|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| In [[astronomy]], a '''co-orbital configuration''' refers to two or more [[Astronomical object|celestial objects]] (such as [[asteroids]], [[moons]], or [[planets]]) that orbit at the same, or very similar, distance from their parent object as each other, i.e. they are in a [[Orbital resonance|1:1 mean motion resonance]]. (or 1:−1 if orbiting in [[Retrograde and prograde motion|opposite directions]]<ref>{{cite journal
| | Environmental Consultant Zelman from Drayton Valley, loves to spend some time skeet shooting, ganhando dinheiro na internet and fitness. Likes to see new towns and locales including the Birthplace of the Lord Buddha.<br><br>Also visit my page; [http://ganhedinheironainternet.comoganhardinheiro101.com como ficar rico] |
| | last = Morais | first = M.H.M.
| |
| | coauthors = F. Namouni
| |
| | title = Asteroids in retrograde resonance with Jupiter and Saturn
| |
| | journal = Monthly Notices of the Royal Astronomical Society Letters (in press)
| |
| | arxiv = arXiv:1308.0216
| |
| | url = http://arxiv.org/abs/1308.0216
| |
| }}</ref>)
| |
| | |
| There are several classes of co-orbital objects, depending on their point of [[libration]]. The most common and best-known class is the [[trojan (astronomy)|trojan]], which librate around one of the two stable [[Lagrangian point]]s (Trojan points), {{L4|nolink=yes}} and {{L5|nolink=yes}}, 60° ahead of and behind the larger body respectively. Another class is the [[horseshoe orbit]], in which objects librate around 180° from the larger body. Objects librating around 0° are called [[quasi-satellite]]s.<ref name=coorbplanet>[http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.0726v1.pdf Dynamics of two planets in co-orbital motion]</ref>
| |
| | |
| An '''exchange orbit''' occurs when two co-orbital objects are of similar masses and thus exert a non-negligible influence on each other. The objects can exchange [[semi-major axis|semi-major axes]] or [[orbital eccentricity|eccentricities]] when they approach each other.
| |
| | |
| ==Parameters==
| |
| Orbital parameters that are used to describe the relation of co-orbital objects are the [[longitude of the periapsis]] difference and the [[mean longitude]] difference. The longitude of the periapsis is the sum of the mean longitude and the [[mean anomaly]] ( <math>{\lambda}=M + \varpi </math> ) and the mean longitude of the sum of the [[longitude of the ascending node]] and the [[argument of periapsis]] ( <math>\varpi = \Omega + \omega\,</math> ).
| |
| | |
| ==Trojans==
| |
| [[File:Lagrange very massive.svg|250px|thumb|Trojan points are the points labelled {{L4}} and {{L5}}, highlighted in red, on the orbital path of the secondary object (blue), around the primary object (yellow).]]
| |
| {{Main|Trojan (astronomy)}}
| |
| Trojan objects orbit 60° ahead ({{L4|nolink=yes}}) or behind ({{L5|nolink=yes}}) a more massive object, both in orbit around an even more massive central object. The best known example are the asteroids that orbit ahead or behind [[Jupiter]] around the [[Sun]]. Trojan objects do not orbit exactly at one of either [[Lagrangian point]]s, but do remain relatively close to it, appearing to slowly orbit it. In technical terms, they librate around <math>({\Delta}{\lambda}, {\Delta}\varpi)</math> = (±60°, ±60°). The point around which they librate is the same, irrespective of their mass or orbital eccentricity.<ref name=coorbplanet/>
| |
| | |
| ===Trojan minor planets===
| |
| There are several thousand known trojan minor planets orbiting the Sun. Most of these orbit near Jupiter's Lagrangian points, the traditional [[Jupiter Trojan]]s. [[Neptune]] has [[Neptune trojan|9 known trojan objects]], [[Mars]] [[List of Mars trojan asteroids|7 known ones]] (and a strong candidate), and [[Earth]] [[Earth trojan asteroid|one]], {{mpl|2010 TK|7}}.
| |
| | |
| ===Trojan moons===
| |
| The Saturnian system contains two sets of trojan moons. Both [[Tethys (moon)|Tethys]] and [[Dione (moon)|Dione]] have two trojan moons, [[Telesto (moon)|Telesto]] and [[Calypso (moon)|Calypso]] in Tethys's {{L4|nolink=yes}} and {{L5|nolink=yes}} respectively, and [[Helene (moon)|Helene]] and [[Polydeuces (moon)|Polydeuces]] in Dione's {{L4|nolink=yes}} and {{L5|nolink=yes}} respectively.
| |
| | |
| Polydeuces is noticeable for its wide [[libration]]: it wanders as far as ±30° from its Lagrangian point and ±2% from its mean orbital radius, along a [[tadpole orbit]] in 790 days (288 times its orbital period around Saturn, the same as Dione's).
| |
| | |
| ===Trojan planets===
| |
| The discovery of a pair of co-orbital [[exoplanet]]s has been reported but later retracted.<ref>[http://www.newscientist.com/article/dn20160-two-planets-found-sharing-one-orbit.html Two planets found sharing one orbit], New Scientist, 24 February 2011</ref>
| |
| | |
| One possibility for the [[habitable zone]] is a '''trojan planet''' of a [[gas giant]] close to its [[star]].<ref>[http://arxiv.org/abs/astro-ph/0408079 Extrasolar Trojan Planets close to Habitable Zones], R. Dvorak, E. Pilat-Lohinger, R. Schwarz, F. Freistetter</ref>
| |
| | |
| ====Formation of the Earth–Moon system====
| |
| According to the [[giant impact hypothesis]], Earth's [[Moon]] was formed after a collision between two co-orbiting objects – Theia, believed to have had about 10% of the mass of Earth (about as massive as [[Mars]]), and proto-Earth – whose orbits were perturbed by other planets, bringing Theia out of its trojan position and causing the collision.
