View source for Astronomy:Effects of Planet Nine on trans-Neptunian objects

The hypothetical [[Astronomy:Planet Nine|Planet Nine]] would modify the orbits of extreme trans-Neptunian objects via a combination of effects. On very long timescales exchanges of angular momentum with Planet Nine cause the perihelia of anti-aligned objects to rise until their precession reverses direction, maintaining their anti-alignment, and later fall, returning them to their original orbits. On shorter timescales mean-motion resonances with Planet Nine provides phase protection, which stabilizes their orbits by slightly altering the objects' semi-major axes, keeping their orbits synchronized with Planet Nine's and preventing close approaches. The inclination of Planet Nine's orbit weakens this protection, resulting in a chaotic variation of semi-major axes as objects hop between resonances. The orbital poles of the objects circle that of the Solar System's [[Astronomy:Laplace plane|Laplace plane]], which at large semi-major axes is warped toward the plane of Planet Nine's orbit, causing their poles to be clustered toward one side.<ref name="Batygin_Morbidelli_2017" />
==Apsidal anti-alignment==

[[File:Secular evolution of eTNOs induced by Planet Nine.png|thumb|260px|Secular evolution of eTNOs induced by Planet Nine for objects with semi-major axis of 250 AU.<ref name="Beust_2016" /><ref name="Batygin_Morbidelli_2017" /> Blue:anti-aligned, Red:aligned, Green:metastable, Orange:circulating. Crossing orbits above black line.{{efn-ua|Similar figures in articles by Beust<ref name="Beust_2016" /> and Batygin and Morbidelli<ref name="Batygin_Morbidelli_2017" /> are plots of the Hamiltonian, showing combinations of orbital eccentricities and orientations that have equal energy. If there are no close encounters with Planet Nine, which would change the energy of the orbit, the object's [[Astronomy:Orbital elements|orbital elements]] remain on one of these curves as the orbits evolve.}}|alt=the aligned orbits appear as red contour lines on either side of a parabolic black line, while the anti-aligned orbits appear as blue contour lines within the parabola.]]

The anti-alignment and the raising of the perihelia of extreme trans-Neptunian objects with semi-major axes greater than 250 AU is produced by the secular effects of Planet Nine. Secular effects act on timescales much longer than orbital periods so the perturbations two objects exert on each other are the average between all possible configurations. Effectively the interactions become like those between two wires of varying thickness, thicker where the objects spend more time, that are exerting [[Physics:Torque|torque]]s on each other, causing exchanges of [[Physics:Angular momentum|angular momentum]] but not energy. Thus secular effects can alter the eccentricities, inclinations and orientations of orbits but not the semi-major axes.<ref name="Naoz_2016">{{cite journal |last1=Naoz |first1=Smadar |title=The Eccentric Kozai-Lidov Effect and Its Applications |journal=Annual Review of Astronomy and Astrophysics |date=2016 |volume=54 |pages=441–489 |doi=10.1146/annurev-astro-081915-023315 |arxiv=1601.07175 |bibcode=2016ARA&A..54..441N |s2cid=119214240 }}</ref><ref name="find_planet_nine_theory" />

Exchanges of angular momentum with Planet Nine cause the perihelia of the anti-aligned objects to rise and fall while their longitudes of perihelion [[Astronomy:Libration|librate]], or [[Oscillation|oscillate]] within a limited range of values. When the angle between an anti-aligned object's perihelion and Planet Nine's (delta longitude of perihelion on diagram) climbs beyond 180° Planet Nine exerts a positive average torque on the object's orbit. This torque increases the object's angular momentum{{efn-ua|Angular momentum in an elliptical orbit <math>L = \sqrt{G M m a (1-e^2)} </math>}} from Planet Nine causing the eccentricity of its orbit to decline (see blue curves on diagram) and its perihelion to rise away from Neptune's orbit. The object's precession then slows and eventually reverses as its eccentricity declines. After delta longitude of perihelion drops below 180° the object begins to feel a negative average torque and loses angular momentum to Planet Nine causing its eccentricity grows and perihelion falls. When the object's eccentricity is once again large it precesses forward, returning the object to its original orbit after several hundred million years.<ref name="Batygin_Morbidelli_2017" /><ref name="Naoz_2016" /><ref name="Shankman_etal_2016_10">{{cite journal |last1=Shankman |first1=Cory |last2=Kavelaars |first2=J. J. |last3=Lawler |first3=Samantha |last4=Bannister |first4=Michelle |date=2017 |title=Consequences of a distant massive planet on the large semi-major axis trans-Neptunian objects |journal=[[Astronomy:The Astronomical Journal|The Astronomical Journal]] |volume=153 |issue=2 |page=63 |arxiv=1610.04251 |bibcode=2017AJ....153...63S |doi=10.3847/1538-3881/153/2/63|s2cid=56067774 |url=https://pure.qub.ac.uk/portal/en/publications/consequences-of-a-distant-massive-planet-on-the-large-semimajor-axis-transneptunian-objects(f94859e2-eab4-46de-8b90-d7028d7bccdd).html |doi-access=free }}</ref>

