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| {{About|eccentricity in astrodynamics||Eccentricity (disambiguation)}}
| | == came the voice communication watch == |
| [[File:Kepler orbits.svg|thumb|An elliptic Kepler orbit with an eccentricity of 0.7 (red ellipse), a parabolic Kepler orbit (green) and a hyperbolic Kepler orbit with an eccentricity of 1.3 (blue outer line)]]
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| The '''orbital eccentricity''' of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect [[circle]]. A value of 0 is a circular orbit, values between 0 and 1 form an [[ellipse|elliptical]] orbit, 1 is a [[parabola|parabolic]] [[escape orbit]], and greater than 1 is a [[hyperbola]]. The term derives its name from the parameters of [[conic section]]s, as every [[Kepler orbit]] is a conic section. It is normally used for the isolated [[two-body problem]], but extensions exist for objects following a [[klemperer rosette|rosette]] orbit through the galaxy.
| | A rather high. This time, we earned a small one. I did not expect the first day there is such a harvest, which is a good start ah. Estimated a month to go, we will not [http://www.nrcil.net/fancybox/lib/rakuten_LV_56.html タイガ ルイヴィトン] harvest small. '<br><br>Luo Feng, Chen Gu, who all of a laugh.<br><br>Luo Feng looked at combat watch, suddenly surprised: 'telephone?'<br><br>communications watch [http://www.nrcil.net/fancybox/lib/rakuten_LV_58.html ルイヴィトン タオル] this fight, even if someone over the phone, it will not [http://www.nrcil.net/fancybox/lib/rakuten_LV_68.html ルイヴィトン最新財布] disturb the [http://www.nrcil.net/fancybox/lib/rakuten_LV_23.html ルイヴィトン 財布 メンズ タイガ] Warrior. Only weapons themselves of the watch, will find someone to call.<br><br>'phone home.' Luo Feng smiled, and [http://www.nrcil.net/fancybox/lib/rakuten_LV_24.html ルイヴィトン 新作 2014] began to voice commands, 'Callback!'<br><br>'beep beep ......'<br><br>communications watches soon Luo Feng outgoing calls home.<br><br>first | night awakening: Episode [http://www.nrcil.net/fancybox/lib/rakuten_LV_125.html ルイヴィトン バッグ 新作] Nine Ray [http://www.nrcil.net/fancybox/lib/rakuten_LV_73.html ルイヴィトン ベルニ] knife eye teeth squad Chapter VII<br><br>'Hey, brother.'<br><br>came the voice communication watch, let Luo Feng could not help laughing:? 'Rituximab, you and your [http://www.nrcil.net/fancybox/lib/rakuten_LV_8.html メンズ ルイヴィトン] little girl is not really hot you how to play there |
| | 相关的主题文章： |
| | <ul> |
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| | <li>[http://qzhzt.mdiscuz.com/forum.php?mod=viewthread&tid=59867 http://qzhzt.mdiscuz.com/forum.php?mod=viewthread&tid=59867]</li> |
| | |
| | <li>[http://www.ex-po.ru/cgi-bin/index.cgi http://www.ex-po.ru/cgi-bin/index.cgi]</li> |
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| | <li>[http://www.antweb.org/cgi-bin/mt/mt-search.cgi http://www.antweb.org/cgi-bin/mt/mt-search.cgi]</li> |
| | |
| | </ul> |
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| ==Definition== | | == 'title task mortality how == |
| In a [[two-body problem]] with inverse-square-law force, every [[orbit]] is a Kepler orbit. The [[eccentricity (mathematics)|eccentricity]] of this [[Kepler orbit]] is a non-negative number that defines its shape.
