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

Jesper Kyd Jakobson (born February 3, 1972) is an award winning Danish video game, television and film score composer. Internationally renowned for composing the unique, signature music soundtracks for multi-million selling franchises Assassin's Creed, Hitman and Borderlands, Kyd’s distinctive scores feature a diverse array of orchestra, choir, acoustic manipulations and electronic soundscapes, immersing audiences with emotional depth often described by critics as ‘rousing,’ ‘surreal’ and ‘beautiful.’^{[citation needed]}

Biography[link]

Early years[link]

Kyd started playing piano at an early age. Later, he took several years of training in classical guitar, note reading, choir singing and classical composition for piano. However, he is mostly self-taught.^[1][2] Kyd was always more interested in the compositional aspects of music and received a Commodore 64 when he was 14, enabling him to compose music for the demoscene.^[3] Several years later he obtained an Amiga, allowing him to compose music with samples in it.^[4] He, along with his good friend and collaborator, Mikael Balle, became a member of the demo group Silents DK, and after some time started collaborating with a group of coders known as Crionics,^[5] which would arguably later prove vital for his professional career. They eventually made the legendary Amiga demoscene production Hardwired.^[6][7] He also created and scored the first wild demo, Global Trash 2, together with Mikael Balle.

Career[link]

At this point Jesper Kyd decided to quit the demo scene and focus on a professional career as a game musician. He and his demoscene friends who had collaborated on the Hardwired demo created the computer game developer Zyrinx and started working on a game called Sub-Terrania for the Sega Genesis. The game was successful and the music of the game received particular acclaim, many stating it was "Some of the best ever" for this particular system.^{[citation needed]}

With the commercial success of the game, Jesper Kyd and the rest of the team relocated to Boston. Kyd composed music for two additional Zyrinx titles, Red Zone and Scorcher as well as the music for two externally developed games, Amok and The Adventures of Batman and Robin before their game publisher Scavenger went bankrupt, forcing the Zyrinx team to dissolve as well.

Freelance[link]

After the demise of Zyrinx, many of its former members returned to Denmark to start IO Interactive. Jesper Kyd decided to move to New York City and set up his own sound studio in Manhattan called "Nano studios". Because of his extensive connections in the industry,^{[citation needed]} Kyd found success as a freelance computer game musician. He also had been planning to score upcoming games from IO Interactive from the beginning.

Breakthrough[link]

Jesper Kyd's real fame came, according to him, with the release of Bioware's MDK2: Armageddon, Shiny's Messiah and IO's Hitman: Codename 47 being released around the same time, all being fairly well known games, with Hitman ending up as one of the most popular of the time.^[8] The soundtrack to Codename 47 was based on urban soundscapes and ethnic instrumentation. It immediately took the focus of many magazines around the world. Mp3.com declared that "The theme song to the original Hitman is arguably one of the best pieces of video game theme music so far this decade".^[9]

His next huge step was recording the soundtrack of Hitman 2: Silent Assassin. The soundtrack was recorded with 110 musicians of the Budapest Symphony Orchestra and Choir. "The music of most big budget action movies won't move you like the music of Hitman 2," said IGN.^[9]

His next soundtrack contained heroic and densely atmospheric music for the epic action/adventure Freedom Fighters. He recorded the score with the Hungarian Radio choir. It further established him as one of the leading, innovative A-list composers in interactive entertainment. It was described by Film Score Monthly Magazine as "Vangelis on steroids". Billboard Digital Entertainment Awards nominated him for Best Use of Soundtrack, meanwhile, Game Audio Network Guild Awards nominated him for "Best Original Vocal Song – Choral" (for Main Title and March of the Empire). Leading video game web site GameSpot awarded Freedom Fighters "Best Music of the Year".

His unique fusion of modern electronica and brooding symphonic and choral grooves featured in Hitman: Contracts garnered international critical acclaim as one of the truly groundbreaking original soundtracks. It was awarded Best Original Music by the British Academy of Film and Television Arts at the 2005 BAFTA Games Awards and won Best Cinematic / Cut-Scene Audio at the 2005 G.A.N.G. Awards. "Many have tried to turn a video game soundtrack into a musical experience. But few have succeeded in creating a coherent, satisfying listening experience as well as Jesper Kyd," noted EQ Magazine.^[9]