The behavior of the orbits of other objects varies with their initial orbits. Stable orbits exist for aligned objects with small eccentricities. Although objects in these orbits have high perihelia and have yet to be observed, they may have been captured at the same time as Planet Nine due to perturbations from a passing star.<ref name="Mustill_etal_2016">{{cite journal |last1=Mustill |first1=Alexander J. |last2=Raymond |first2=Sean N. |last3=Davies |first3=Melvyn B. |date=21 July 2016 |title=Is there an exoplanet in the Solar System? |journal=Monthly Notices of the Royal Astronomical Society: Letters |volume=460 |issue=1 |pages=L109–L113 |arxiv=1603.07247 |bibcode=2016MNRAS.460L.109M |doi=10.1093/mnrasl/slw075}}</ref><ref name="Khain_etal_2018" /> Aligned objects with lower perihelia are only temporarily stable, their orbits precess until parts of the orbits are [[Tangent|tangent]] to that of Planet Nine, leading to frequent close encounters.<ref name="find_planet_nine_theory">{{cite web |last1=Batygin |first1=Konstantin |title=Theory |url=http://www.findplanetnine.com/2017/10/theory.html |website=The Search for Planet Nine |accessdate=11 October 2017}}</ref><ref name="Batygin_Morbidelli_2017">{{cite journal |last1=Batygin |first1=Konstantin |last2=Morbidelli |first2=Alessandro |title=Dynamical Evolution Induced by Planet Nine |journal=The Astronomical Journal |date=2017 |volume=154 |issue=6 |page=229 |doi=10.3847/1538-3881/aa937c |arxiv=1710.01804 |bibcode=2017AJ....154..229B|s2cid=119704953 |doi-access=free }}</ref> After crossing this region the perihelia of their orbits decline, causing them to encounter the other planets, leading to their ejection.<ref name="Khain_etal_2018">{{cite journal|last1=Khain|first1=Tali|last2=Batygin|first2=Konstantin|last3=Brown|first3=Michael E.|title=The Generation of the Distant Kuiper Belt by Planet Nine from an Initially Broad Perihelion Distribution|journal=The Astronomical Journal|volume=155|issue=6|pages=250|date=2018|arxiv=1804.11281|bibcode=2018AJ....155..250K|doi=10.3847/1538-3881/aac212|s2cid=54547607 |doi-access=free }}</ref>{{efn-ua|The observed aligned eTNOs are either objects recently scattered into large semi-major axis orbits or objects circulating while in mean motion resonance as discussed in the next section.}}