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| The eccentricity may take the following values:
| | Task? 'Luo Fengsi cable with.<br><br>mandate he understood.<br><br>every era, has a military mission. And within a millennium, it is only on such a mission.<br><br>want to draw a task, you must wait for the next era begin!<br><br>'title task [http://www.nrcil.net/fancybox/lib/rakuten_LV_0.html ルイヴィトン最新財布] mortality [http://www.nrcil.net/fancybox/lib/rakuten_LV_16.html ルイヴィトン 中古] how?' Luo Feng asked.<br><br>'title tasks, each era will have to apply the sergeant.' golden figure indifference road, 'Sgt Dong Jun Confederate Army of North [http://www.nrcil.net/fancybox/lib/rakuten_LV_91.html 新作ルイヴィトン] West Army, the title will be together for the task. mortality [http://www.nrcil.net/fancybox/lib/rakuten_LV_64.html ルイヴィトン 箱] titles tasks, approximately 90% occupied. remaining Under one into barely survive, so far ...... who never completed the task title. [http://www.nrcil.net/fancybox/lib/rakuten_LV_103.html ルイヴィトン ボストンバッグ] '<br><br>Luo Feng amazing.<br><br>title task endless years to complete the number 0! Jiucheng participants [http://www.nrcil.net/fancybox/lib/rakuten_LV_97.html ルイヴィトンのキーケース] fall! Participants live under a lucky one, of course, is a loser.<br><br>'What?' Luo [http://www.nrcil.net/fancybox/lib/rakuten_LV_63.html ルイヴィトン 財布 新作] Feng could not help but curiously asked.<br><br>'Manghe Army sergeant, you simply apply the task to the next task period, one [http://www.nrcil.net/fancybox/lib/rakuten_LV_86.html ルイヴィトン最新作] will know. |
| *[[circular orbit]]: <math>e=0\,\!</math>
| | 相关的主题文章： |
| *[[elliptic orbit]]: <math>0<e<1\,\!</math> (see [[Ellipse]])
| | <ul> |
| *[[parabolic trajectory]]: <math>e=1\,\!</math> (see [[Parabola]])
| | |
| *[[hyperbolic trajectory]]: <math>e>1\,\!</math> (see [[Hyperbola]])
| | <li>[http://www.panierscadeauxinternationaux.com/cgi-bin/store/index.cgi http://www.panierscadeauxinternationaux.com/cgi-bin/store/index.cgi]</li> |
| | | |
| The eccentricity <math>e</math> is given by
| | <li>[http://www.feb25.com/cgi-bin/gb/guestbook.cgi http://www.feb25.com/cgi-bin/gb/guestbook.cgi]</li> |
| | | |
| :<math>
| | <li>[http://61.191.56.145/forum.php/home.php?mod=space&uid=220 http://61.191.56.145/forum.php/home.php?mod=space&uid=220]</li> |
| e = \sqrt{1 + \frac{2 E L^{2}}{m_\text{red} \alpha ^{2}}}
| | |
| </math>
| | </ul> |
| | |
| where ''E'' is the total [[orbital energy]], <math>L</math> is the [[angular momentum]], <math>m_\text{red}</math> is the [[reduced mass]]. and <math>\alpha</math> the coefficient of the inverse-square law [[central force]] such as [[gravity]] or [[electrostatics]] in [[classical physics]]:
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| :<math>
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| F = \frac{\alpha}{r^{2}}
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| </math> | |
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| (<math>\alpha</math> is negative for an attractive force, positive for a repulsive one) (see also [[Kepler problem]]).
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| or in the case of a gravitational force:
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| :<math>
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| e = \sqrt{1 + \frac{2 \epsilon h^{2}}{\mu^2}}
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| </math>
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| where <math>\epsilon</math> is the [[specific orbital energy]] (total energy divided by the reduced mass), <math>
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| \mu</math> the [[standard gravitational parameter]] based on the total mass, and <math>h</math> the [[specific relative angular momentum]] ([[angular momentum]] divided by the reduced mass).
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| For values of ''e'' from 0 to 1 the orbit's shape is an increasingly elongated (or flatter) ellipse; for values of ''e'' from 1 to infinity the orbit is a hyperbola branch making a total turn of 2 [[arccsc]] ''e'', decreasing from 180 to 0 degrees. The limit case between an ellipse and a hyperbola, when ''e'' equals 1, is parabola.
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| Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while ''e'' tends to 1 (or in the parabolic case, remains 1).
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| For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable.
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| For elliptical orbits, a simple proof shows that arcsin(<math>e</math>) yields the projection angle of a perfect circle to an [[ellipse]] of eccentricity <math>e</math>. For example, to view the eccentricity of the planet Mercury (<math>e</math>=0.2056), one must simply calculate the [[inverse trigonometric functions|inverse sine]] to find the projection angle of 11.86 degrees. Next, tilt any circular object (such as a coffee mug viewed from the top) by that angle and the apparent [[ellipse]] projected to your eye will be of that same eccentricity.
