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| [[Image:Solar system barycenter.svg|thumb|250px|Motion of the [[Solar System]] barycenter relative to the Sun]]
| | Greetings! I am Marvella and I really feel comfortable when people use the complete name. My day job is a meter reader. Years ago he moved to North Dakota and his family members enjoys it. The favorite hobby for my children and me is to play baseball but I haven't produced a dime with it.<br><br>Review my page [http://www.animecontent.com/user/D2456 home std test] |
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| In [[astronomy]], '''barycentric coordinates''' are non-rotating coordinates with origin at the [[center of mass]] of two or more bodies.
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| The '''barycenter''' (or '''barycentre'''; from the Greek βαρύ-ς ''heavy'' + κέντρ-ον ''centre'' + ''-ic''<ref>Oxford English Dictionary, Second Edition.</ref>) is the point between two objects where they balance each other. For example, it is the center of mass where two or more celestial bodies [[orbit]] each other. When a [[natural satellite|moon]] orbits a [[planet]], or a planet orbits a [[star]], both bodies are actually orbiting around a point that is not at the center of the primary (the larger body). For example, the Moon does not orbit the exact center of the [[Earth]], but a point on a line between the center of the Earth and the Moon, approximately 1,710 km below the surface of the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the [[Sun]].
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| ==Two-body problem==
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| The barycenter is one of the [[focus (geometry)|foci]] of the [[elliptic orbit|elliptical orbit]] of each body. This is an important concept in the fields of [[astronomy]], [[astrophysics]], and the like (see [[two-body problem]]). In a simple two-body case, ''r''<sub>1</sub>, the distance from the center of the primary to the barycenter is given by:
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| :<math>r_1 = a \cdot {m_2 \over m_1 + m_2} = {a \over 1 + m_1/m_2}</math>
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| where:
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| :''a'' is the distance between the centers of the two bodies;
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| :''m''<sub>1</sub> and ''m''<sub>2</sub> are the [[mass]]es of the two bodies.
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| If ''a'' is the semi-major axis of the system, ''r''<sub>1</sub> is the [[semi-major axis]] of the primary's orbit around the barycenter, and ''r''<sub>2</sub> = ''a'' − ''r''<sub>1</sub> is the semi-major axis of the secondary's orbit. When the barycenter is located ''within'' the more massive body, that body will appear to "wobble" rather than following a discernible orbit.
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| ===Examples===
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| {{anchor|Sun-Jupiter barycenter}}
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| The following table sets out some examples from the [[Solar System]]. Figures are given rounded to three [[significant figures]]. The last two columns show ''R''<sub>1</sub>, the radius of the first (more massive) body, and ''r''<sub>1</sub> / ''R''<sub>1</sub>, the ratio of the distance to the barycenter and that radius: a value less than one shows that the barycenter lies inside the first body.
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| {| class="wikitable" style="text-align:center"
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| |+ '''Examples'''
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| ! Larger <br />body | |
| ! ''m''<sub>1</sub> <br />(''m''<sub>E</sub>=1)
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| ! Smaller <br />body
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| ! ''m''<sub>2</sub> <br />(''m''<sub>E</sub>=1)
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| ! ''a'' <br />([[kilometre|km]])
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| ! ''r''<sub>1</sub> <br />(km)
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| ! ''R''<sub>1</sub> <br />(km)
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| ! ''r''<sub>1</sub> / ''R''<sub>1</sub>
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| |-
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| !colspan=8| Remarks
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| |-
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| | [[Earth]]
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| | 1
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| | [[Moon]]
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| | 0.0123
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| | 384,000
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| | 4,670
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| | 6,380
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| | 0.732
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| |-
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| |colspan=8| The Earth has a perceptible "wobble"; see [[tide]]s.
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| |-
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| | [[Pluto]]
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| | 0.0021
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| | [[Charon (moon)|Charon]]
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| | 0.000254 <br /> (0.121 ''m''<sub>Pluto</sub>)
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| | 19,600
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| | 2,110
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| | 1,150
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| | 1.83
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| |-
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| |colspan=8| Both bodies have distinct orbits around the barycenter, and as such Pluto and Charon were considered as a [[double planet]] by many before the redefinition of [[planet]] in August 2006.