The curves the orbits follow vary with semi-major axis of the object and if the object is in resonance. At smaller semi-major axes the aligned and anti-aligned regions shrink and eventually disappear below 150 AU, leaving typical Kuiper belt objects unaffected by Planet Nine. At larger semi-major axes the region with aligned orbits becomes narrower and the region with anti-aligned orbits becomes wider.<ref name="Beust_2016">{{cite journal |last1=Beust |first1=H. |title=Orbital clustering of distant Kuiper belt objects by hypothetical Planet 9. Secular or resonant? |journal=Astronomy & Astrophysics |date=2016 |volume=590 |page=L2 |doi=10.1051/0004-6361/201628638 |arxiv=1605.02473 |bibcode=2016A&A...590L...2B|s2cid=53994177 }}</ref> These regions also shift to lower perihelia, with perihelia of 40 AU becoming stable for anti-aligned objects at semi-major axes greater than 1000 AU.<ref name="Saillenfest_etal_2017b" /><ref name="Hadden_etal_2017" /> The anti-alignment of resonant objects, for example if Sedna is in a 3:2 resonance with Planet Nine as proposed by Malhotra, Volk and Wang,<ref name="Malhotra_Volk_Wang">{{cite journal |last1=Malhotra |first1=Renu |last2=Volk |first2=Kathryn |last3=Wang |first3=Xianyu |date=2016 |title=Corralling a distant planet with extreme resonant Kuiper belt objects |journal=The Astrophysical Journal Letters |volume=824 |issue=2 |pages=L22 |arxiv=1603.02196 |bibcode=2016ApJ...824L..22M |doi=10.3847/2041-8205/824/2/L22|s2cid=118422279 |doi-access=free }}</ref><ref>[https://www.youtube.com/watch?v=MptrypvBTag The Search for Planet 9] Talk by author Dr. Renu Malhotra, Public talk at TEDxPortland, Published on 17 July 2017</ref> is maintained by a similar evolution inside the mean-motion resonances.<ref name="Batygin_Morbidelli_2017" /><ref name="Beust_2016" /> The objects behavior is more complex if Planet Nine and the eTNOs are in inclined orbits. Objects then undergo a chaotic evolution of their orbits, but spend much of their time in the aligned or anti-aligned orbits regions of relative stability associated with [[Astronomy:Secular resonance|secular resonance]]s.<ref name="Saillenfest_etal_2017b">{{cite journal |last1=Saillenfest |first1=Melaine |last2=Fouchard |first2=Marc |last3=Tommei |first3=Giacomo |last4=Valsecchi |first4=Giovanni B. |title=Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth |journal=Celestial Mechanics and Dynamical Astronomy |volume=129 |issue=3 |pages=329 |date=2017 |arxiv=1707.01379 |doi=10.1007/s10569-017-9775-7 |bibcode=2017CeMDA.129..329S|s2cid=119010082 }}</ref>

==Evolution and long-term stability of anti-aligned orbits==

[[File:OrcusandPlutoRotatingFrame.gif|300px|thumb|right|An example of phase-protection in a mean-motion resonance: The orbital resonances of Orcus and Pluto in a rotating frame with a period equal to Neptune's orbital period. (Neptune is held stationary.)|alt=The orbits of Pluto and Orcus appear as blue and yellow spirals twisting around each other while within them the orbit of Neptune spins rapidly]]

The long term stability of anti-aligned extreme trans-Neptunian objects with orbits that intersect that of Planet Nine is due to their being captured in mean-motion resonances. Objects in mean-motion resonances with a massive planet are phase protected, preventing them from making close approaches to the planet. When the orbit of a resonant object drifts out of [[Physics:Phase (waves)|phase]],{{efn-ua|Formally this is defined by the resonant angle: <math> \Phi_{\rm res} = \rm k\cdot\lambda - \rm l\cdot\lambda_{\rm P} - (\rm k-\rm l)\cdot\varpi </math> where k and l are integers, λ and λ<sub>P</sub>} are the [[Astronomy:Mean longitude|mean longitude]]s of the object and the planet, and ϖ is the longitude of perihelion.<ref name="Batygin_Morbidelli_2017" />}} causing it to make [[Astronomy:Gravity assist#Explanation|closer approaches]] to a massive planet, the gravity of the planet [[Astronomy:Perturbation|modifies its orbit]], altering its semi-major axis in the direction that reverses the drift. This process repeats as the drift continues in the other direction causing the orbit to appear to rock back and forth, or librate, about a stable center when viewed in a rotating frame of reference.<ref name="Nesvorny_etal_2002">{{Cite journal |last1=Nesvorný |first1=D. |last2=Ferraz-Mello |first2=S. |last3=Holman |first3=M. |last4=Morbidelli |first4=A. |title=Regular and Chaotic Dynamics in the Mean-Motion Resonances: Implications for the Structure and Evolution of the Asteroid Belt |journal=Asteroids III |pages=379 |date=2002 |doi=10.2307/j.ctv1v7zdn4.31 |url=https://www.researchgate.net/publication/255606753|bibcode=2002aste.book..379N }}</ref><ref name="Batygin_Morbidelli_2017" /> In the example at right, when the orbit of a plutino drifts backward it loses angular momentum when it makes closer approaches ahead of Neptune,{{efn-ua|In a normal reference frame the plutino's orbit does not rock back and forth, instead when its period is greater than 3/2 that of Neptune it arrives later at perihelion when Neptune is closer.}} causing its semi-major axis and period to shrink, reversing the drift.<ref name="Cohen_Hubbard_1965">{{cite journal |last1=Cohen |first1=C. J. |last2=Hubbard |first2=E. C. |title=Libration of the close approaches of Pluto to Neptune |journal=Astronomical Journal |date=1965 |volume=70 |page=10 |doi=10.1086/109674 |bibcode=1965AJ.....70...10C|doi-access=free }}</ref>