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| ==Etymology==
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| From Medieval Latin ''eccentricus'', derived from Greek ''ekkentros'' "out of the center", from ''ek''-, ''ex''- "out of" + ''kentron'' "center". Eccentric first appeared in English in 1551, with the definition "a circle in which the earth, sun. etc. deviates from its center." Five years later, in 1556, an adjective form of the word was added.
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| ==Calculation==
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| The '''eccentricity''' of an [[orbit]] can be calculated from the [[orbital state vectors]] as the [[magnitude (mathematics)|magnitude]] of the [[eccentricity vector]]:
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| :<math>e= \left | \mathbf{e} \right |</math> | |
| where:
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| *<math>\mathbf{e}\,\!</math> is the [[eccentricity vector]].
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| For [[elliptical orbit]]s it can also be calculated from the [[periapsis]] and [[apoapsis]] since <math>r_p=a(1-e)</math> and <math>r_a=a(1+e)</math>, where <math>a</math> is the [[semimajor axis]].
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| :<math>e={{r_a-r_p}\over{r_a+r_p}}</math>
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| ::<math>=1-\frac{2}{(r_a/r_p)+1}</math>
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| where:
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| *<math>r_a\,\!</math> is the radius at [[apoapsis]] (i.e., the farthest distance of the orbit to the [[center of mass]] of the system, which is a [[focus (geometry)|focus]] of the ellipse).
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| *<math>r_p\,\!</math> is the radius at [[periapsis]] (the closest distance).
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| The eccentricity of an elliptical orbit can also be used to obtain the ratio of the [[periapsis]] to the [[apoapsis]]:
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| :<math>{{r_p}\over{r_a}}={{1-e}\over{1+e}}</math>
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| ==Examples==
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| [[File:Eccentricity rocky planets.jpg|500px|thumb|right|[http://www.orbitsimulator.com/gravity/articles/what.html Gravity Simulator] plot of the changing orbital eccentricity of [[Mercury (planet)|Mercury]], [[Venus]], [[Earth]], and [[Mars]] over the next 50,000 years. The 0 point on this plot is the year 2007.]]
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| The eccentricity of the [[Earth]]'s orbit is currently about 0.0167; the Earth's orbit is nearly circular. Over hundreds of thousands of years, the eccentricity of the Earth's orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets (see [http://www.museum.state.il.us/exhibits/ice_ages/eccentricity_graph.html graph]).<ref name="Berger1991">{{cite web
| |
| |date=1991 (old, but published)
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| |title=Graph of the eccentricity of the Earth's orbit
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| |publisher=Illinois State Museum (Insolation values for the climate of the last 10 million years)
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| |author=A. Berger and M.F. Loutre
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| |url=http://www.museum.state.il.us/exhibits/ice_ages/eccentricity_graph.html
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| |accessdate=2009-12-17}}</ref>
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| [[Mercury (planet)|Mercury]] has the greatest orbital eccentricity of any planet in the Solar System (e=0.2056). [[2006 definition of planet|Before 2006]], [[Pluto]] was considered to be the planet with the most eccentric orbit (e=0.248). The [[Moon]]'s value is 0.0549. For the values for all planets and other celestial bodies in one table, see ''[[List of gravitationally rounded objects of the Solar System]]''.
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| Most of the Solar System's [[asteroid]]s have orbital eccentricities between 0 and 0.35 with an average value of 0.17.<ref>[http://filer.case.edu/sjr16/advanced/asteroid.html Asteroids<!-- Bot-generated title -->]</ref> Their comparatively high eccentricities are probably due to the influence of [[Jupiter]] and to past collisions.