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| |-
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| | [[Sun]]
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| | 333,000
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| | Earth
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| | 1
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| | 150,000,000 <br /> (1 [[astronomical unit|AU]])
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| | 449
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| | 696,000
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| | 0.000646
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| |-
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| |colspan=8| The Sun's wobble is barely perceptible.
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| |-
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| | Sun
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| | 333,000
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| | [[Jupiter]]
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| | 318 <br /> (0.000955 ''m''<sub>Sun</sub>)
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| | 778,000,000 <br />(5.20 AU)
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| | 742,000
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| | 696,000
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| | 1.07
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| |-
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| |colspan=8| The Sun orbits a barycenter just above its surface.<ref name="NASA2005">{{cite web
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| |date=2005-09-08
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| |title=What's a Barycenter?
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| |publisher=Space Place @ NASA
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| |url=http://spaceplace.nasa.gov/en/kids/barycntr.shtml
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| |accessdate=2011-01-20| archiveurl= http://web.archive.org/web/20101223075230/http://spaceplace.nasa.gov/en/kids/barycntr.shtml| archivedate= 23 December 2010 <!--DASHBot-->| deadurl= no}}</ref>
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| |}
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| ===Inside or outside the Sun?===
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| If ''m''<sub>1</sub> ≫ ''m''<sub>2</sub> — which is true for the Sun and any planet — then the ratio ''r''<sub>1</sub>/''R''<sub>1</sub> approximates to:
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| :<math>{a \over R_1} \cdot {m_2 \over m_1}</math>
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| Hence, the barycenter of the Sun–planet system will lie outside the Sun only if:
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| :<math>{a \over R_{\bigodot}} \cdot {m_{planet} \over m_{\bigodot}} > 1 \; \Rightarrow \; {a \cdot m_{planet}} > {R_{\bigodot} \cdot m_{\bigodot}} \approx 2.3 \times 10^{11} \; m_{Earth} \; \mbox{km} \approx 1530 \; m_{Earth} \; \mbox{AU}</math>
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| That is, where the planet is heavy ''and'' far from the Sun.
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| If Jupiter had [[Mercury (planet)|Mercury]]'s orbit (57,900,000 km, 0.387 AU), the Sun–Jupiter barycenter would be approximately 55,000 km from the center of the Sun (''r''<sub>1</sub>/''R''<sub>1</sub> ~ 0.08). But even if the Earth had [[Eris (dwarf planet)|Eris']] orbit (68 AU), the Sun–Earth barycenter would still be within the Sun (just over 30,000 km from the center).
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| To calculate the actual motion of the Sun, you would need to sum all the influences from all the [[planet]]s, [[comet]]s, [[asteroid]]s, etc. of the [[Solar System]] (see [[n-body problem|''n''-body problem]]). If all the planets were aligned on the same side of the Sun, the combined center of mass would lie about 500,000 km above the Sun's surface.
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| The calculations above are based on the mean distance between the bodies and yield the mean value ''r''<sub>1</sub>. But all celestial orbits are elliptical, and the distance between the bodies varies between the [[apsis|apses]], depending on the [[eccentricity (orbit)|eccentricity]], ''e''. Hence, the position of the barycenter varies too, and it is possible in some systems for the barycenter to be ''sometimes inside and sometimes outside'' the more massive body. This occurs where:
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| :<math>{1 \over {1-e}} > {r_1 \over R_1} > {1 \over {1+e}}</math>
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| Note that the Sun–Jupiter system, with ''e''<sub>Jupiter</sub> = 0.0484, just fails to qualify: 1.05 '''≯''' 1.07 > 0.954.
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| === Animations <!-- This section is linked from [[Tide]] -->===
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| Images are representative (made by hand), not simulated.