In a simplified model where all objects orbit in the same plane and the giant planets are represented by rings,{{efn-ua|In this case a J2 quadrupolar gravitational moment is used to model the effects of the giant planets.}} objects captured in strong resonances with Planet Nine could remain in them for the lifetime of the Solar System. At large semi-major axes, beyond a 3:1 resonance with Planet Nine, most of these objects would be in anti-aligned orbits. At smaller semi-major axes the longitudes of perihelia of an increasing number of objects could circulate, passing through all values ranging from 0° to 360°, without being ejected,{{efn-ua|The resonant angle for the circulating objects is <math> \phi_{\rm res} = \rm k\cdot\lambda_{\rm P9} - \rm l\cdot\lambda - \varpi - (\rm k-\rm l-1)\cdot\varpi_{\rm P9} </math> i.e. <math> \phi_{\rm res} = \Phi_{\rm res} - \Delta\varpi</math>. As the resonant angle contains <math> \Delta\varpi </math> the resonant angle can librate while the object's perihelion circulates.}} reducing the fraction of objects that are anti-aligned.<ref name="Batygin_Morbidelli_2017" /><ref name="find_planet_nine_theory" /> {{mpl|2015 GT|50}} may be in one of these circulating orbits.<ref name="Status update 1">{{cite web |last1=Batygin |first1=Konstantin |title=Status Update (Part 1) |url=http://www.findplanetnine.com/2017/06/status-update-part-1.html |website=The Search for Planet Nine |accessdate=18 November 2017}}</ref>

If this model is modified with Planet Nine and the eTNOs in inclined orbits the objects alternate between extended periods in stable resonances and periods of chaotic diffusion of their semi-major axes. The distance of the closest approaches varies with the inclinations and orientations of the orbits, in some cases weakening the phase protection and allowing close encounters. The close encounters can then alter the eTNO's orbit, producing [[Stochastic|stochastic]] jumps in its semi-major axis as it hops between resonances, including higher order resonances. This results in a [[Random walk|chaotic diffusion]] of an object's semi-major axis until it is captured in a new stable resonance and the secular effects of Planet Nine shift its orbit to a more stable region.<ref name="Batygin_Morbidelli_2017" /><ref name="find_planet_nine_theory" /> The chaotic diffusion reduces the range of longitudes of perihelion that anti-aligned objects can reach while remaining in stable orbits.<ref name="Khain_etal_2018" />

Neptune's gravity can also drive a chaotic diffusion of semi-major axes when all objects are in the same plane.<ref name=TAJ201601 /> Distant encounters with Neptune can alter the orbits of the eTNOs, causing their semi-major axes to vary significantly on million year timescales.<ref name="trujillo20160912">{{cite journal |last1=Sheppard, Scott S. |first1=Scott S. |last2=Trujillo |first2=Chadwick |title=New Extreme Trans-Neptunian Objects: Toward a Super-Earth in the Outer Solar System |journal=The Astronomical Journal |date=2016 |volume=152 |issue=6 |page=221 |doi=10.3847/1538-3881/152/6/221 |arxiv=1608.08772 |bibcode=2016AJ....152..221S |s2cid=119187392 |doi-access=free }}</ref> These perturbations can cause the semi-major axes of the anti-aligned objects to diffuse chaotically while occasionally sticking in resonances with Planet Nine. At semi-major axes larger than Planet Nine's, where the objects spend more time, anti-alignment may be due to the secular effects outside mean-motion resonances.<ref name="Hadden_etal_2017">{{Cite journal|last1=Hadden|first1=Sam|last2=Li|first2=Gongjie|last3=Payne|first3=Matthew J.|last4=Holman|first4=Matthew J.|title=Chaotic Dynamics of Trans-Neptunian Objects Perturbed by Planet Nine|journal=The Astronomical Journal|volume=155|issue=6|pages=249|year=2017|arxiv=1712.06547|doi=10.3847/1538-3881/aab88c|bibcode=2018AJ....155..249H|s2cid=54038575 |doi-access=free }}</ref>