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| The eccentricity of [[comet]]s is most often close to 1. [[Periodic comet]]s have highly eccentric [[elliptical orbit]]s with eccentricities just below 1; [[Halley's Comet]]'s elliptical orbit, for example, has a value of 0.967. Non-periodic comets follow near-[[parabolic orbit]]s and thus have eccentricities even closer to 1. Examples include [[Comet Hale–Bopp]] with a value of 0.995<ref name=Hale-Bopp-jpl/> and comet [[C/2006 P1]] (McNaught) with a value of 1.000019.<ref name=McNaught-jpl>{{cite web
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| |date=2007-07-11 last obs
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| |title=JPL Small-Body Database Browser: C/2006 P1 (McNaught)
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| |url=http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=C/2006+P1
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| |accessdate=2009-12-17}}</ref> As Hale–Bopp's value is less than 1, its orbit is elliptical and will in fact return.<ref name=Hale-Bopp-jpl>{{cite web
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| |date=2007-10-22 last obs
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| |title=JPL Small-Body Database Browser: C/1995 O1 (Hale-Bopp)
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| |url=http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Hale-Bopp
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| |accessdate=2008-12-05}}</ref> Comet McNaught has a [[hyperbolic orbit]] while within the influence of the planets, but is still bound to the Sun with an orbital period of about 10<sup>5</sup> years.<ref name="Perth">{{cite web |date=2007-01-22 |title=Comet C/2006 P1 (McNaught) - facts and figures |publisher=Perth Observatory in Australia |url=http://www.perthobservatory.wa.gov.au/information/comet_mcnaught_info.html |accessdate=2011-02-01}}</ref> As of a 2010 [[Epoch (astronomy)|Epoch]], Comet [[C/1980 E1]] has the largest eccentricity of any known hyperbolic comet with an eccentricity of 1.057,<ref name=C/1980E1-jpl>{{cite web
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| |date=1986-12-02 last obs
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| |title=JPL Small-Body Database Browser: C/1980 E1 (Bowell)
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| |url=http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1980E1
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| |accessdate=2010-03-22}}</ref> and will leave the [[Solar System]] indefinitely.
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| [[Neptune]]'s largest moon [[Triton (moon)|Triton]] has an eccentricity of 1.6 × 10<sup>−5</sup>,<ref name=Triton>{{cite web
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| |title=Neptunian Satellite Fact Sheet
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| |publisher=NASA
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| |author=David R. Williams
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| |date=22 January 2008
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| |url=http://nssdc.gsfc.nasa.gov/planetary/factsheet/neptuniansatfact.html
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| |accessdate=2009-12-17 }}</ref> the smallest eccentricity of any known body in the Solar System; its orbit is as close to a perfect circle as can be currently measured.
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| ==Mean eccentricity==
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| The mean eccentricity of an object is the average eccentricity as a result of [[Perturbation (astronomy)|perturbations]] over a given time period. Neptune currently has an instant (current [[Epoch (astronomy)|Epoch]]) eccentricity of 0.0113,<ref name="nssdc-Neptune">{{cite web
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| |title=Neptune Fact Sheet | |
| |date=2007-11-29
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| |url=http://nssdc.gsfc.nasa.gov/planetary/factsheet/neptunefact.html
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| |publisher=NASA
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| |last=Williams |first=David R.
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| |accessdate=2009-12-17}}</ref> but from 1800 A.D. to 2050 A.D. has a ''mean'' eccentricity of 0.00859.<ref name=ssd-mean>{{cite web
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| |title=Keplerian elements for 1800 A.D. to 2050 A.D.
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| |publisher=[http://ssd.jpl.nasa.gov/?planet_pos JPL Solar System Dynamics]
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| |url=http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt
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| |accessdate=2009-12-17}}</ref>
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| ==Climatic effect==
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| Orbital mechanics require that the duration of the seasons be proportional to the area of the Earth's orbit swept between the [[solstices]] and [[equinoxes]], so when the orbital eccentricity is extreme, the seasons that occur on the far side of the orbit ([[aphelion]]) can be substantially longer in duration. Today, northern hemisphere fall and winter occur at closest approach ([[perihelion]]), when the earth is moving at its maximum velocity -- while the opposite occurs in the southern hemisphere. As a result, in the northern hemisphere, fall and winter are slightly shorter than spring and summer -- but in global terms this is balanced with them being longer below the equator. In 2006, the northern hemisphere summer was 4.66 days longer than winter and spring was 2.9 days longer than fall.<ref>This information is concerning the summer of the year 2006 not the current year we are in now.</ref>{{Citation needed|date=November 2008}} [[Apsidal precession]] slowly changes the place in the Earth's orbit where the solstices and equinoxes occur (this is not the [[precession of the axis]]). Over the next 10,000 years, northern hemisphere winters will become gradually longer and summers will become shorter. Any cooling effect in one hemisphere is balanced by warming in the other -- and any overall change will, however, be counteracted by the fact that the eccentricity of Earth's orbit will be almost halved{{Citation needed|date=October 2009}}, reducing the mean orbital radius and raising temperatures in both hemispheres closer to the mid-interglacial peak.
