Apsides 1) Apoapsis; 2) Periapsis; 3) Focus

An apsis (Greek ἁψίς, gen. ἁψίδος), plural apsides ( /ˈæpsɨdiːz/; Greek: ἁψίδες), is the point of greatest or least distance of a body from one of the foci of its elliptical orbit. In modern celestial mechanics this focus is also the center of attraction, which is usually the center of mass of the system. Historically, in geocentric systems, apsides were measured from the center of the Earth.

The point of closest approach (the point at which two bodies are the closest) is called the periapsis or pericentre, from Greek περί, peri, around, and κέντρον kentron. The point of farthest excursion is called the apoapsis (ἀπό, apó, "from", apocentre or apapsis [from ἀπ-, ap-, before an unaspirated, or ἀφ-, aph-, before an aspirated vowel, respectively]), (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  /ˈpɛrɨdʒiː/ and apogee  /ˈæpɵdʒiː/, referring to orbits around the Earth (Greek γῆ, gê, "earth"), and perihelion  /ˌpɛrɨˈhiːliən/ and aphelion  /əˈfiːliən/, 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.^[1]

Mathematical formulae[link]

Keplerian orbital elements: F is the periapsis, H the apoapsis and the red line between them the line of apsides

These formulas characterize the periapsis and apoapsis of an orbit:

• Periapsis: maximum speed Failed to parse (Missing texvc executable; please see math/README to configure.): v_\mathrm{per} = \sqrt{ \tfrac{(1+e)\mu}{(1-e)a} } \,

at minimum (periapsis) distance Failed to parse (Missing texvc executable; please see math/README to configure.): r_\mathrm{per}=(1-e)a\!\,

• Apoapsis: minimum speed Failed to parse (Missing texvc executable; please see math/README to configure.): v_\mathrm{ap} = \sqrt{ \tfrac{(1-e)\mu}{(1+e)a} } \,

at maximum (apoapsis) distance Failed to parse (Missing texvc executable; please see math/README to configure.): r_\mathrm{ap}=(1+e)a\!\,

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

• specific relative angular momentum Failed to parse (Missing texvc executable; please see math/README to configure.): h = \sqrt{(1-e^2)\mu a}

• specific orbital energy Failed to parse (Missing texvc executable; please see math/README to configure.): \epsilon=-\frac{\mu}{2a}

where:

• Failed to parse (Missing texvc executable; please see math/README to configure.): a\!\,

is the semi-major axis

• Failed to parse (Missing texvc executable; please see math/README to configure.): \mu\!\,

is the standard gravitational parameter

• Failed to parse (Missing texvc executable; please see math/README to configure.): e\!\,

is the eccentricity, defined as Failed to parse (Missing texvc executable; please see math/README to configure.): 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 Failed to parse (Missing texvc executable; please see math/README to configure.): a . The geometric mean of the two distances is the length of the semi-minor axis Failed to parse (Missing texvc executable; please see math/README to configure.): b .

The geometric mean of the two limiting speeds is Failed to parse (Missing texvc executable; please see math/README to configure.): \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[link]

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.^[2]

Since "peri" and "apo" are Greek, it is considered by some purists^[3] 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 cases other than the Sun and Earth.

• In the Moon's case, in practice all three forms are used, albeit very infrequently. The '-cynthion' form (from the moon goddess Artemis' Ancient Greek epithet "Cynthia")^[4] 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)).

The perihelion and aphelion of the Earth[link]

For the orbit of the Earth around the sun, the time of apsis is often expressed in terms of a time relative to seasons, since this determines the contribution of the elliptical orbit to seasonal variations. The variation of the seasons is primarily controlled by the annual cycle of the elevation angle of the sun, which is a result of the tilt of the axis of the Earth measured from the plane of the ecliptic.

Currently, the annual perihelion happens at about 14 days after the December Solstice, thus on or about January 4. At perihelion, the Earth is about 0.98329 astronomical units (AU) or 147,098,070 kilometers (about 91,402,500 miles) from the sun. (The eccentricity of the orbit also varies slowly over many millennia.)

Likewise, the annual aphelion currently occurs in early July, about 14 days after the June Solstice. At this time, the distance of the aphelion is currently about 1.01671 AU or 152,097,700 kilometers (94,509,100 mi).

On a very long time scale, the dates of the perihelion and of the aphelion progress through the seasons, and they make one complete cycle in 22,000 to 26,000 years. There is a corresponding movement of the position of the stars as seen from Earth that is called the apsidal precession. (This is not the precession of the axis.)

Astronomers commonly express the timing of perihelion relative to the vernal equinox not in terms of days and hours, but rather as an angle of orbital displacement, the so-called longitude of the periapsis. For the orbit of the Earth, this is called the longitude of perihelion, and in 2000 was about 282.895 degrees. By the year 2010, this had advanced by a small fraction of a degree to about 283.067 degrees.^[5]

The dates and times of the perihelions and aphelions for several past and future years are listed in the following table:^[6]

Planetary perihelion and aphelion[link]

The following table shows the distances of the planets and dwarf planets from the Sun at their perihelion and aphelion.^[7]

The following chart shows the range of distances of the planets, dwarf planets and Halley's Comet from the Sun.