The phase protection of Planet Nine's resonances stabilizes the orbits of objects that interact with Neptune via its resonances, for example {{mpl|2013 FT|28}}, or by close encounters for objects with low perihelia like {{mpl|2007 TG|422}} and {{mpl|2013 RF|98}}.<ref name="trujillo20160912" /> Instead of being ejected following a series of encounters these objects can hop between resonances with Planet Nine and evolve into orbits no longer interacting with Neptune.<ref name="Becker_etal_2017">{{cite journal |last1=Becker |first1=Juliette C. |last2=Adams |first2=Fred C. |last3=Khain |first3=Tali |last4=Hamilton |first4=Stephanie J. |last5=Gerdes |first5=David |title=Evaluating the Dynamical Stability of Outer Solar System Objects in the Presence of Planet Nine |journal=The Astronomical Journal |date=2017 |volume=154 |issue=2 |page=61 |doi=10.3847/1538-3881/aa7aa2 |arxiv=1706.06609 |bibcode=2017AJ....154...61B|s2cid=111384673 |doi-access=free }}</ref><ref name=newevidenceP9>{{cite web
|url=https://cosmosmagazine.com/space/new-evidence-for-the-mysterious-planet-nine
|title=New evidence for the mysterious Planet Nine
|date=18 October 2017
|quote="Sedna itself is in a stable orbit, but others are on orbits so easily affected by Neptune that they should have been knocked out of orbit. Interactions with Planet Nine dampen the effect of Neptune's occasional gravitational kicks. Instead of getting kicked out of the Solar System it hops to a new orbit, Planet Nine enhances the dynamic stability of these objects."
}}</ref> A shift in the position of Planet Nine in simulations from the location favored by an analysis of Cassini data to a position near aphelion has been shown to increase the stability of some of the observed objects, possibly due to this shifting the phases of their orbits to a stable range.<ref name=n-body>{{cite journal |last1=de la Fuente Marcos |first1=Carlos |last2=de la Fuente Marcos |first2=Raúl |last3=Aarseth |first3=Sverre J. |year=2016 |title=Dynamical impact of the Planet Nine scenario: ''N''-body experiments |journal=Monthly Notices of the Royal Astronomical Society Letters |volume=460 |issue=1 |pages=L123–L127 |arxiv=1604.06241 |bibcode=2016MNRAS.460L.123D |doi=10.1093/mnrasl/slw078}}</ref><ref name="n-body_phys.org">{{cite web |title=Extreme trans-Neptunian objects lead the way to Planet Nine |url=https://phys.org/news/2016-06-extreme-trans-neptunian-planet.html 
|quote="If the ETNOs are transient, they are being continuously ejected and must have a stable source located beyond 1,000 astronomical units (in the Oort cloud) where they come from", notes Carlos de la Fuente Marcos. "But if they are stable in the long term, then there could be many in similar orbits although we have not observed them yet"
|website=Phys.org |accessdate=29 July 2017}}</ref>

==Clustering of orbital poles (nodal alignment)==

[[File:Tilting of Laplace Plane by Planet Nine.png|thumb|240px|Tilting of Laplace Plane by Planet Nine|alt=The orbit of Planet Nine is seen side-on with the orbit of the Solar System seen in the middle. Planet Nine's orbit is highly inclined compared to the Solar System. The orbital poles of the Solar System, Planet Nine, an extreme trans-Neptunian object, and the Laplace Plane are all shown, with the precessional circle for the eTNO plotted]]