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| ==See also==
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| *[[Eccentricity (mathematics)]]
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| *[[Eccentricity vector]]
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| *[[Equation of time]]
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| *[[Milankovitch cycles]]
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| *[[Orbit]]s
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| ==References==
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| {{Reflist}}
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| Prussing, John E., and Bruce A. Conway. Orbital Mechanics. New York: Oxford University Press, 1993.
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| ==External links==
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| * [http://scienceworld.wolfram.com/physics/Eccentricity.html World of Physics: Eccentricity]
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| * [http://www.ncdc.noaa.gov/paleo/forcing.html The NOAA page on Climate Forcing Data] includes (calculated) data from [ftp://ftp.ncdc.noaa.gov/pub/data/paleo/insolation/ Berger (1978), Berger and Loutre (1991)]. [http://www.imcce.fr/Equipes/ASD/insola/earth/earth.html Laskar et al. (2004)] on Earth orbital variations, Includes eccentricity over the last 50 million years and for the coming 20 million years.
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| * [http://astrobiology.ucla.edu/OTHER/SSO/ The orbital simulations by Varadi, Ghil and Runnegar (2003)] provides series for Earth orbital eccentricity and orbital inclination.
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| * [http://www.walter-fendt.de/ph14e/keplerlaw2.htm Kepler's Second law's simulation]
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| {{orbits}}
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| {{Use dmy dates|date=August 2011}}
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| [[Category:Orbits]]
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| [[ru:Кеплеровы элементы орбиты#Эксцентриситет]]
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came the voice communication watch
A rather high. This time, we earned a small one. I did not expect the first day there is such a harvest, which is a good start ah. Estimated a month to go, we will not タイガ ルイヴィトン harvest small. '
Luo Feng, Chen Gu, who all of a laugh.
Luo Feng looked at combat watch, suddenly surprised: 'telephone?'
communications watch ルイヴィトン タオル this fight, even if someone over the phone, it will not ルイヴィトン最新財布 disturb the ルイヴィトン 財布 メンズ タイガ Warrior. Only weapons themselves of the watch, will find someone to call.
'phone home.' Luo Feng smiled, and ルイヴィトン 新作 2014 began to voice commands, 'Callback!'
'beep beep ......'
communications watches soon Luo Feng outgoing calls home.
first | night awakening: Episode ルイヴィトン バッグ 新作 Nine Ray ルイヴィトン ベルニ knife eye teeth squad Chapter VII
'Hey, brother.'
came the voice communication watch, let Luo Feng could not help laughing:? 'Rituximab, you and your メンズ ルイヴィトン little girl is not really hot you how to play there
相关的主题文章：
'title task mortality how
Task? 'Luo Fengsi cable with.
mandate he understood.
every era, has a military mission. And within a millennium, it is only on such a mission.
want to draw a task, you must wait for the next era begin!
'title task ルイヴィトン最新財布 mortality ルイヴィトン 中古 how?' Luo Feng asked.
'title tasks, each era will have to apply the sergeant.' golden figure indifference road, 'Sgt Dong Jun Confederate Army of North 新作ルイヴィトン West Army, the title will be together for the task. mortality ルイヴィトン 箱 titles tasks, approximately 90% occupied. remaining Under one into barely survive, so far ...... who never completed the task title. ルイヴィトン ボストンバッグ '
Luo Feng amazing.
title task endless years to complete the number 0! Jiucheng participants ルイヴィトンのキーケース fall! Participants live under a lucky one, of course, is a loser.
'What?' Luo ルイヴィトン 財布 新作 Feng could not help but curiously asked.
'Manghe Army sergeant, you simply apply the task to the next task period, one ルイヴィトン最新作 will know.
相关的主题文章：