id:grid_major value:gray(0.75)
id:grid_minor value:rgb(0.75,0.75,1)

bar:au
bar:dummy1 text:PLANETS
bar:planets
bar:dummy2 text:COMET (e.g.)
bar:comet text:
bar:dwarf_planets1 text:DWARF _
bar:dwarf_planets2 text:PLANETS
bar:dwarf_planets3
bar:dwarf_planets4

fontsize:M
bar:dummy1 text:_ color:white at:0
bar:dummy2 text:_ color:white at:0
bar:planets width:48 text:Mercury color:lightpurple from:46 till:70 shift:(0,14)
bar:planets width:48 text:Venus color:redorange from:107 till:109 shift:(0,1)
bar:planets width:48 text:Earth color:oceanblue from:147 till:152 shift:(0,-12)
bar:planets width:48 text:Mars color:coral from:207 till:249 shift:(0,-25)
bar:planets width:48 text:Jupiter color:orange from:741 till:816
bar:planets width:48 text:Saturn color:yellow from:1350 till:1504
bar:planets width:48 text:Uranus color:skyblue from:2735 till:3006
bar:planets width:48 text:Neptune color:blue from:4460 till:4537
bar:dwarf_planets2 width:18 text:Ceres color:tan2 from:381 till:446 shift:(0,-4)
bar:dwarf_planets1 width:18 text:Pluto color:lavender from:4437 till:7376 shift:(0,-4)
bar:dwarf_planets2 width:18 text:Haumea color:tan1 from:5158 till:7706 shift:(0,-4)
bar:dwarf_planets3 width:18 text:Makemake color:pink from:5672 till:7895 shift:(0,-4)
bar:dwarf_planets4 width:18 text:Eris color:lightorange from:5766 till:14595 shift:(0,-4)
bar:dwarf_planets4 text:SUN color:yellow from:0 till:0.696 shift:(2,-20)
bar:comet width:12 text:Halley's_Comet color:yellowgreen from:88 till:5251 shift:(0,-4)
bar:au shift:(1,-12) text:0AU at:0
bar:au shift:(1,-12) text:10_AU at:1326
bar:au shift:(1,-12) text:20_AU at:2822
bar:au shift:(1,-12) text:30_AU at:4318
bar:au shift:(1,-12) text:40_AU at:5814
bar:au shift:(1,-12) text:50_AU at:7310
bar:au shift:(1,-12) text:60_AU at:8806
bar:au shift:(1,-12) text:70_AU at:10302
bar:au shift:(1,-12) text:80_AU at:11798
bar:au shift:(1,-12) text:90_AU at:13294

at:10 color:yellow layer:front

pos:(10,192) text:Astronomical
pos:(10,182) text:units from Sun
pos:(20,15) text:Million km\nfrom Sun

The images below show the perihelion and aphelion points of the inner and outer planets.

• Perihelion and aphelion points
• 

  The perihelion and aphelion points of the inner planets of the Solar System

• 

  The perihelion and aphelion points of the outer planets of the Solar System

See also[link]

• Eccentric anomaly
• Elliptic orbit
• Apsidal precession

Notes and references[link]

External links[link]

Look up apsis in Wiktionary, the free dictionary.

• Apogee - Perigee Photographic Size Comparison, perseus.gr
• Aphelion - Perihelion Photographic Size Comparison, perseus.gr
• Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion, 2000-2020, usno.navy.mil

Nathaniel "Nate" Weiss (born July 16, 1987 in Brooklyn, New York) is an American-Israeli professional soccer player, and currently plays for FSV Erlangen-Bruck in Germany. Weiss is the first American player to play in the LMT Virsliga, the Latvian premier league, and only the tenth American player to ever win a domestic cup in Europe.^[1]

Career[link]

Early life[link]

A member of Weston Warriors youth soccer club, Weiss continued to play at Stoneman Douglas High School where he received All-State and All-Broward County honors. At 15 Weiss also spent time in England at the Stockport County academy.^[2]

Professional[link]

During the 2007-8 season, Weiss played with the Spanish club UD Arenal in the Tercera. After spending the 2008 season with Longford Town in Ireland, Weiss joined the Swedish club Djurgårdens IF on trial.^[3] Weiss then left Sweden to join Serbian club FK Metalac Gornji Milanovac, but financial difficulties prevented him from a prolonged stay. On October 7, 2009, Weiss arrived at Hapoel Beersheba in Israel.^[4][5] During Weiss' time in Israel, he trained with Israeli coach George Borba and acquired Israeli citizenship by virtue of the Law of Return.^[6]

As the only offers Weiss received during his time there were from Liga Leumit clubs, he decided to take a contract offer in Latvia with FK Jelgava.^[7] Weiss made his league debut on April 18, 2010 in a league match against Skonto FC.^[8] While at FK Jelgava, Weiss played in 20 matches and scored a total of 4 goals, even though his position was defender. When the 2010 season ended in Latvia, Weiss chose to move on, in the hope of finding a higher profile European country and team, with the express hope of coming to the attention of the then U.S. men's soccer team coach, Bob Bradley.^[9] In 2011, after playing a friendly for IK Sirius against Leicester City FC, Weiss reported that several clubs had expressed interest in seeing him play; finally, he chose to trial for Örebro.^[1] Weiss has since left Sweden, and currently plays in the Fußball-Bayernliga with FSV Erlangen-Bruck. ^[10]

Honours[link]

Club[link]

FK Jelgava[link]

• Latvian Cup: 2010

See also[link]

• List of select Jewish football (association; soccer) players

References[link]

External links[link]

• Stetson bio