Following his Bafta-winning music for the globally acclaimed Hitman series, Kyd’s next assignment was to provide the rich and melodic sound for what would become Ubisoft’s flagship franchise, Assassin's Creed, created by visionary developer Patrice Desilets. Kyd’s cinematic score for Altair’s Middle-Eastern story delivers a deeply meditative and spiritual aesthetic with dramatic effect. For Assassin's Creed II, Kyd took the music in an adventurous new direction, crafting a melodic, acoustic and orchestral music score recorded with A-list musicians in Los Angeles. The music propels the action, captures the allure and mystery of Ezio’s story and immerses players in the breathtakingly detailed settings of Renaissance Italy. Kyd’s original score for Assassin's Creed Brotherhood draws influence and authentic instrumentation from the Renaissance period, immersing players in master assassin Ezio’s mission to liberate Rome from the corrupt and tyrant regime of the Borgias. For the epic conclusion to Ezio’s story, Assassin's Creed Revelations, Kyd composed a rich and evocative hybrid music style drawing on Greek, Renaissance and Middle-Eastern instrumentation, while combining his emotional melodic writing and acoustic/electronic styles associated with the series.

Kyd’s emotionally dynamic score for the highly anticipated action/adventure Darksiders II combines dark ethereal themes and melodic fantasy with sublime atmosphere that enrich the player’s cinematic journey through each of the unique realms. Darksiders II II follows the exploits of Death, one of the four horsemen of the Apocalypse, during his epic journey through various light and dark realms as he tries to redeem his brother WAR, the horseman who was blamed for prematurely starting the Apocalypse. Darksiders II is set for release on August 21, 2012.

Kyd is currently scoring new episodes of the upcoming live action TV series Metal Hurlant Chronicles (Heavy Metal), Cameron Romero’s next film Radical, Undead Labs’ ‘Class3′ and other projects to be announced.

He resides in Burbank, California and is represented by The Gorfaine-Schwartz Agency.

Works[link]

Kyd has composed music for many different forms of visual and non-visual media, below is a run-down of his works.

Games[link]

• 2012 - Darksiders II
• 2012 - Heroes and Generals
• 2012 - Soulcalibur V (provided a remix of the track "Venice Rooftops" from Assassin's Creed II)
• 2011 - Forza Motorsport 4
• 2011 - Assassin's Creed: Revelations (with Lorne Balfe)
• 2010 - Assassin's Creed: Brotherhood^[10]
• 2009 - Assassin's Creed II
• 2009 - Borderlands
• 2008 - The Chronicles of Spellborn
• 2008 - The Club (main theme)
• 2007 - Assassin's Creed
• 2007 - Unreal Tournament 3 (with Rom Di Prisco)
• 2007 - Kane & Lynch: Dead Men
• 2006 - Hitman: Blood Money
• 2006 - Gears of War (concept music)
• 2005 - Splinter Cell: Chaos Theory (cinematics)
• 2004 - Dance Dance Revolution ULTRAMIX 2 (songs .59 -remix-, Istanbul café, and Red Room)^[11]
• 2004 - Robotech: Invasion
• 2004 - Hitman: Contracts
• 2004 - McFarlane's Evil Prophecy
• 2003 - Freedom Fighters
• 2003 - Brute Force
• 2002 - Hitman 2: Silent Assassin
• 2002 - Minority Report: The Video Game
• 2001 - Shattered Galaxy
• 2001 - The Nations: Alien Nations 2
• 2000 - Hitman: Codename 47
• 2000 - Messiah
• 2000 - MDK2
• 2000 - Soldier (unreleased)
• 1999 - Time Tremors
• 1996 - Scorcher
• 1996 - Amok
• 1995 - Adventures of Batman and Robin
• 1994 - Red Zone
• 1993 - Sub-Terrania
• 1993 - AWS Pro Moves Soccer
• 1989 - USS John Young

Movies[link]

• 2010 - A Perfect Soldier
• 2008 - Staunton Hill
• 2007 - La Passion de Jeanne d'Arc (1928, new score)
• 2006 - Sweet Insanity
• 2003 - Night All Day
• 2002 - Pure
• 2002 - Death of a Saleswoman

Short films[link]

• 2011 - Somnolence
• 2010 - The Auctioneers
• 2006 - Virus
• 2006 - Impulse
• 2003 - Cycle
• 2002 - Pure
• 2002 - Paper Plane Man
• 2002 - Day Pass
• 2001 - Going with Neill
• 2001 - The Lion Tamer
• 2000 - Organizm

TV series[link]

• 2012 - Metal Hurlant Chronicles / Heavy Metal (US title)
• 2009 - The Resistance

Trailers[link]