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| {| class="wikitable" width=640
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| |valign=top|[[Image:orbit1.gif|200px]]<BR>Two bodies with the same mass orbiting a common barycenter (similar to the [[90 Antiope]] system)
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| |valign=top|[[Image:orbit2.gif|200px]]<BR>Two bodies with a difference in mass orbiting a common barycenter external to both bodies, as in the [[Pluto]]–[[Charon (moon)|Charon]] system
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| |valign=top|[[Image:orbit3.gif|200px]]<BR>Two bodies with a major difference in mass orbiting a common barycenter internal to one body (similar to the [[Earth]]–[[Moon]] system)
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| |valign=top|[[Image:orbit4.gif|200px]]<BR>Two bodies with an extreme difference in mass orbiting a common barycenter internal to one body (similar to the [[Sun]]–[[Earth]] system)
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| |-
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| |valign=top colspan=2|[[Image:orbit5.gif|400px]]<BR>Two bodies with the same mass orbiting a common barycenter, external to both bodies, with eccentric [[elliptic orbit]]s (a common situation for [[binary star]]s)
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| |}
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| ==Relativistic corrections==
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| In [[classical mechanics]], this definition simplifies calculations and introduces no known problems. In [[general relativity]], problems arise because, while it is possible, within reasonable approximations, to define the barycenter, the associated coordinate system does not fully reflect the inequality of clock rates at different locations. Brumberg explains how to set up barycentric coordinates in general relativity.<ref>''Essential Relativistic Celestial Mechanics'' by [[Victor A. Brumberg]] (Adam Hilger, London, 1991) ISBN 0-7503-0062-0.</ref>
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| The coordinate systems involve a world-time, i.e. a global time coordinate that could be set up by [[telemetry]]. Individual clocks of similar construction will not agree with this standard, because they are subject to differing [[gravitational potential]]s or move at various velocities, so the world-time must be slaved to some ideal clock that is assumed to be very far from the whole self-gravitating system. This time standard is called [[Barycentric Coordinate Time]], "TCB".
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| ==Selected barycentric orbital elements==
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| Barycentric osculating orbital elements for some objects in the Solar System:<ref name=barycenter>{{cite web
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| |date=2011-01-30
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| |author=[[JPL Horizons On-Line Ephemeris System|Horizons]] output
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| |url=http://home.surewest.net/kheider/astro/2007TG422Barycenter.txt
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| |title=Barycentric Osculating Orbital Elements for 2007 TG422
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| |accessdate=2011-01-31}} (Select Ephemeris Type:Elements and Center:@0)</ref>
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| {| border="1" class="wikitable sortable" style="width:95%; text-align:center;"
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| |-----
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| ! [[Small Solar System body|Object]]<br>
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| ! [[Semi-major axis]]<br>(in [[Astronomical unit|AU]])<br>
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| ! [[Apoapsis]]<br>(in AU)<br>
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| ! [[Orbital period]]<br>(in years)<br>
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| |-----
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| | [[C/2006 P1|C/2006 P1 (McNaught)]]
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| | 2050
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| | 4100
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| | 92600
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| |-----
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| | [[Comet Hyakutake]]
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| | 1700
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| | 3410
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| | 70000
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| |-----
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| | [[C/2006 M4 (SWAN)]]
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| | 1300
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| | 2600
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| | 47000
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| |-----
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| | {{mpl|(308933) 2006 SQ|372}}
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| | 799
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| | 1570
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| | 22600
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| |-----
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| | {{mpl|(87269) 2000 OO|67}}
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| | 549
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| | 1078
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| | 12800
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| |-----
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| | [[90377 Sedna]]
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| | 506
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| | 937
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| | 11400
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| |-----
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| | {{mpl|2007 TG|422}}
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| | 501
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| | 967
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| | 11200
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| |}
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| For objects at such high eccentricity, the Sun's barycentric coordinates are more stable than heliocentric coordinates.<ref name="Kaib2009">{{cite journal
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| |last=Kaib |first=Nathan A.
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| |coauthors=Becker, Andrew C.; Jones, R. Lynne; Puckett, Andrew W.; Bizyaev, Dmitry; Dilday, Benjamin; Frieman, Joshua A.; Oravetz, Daniel J.; Pan, Kaike; Quinn, Thomas; Schneider, Donald P.; Watters, Shannon
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| |title=2006 SQ372: A Likely Long-Period Comet from the Inner Oort Cloud
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| |journal=[[The Astrophysical Journal]]
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| |volume=695 |issue=1 |pages=268–275 |year=2009
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| |doi=10.1088/0004-637X/695/1/268
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| |id= |arxiv=0901.1690 |bibcode=2009ApJ...695..268K}}</ref>
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| ==References==
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| {{Reflist}}
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| [[Category:Celestial coordinate system]]
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| [[Category:Celestial mechanics]]
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