| |
| | |
| ==Horseshoe orbits==
| |
| [[Image:Epimetheus-Janus Orbit.png|thumb|right|300px|[[Rotating reference frame|Rotating-frame]] depiction of the [[horseshoe orbit|horseshoe]] exchange orbits of Janus and Epimetheus]]
| |
| {{Main|Horseshoe orbit}}
| |
| | |
| Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral Lagrangian points, i.e. {{L4|nolink=yes}} and {{L5|nolink=yes}}.<ref name=coorbplanet/>
| |
| | |
| ===Co-orbital moons===
| |
| {{See also|Epimetheus (moon)#Orbital relationship between Epimetheus and Janus}}
| |
| The [[Saturn]]ian moons [[Janus (moon)|Janus]] and [[Epimetheus (moon)|Epimetheus]] share their orbits, the difference in semi-major axes being less than either's mean diameter. This means the moon with the smaller semi-major axis will slowly catch up with the other. As it does this, the moons gravitationally tug at each other, increasing the semi-major axis of the moon that has caught up and decreasing that of the other. This reverses their relative positions (proportionally to their masses) and causes this process to begin anew with the moons' roles reversed. In other words, they effectively swap orbits, ultimately oscillating both about their mass-weighted mean orbit.
| |
| | |
| ===Earth co-orbital asteroids===
| |
| A small number of asteroids have been found which are co-orbital with Earth. The first of these to be discovered, asteroid [[3753 Cruithne]], orbits the Sun with a period slightly less than one Earth year, resulting in an orbit that (from the point of view of Earth) appears as a bean-shaped orbit centered on a position ahead of the position of Earth. This orbit slowly moves further ahead of Earth's orbital position. When Cruithne's orbit moves to a position where it trails Earth's position, rather than leading it, the gravitational effect of Earth increases the orbital period, and hence the orbit then begins to lag, returning to the original location. The full cycle from leading to trailing Earth takes 770 years, leading to a horseshoe-shaped movement with respect to Earth.<ref>{{cite journal|doi=10.1111/j.1365-2966.2011.18595.x|title=A long-lived horseshoe companion to the Earth|year=2011|last1=Christou|first1=A. A.|last2=Asher|first2=D. J.|journal=Monthly Notices of the Royal Astronomical Society|volume=414|issue=4|pages=2965|arxiv = 1104.0036 |bibcode = 2011MNRAS.414.2965C }}</ref>
| |
| | |
| More resonant [[near-Earth object]]s (NEOs) have since been discovered. These include [[54509 YORP]], {{mpl|(85770) 1998 UP|1}}, {{mpl|2002 AA|29}}, and {{mpl|2009 BD|}}, which exist in resonant orbits similar to Cruithne's. {{mpl|2010 TK|7}} is the first and so far only identified [[Earth trojan asteroid|Earth trojan]].
| |
| | |
| ==Quasi-satellite==
| |
| {{Main|Quasi-satellite}}
| |
| | |
| Quasi-satellites are co-orbital objects that librate around 0° from the primary. Low-eccentricity quasi-satellite orbits are highly unstable, but for moderate to high eccentricities such orbits can be stable.<ref name=coorbplanet/> From a co-rotating perspective the quasi-satellite appears to orbit the primary like a [[Retrograde motion|retrograde satellite]], although at distances so large that it is not gravitionally bound to it.<ref name=coorbplanet/>
| |
| | |
| ==Exchange orbits==
| |
| In addition to swapping semi-major axes like Saturn's moons Epimetheus and Janus, another possibility is to share the same axis, but swap eccentricities instead.<ref>[http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2010.17453.x/full Exchange orbits: a possible application to extrasolar planetary systems?], B. Funk, R. Schwarz, R. Dvorak, M. Roth</ref>
| |
| | |
| ==See also==
| |
| * [[Kordylewski cloud]]
| |
| * [[Double planet]]
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| * {{cite journal | url=http://www.iop.org/EJ/article/0004-637X/571/1/528/55113.html | author=Eric B. Ford and Matthew J. Holman | title=Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets | journal=The [[Astrophysical Journal]] Letters | volume=664 | issue=1 | year=2007 | pages=L51–L54 | doi= 10.1086/520579 |bibcode = 2007ApJ...664L..51F |arxiv = 0705.0356 }}
| |
| | |
| == External links ==
| |
| * [http://ssdbook.maths.qmw.ac.uk/animations/Coorbital.mov QuickTime animation of co-orbital motion] from Murray and Dermott
| |
| * [http://planetary.org/news/2006/0120_Cassini_Observes_the_Orbital_Dance_of.html Cassini Observes the Orbital Dance of Epimetheus and Janus] The Planetary Society
| |
| * [http://www.trojanplanets.appstate.edu/ A Search for Trojan Planets] Web page of group of astronomers searching for extrasolar trojan planets at Appalachian State University
| |
| | |
| {{DEFAULTSORT:Co-Orbital Moon}}
| |
| [[Category:Co-orbital objects| ]]
| |
Environmental Consultant Zelman from Drayton Valley, loves to spend some time skeet shooting, ganhando dinheiro na internet and fitness. Likes to see new towns and locales including the Birthplace of the Lord Buddha.
Also visit my page; como ficar rico