• Game of Thrones TV Series
• Conan the Barbarian
• Assassin's Creed TV launch trailer
• Assassin's Creed cello TV trailer
• Assassin's Creed E3 trailer
• Gears of War E3 trailer
• V For Vendetta (Warner Bros. Pictures)
• Hitman: Blood Money TV trailers
• Hitman: Contracts TV trailers
• Hitman 2: Silent Assassin TV trailers
• Freedom Fighters TV trailers

Awards and nominations[link]

• 2012 BAFTA British Academy of Film and Television Arts - Best Original Score Nomination
• 2011 GameSpot Readers Choice Special Achievement Awards - Best Music Winner
• 2011 GameSpot Editors Choice Special Achievement Awards - Best Music Nomination
• 2011 Gold Spirit Awards - Best Video Game Score Nomination
• 2011 Academy of Interactive Arts & Sciences - Outstanding Achievement in Original Music Nomination
• 2011 Game Audio Network Guild Awards - Music of the Year Nomination
• 2011 Soundtrack Geek Awards - Best Video Game Score Nomination
• 2010 Hollywood Music in Media Awards - Best Original Score (VG) Nomination
• 2010 Gold Spirit Awards: Best Video Game Score Winner
• 2010 BAFTA British Academy of Film and Television Arts - Best Original Score Nomination
• 2010 International Film Music Critics Association - Best Original Video Game Score Nomination
• 2010 Academy of Interactive Arts & Sciences - Outstanding Achievement in Original Music Nomination
• 2010 Game Audio Network Guild Awards - Music of the Year Winner
• 2009 IGN Best of the Year Awards - Best Soundtrack Winner (PlayStation 3)
• 2009 GameSpot Readers Choice Special Achievement Awards - Best Original Score Winner
• 2009 GameSpot Editors Choice Special Achievement Awards - Best Original Score Nomination
• 2009 Hollywood Music in Media Awards - Best Original Score (VG) Winner
• 2009 Gamespy Editors' Choice Awards - Best Original Music Winner
• 2009 Spike Video Game Awards - Best Original Score Nomination
• 2009 G4TV X-Play Awards - Best Original Soundtrack Nomination
• 2009 Machinima Awards - Best Original Score Nomination
• 2008 BAFTA - Best Original Music Nomination (British Academy Award)
• 2008 Hollywood Music Awards - Best Original Score Nomination
• 2008 Golden Joystick Awards - Soundtrack of the Year Nomination
• 2008 ELAN Awards - Best Video Game Score Winner
• 2007 GameSpot - Best Video Game Score Nomination
• 2007 3 G.A.N.G. Nominations, including Music of the Year
• 2006 MTV Video Music Awards - Best Video Game Score Nomination
• 2006 IGN Best Original Score Winner
• 2006 Golden Joystick Awards - Best Game Soundtrack Nomination
• 2006 4 G.A.N.G. Nominations Including Music of the Year
• 2005 BAFTA - Winner Best Original Music Award (British Academy Award)
• 2005 G.A.N.G. Winner Best Music for Cinamatic/Cut Scene
• 2005 PSE2 Editor's Choice GOLD - Freedom Fighters Soundtrack CD
• 2004 Billboard Awards Best Music Nomination 2004
• 2004 IGN - Best Soundtrack Nomination
• 2004 3 G.A.N.G. Nominations
• 2004 PSE2 Editor's Choice GOLD - Hitman Contracts Soundtrack CD
• 2003 GameSpot - Best Soundtrack of the Year Winner
• 2003 Game Reactor - Best Original Soundtrack Winner
• 2003 PSE2 Editor's Choice GOLD - Hitman 2 Soundtrack CD
• 2002 Games Agent - Best Original Soundtrack Winner
• 2002 GameSpot - Best Original Soundtrack of the Year Nomination
• 2002 X-Sages - Soundtrack of the Year Nomination
• 2002 IGN - Best Sound Nomination
• 2002 Action Vault - Outstanding Achievement In Music
• 2002 Bolt Games - Bolt Games Music Award

References[link]

External links[link]

• Official website
• Official MySpace
• Jesper Kyd discography at MusicBrainz
• MobyGames rap sheet
• Artist profile at OverClocked ReMix
• An insight into Kyd's demoscene days with a video from 1991 he did the music for
• A more in depth look at his career including his demoscene days

Interviews[link]

• Interview at Nerd Reactor
• Interview at Tracksounds
• Interview at SoundtrackNet
• Interview at Go! Game Music
• Interview at BSOSpirit
• Interview at SpelMusik
• Interview & Module Downloads at Amiga Music Preservation
• Interview at DVD.Reviewer for Jesper Kyd's work on Staunton Hill
• Interview at GameStar.ru