
Jupiter Perizene/Perijove Apozene/Apojove
Saturn Perikrone/Perisaturnium Apokrone/Aposaturnium
Uranus Periuranion Apouranion
Neptune Periposeidion Apoposeidion

Since "peri" and "apo" are Greek, it is considered by some purists more correct to use the Greek form for the body, giving forms such as '-zene' for Jupiter and '-krone' for Saturn. 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.

• 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. The '-cynthion' form was the version used in the Apollo Project, following a NASA decision in 1964.
• For Venus, the form '-cytherion' is derived from the commonly used adjective 'cytherean'; the alternate form '-krition' (from Kritias, an older name for Aphrodite) has also been suggested.
• For Jupiter, the '-jove' form is occasionally used by astronomers whilst the '-zene' form is never used, like the other pure Greek forms ('-areion' (Mars), '-hermion' (Mercury), '-krone' (Saturn), '-uranion' (Uranus), '-poseidion' (Neptune) and '-hadion' (Pluto)).

## Earth's perihelion and aphelion

For the Earth's orbit around the sun, the time of apsis is most relevantly expressed in terms of a time relative to seasons, for that will determine the contribution of the elliptic orbit to seasonal forcing, meaning the annual variation in insolation at the top of the atmosphere. This forcing is primarily controlled by the annual cycle of the declination of the sun, a consequence of the tilt of the Earth's rotation axis relative to the plane of the orbit. Currently, perihelion occurs about 14 days after the winter solstice, making northern hemisphere winters milder than they would be otherwise, and southern hemisphere winters more extreme. The time of perihelion progresses through the seasons, making one complete cycle in 22,000 to 26,000 years, a contribution to Milankovitch cycles, a forcing of the ice ages, known as precession.

A common convention is to express the timing of perihelion relative to the vernal equinox not in days, but as an angle of orbital displacement, a longitude of the periapsis. For Earth's orbit, this would be a longitude of perihelion, which in 2000 AD was 282.895 degrees .

The day and hour (UT) of perihelion and aphelion for the next few years are:

Year Perihelion Aphelion
Date Hour Date Hour
2007 January 3 2000 July 7 0000
2008 January 3 0000 July 4 0800
2009 January 4 1500 July 4 0200
2010 January 3 0000 July 6 1100
2011 January 3 1900 July 4 1500
2012 January 5 0000 July 5 0300
2013 January 2 0500 July 5 1500
2014 January 4 1200 July 4 0000
2015 January 4 0700 July 6 1900
2016 January 2 2300 July 4 1600
2017 January 4 1400 July 3 2000
2018 January 3 0600 July 6 1700
2019 January 3 0500 July 4 2200
2020 January 5 0800 July 4 1200

## Planetary perihelion and aphelion

The images below show the Perihelion and Aphelion points of the inner and outer planets respectively.

## Notes and references

Published in July 2009.