The clustering of the orbital poles, which produces an apparent clustering of the longitude of the ascending nodes and arguments of perihelion of the extreme TNOs, is the result of a warping of the Laplace plane of the Solar System toward that of Planet Nine's orbit. The Laplace plane defines the center around which the pole of an object's orbit [[Physics:Precession|precesses]] with time. At larger semi-major axes the angular momentum of Planet Nine causes the Laplace plane to be warped toward that of its orbit.{{efn-ua|At smaller semi-major axes the Laplace Plane is close to the [[Astronomy:Invariable plane|invariable plane]] so the precession of the poles of typical Kuiper belt objects is unaffected by Planet Nine.}} As a result, when the poles of the eTNO orbit [[Astronomy:Axial precession|precess around]] the Laplace plane's pole they tend to remain on one side of the ecliptic pole. For objects with small inclination relative to Planet Nine, which were found to be more stable in simulations, this off-center precession produces a libration of the longitudes of ascending nodes with respect to the ecliptic making them appear clustered.<ref name="Batygin_Morbidelli_2017" /> In simulations the precession is broken into short arcs by encounters with Planet Nine and the positions of the poles are clustered in an off-center elliptical region.<ref name="score-card">{{cite web |last1=Brown |first1=Mike |title=Planet Nine: the score card |url=http://www.findplanetnine.com/2017/05/planet-nine-score-card.html |website=The Search for Planet Nine |accessdate=11 November 2017 |archive-date=13 June 2017 |archive-url=https://web.archive.org/web/20170613155333/http://www.findplanetnine.com/2017/05/planet-nine-score-card.html |url-status=dead }}</ref> In combination with the anti-alignment of the longitudes of perihelion this can also produce clustering of the arguments of perihelion.<ref name="Batygin_Morbidelli_2017" /> Node-crossings may also be avoided for enhanced stability.<ref name=nodes>{{cite journal |last1=de la Fuente Marcos |first1=Carlos |last2=de la Fuente Marcos |first2=Raúl |year=2017 |title=Evidence for a possible bimodal distribution of the nodal distances of the extreme trans-Neptunian objects: avoiding a trans-Plutonian planet or just plain bias? |journal=Monthly Notices of the Royal Astronomical Society Letters |volume=471 |issue=1 |pages=L61–L65 |arxiv=1706.06981 |bibcode=2017MNRAS.471L..61D |doi=10.1093/mnrasl/slx106}}</ref>

==Objects in perpendicular orbits with large semi-major axis==

[[File:Planet nine TNO orbits.svg|320px|thumb|The orbits of the five objects with high-inclination orbits (nearly perpendicular to the ecliptic) are shown here as cyan ellipses with the hypothetical Planet Nine in orange. Those of four are towards the left in this view, and that of one ({{mpl|2012 DR|30}}) is towards the right, with an aphelion over {{val|2000|u=AU|fmt=commas}}.|alt=Planet Nine's orbit is seen pointing towards the top, while the clustered comets are seen towards the bottom.]]

Planet Nine can deliver extreme trans-Neptunian objects into orbits roughly perpendicular to the plane of the Solar System.<ref name=extremeTech>{{cite web |last=Hruska |first=Joel |date=20 January 2016 |title=Our solar system may contain a ninth planet, far beyond Pluto |url=http://www.extremetech.com/extreme/221595-new-research-suggests-our-solar-system-may-contain-a-ninth-planet-far-beyond-pluto |website=[[ExtremeTech]] |accessdate=18 July 2016}}</ref><ref name=Siegel /> Several objects with high inclinations, greater than 50°, and large semi-major axes, above 250 AU, have been observed.<ref name="mpc-6" /> Their high inclination orbits can be generated by a high order secular resonance with Planet Nine involving a [[Linear combination|linear combination]] of the orbit's arguments and longitudes of perihelion: Δϖ - 2ω. Low inclination eTNOs can enter this resonance after first reaching low eccentricity orbits. The resonance causes their eccentricities and inclinations to increase, delivering them into perpendicular orbits with low perihelia where they are more readily observed. The orbits then evolve into [[Astronomy:Retrograde and prograde motion|retrograde]] orbits with lower eccentricities after which they pass through a second phase of high eccentricity perpendicular orbits before returning to low eccentricity, low inclination orbits. Unlike the Kozai mechanism this resonance causes objects to reach their maximum eccentricities when in nearly perpendicular orbits. In simulations conducted by Batygin and Brown this evolution was relatively common, with 38% of stable objects undergoing it at least once.<ref name="Batygin_Morbidelli_2017" /> Saillenfest et al. also observed this behavior in their study of the secular dynamics of eTNOs and noted that it caused the perihelia to fall below 30 AU for objects with semi-major axes greater than 300 AU, and with Planet Nine in an inclined orbit it could occur for objects with semi-major axes as small as 150 AU.<ref name="Saillenfest_etal_2017b" /> In simulations the arguments of perihelion of the objects with roughly perpendicular orbits and reaching low perihelia are clustered near or opposite Planet Nine's and their longitudes of ascending node are clustered around 90° in either direction from Planet Nine's.<ref name="Li_etal_2018">{{cite journal |last1=Li |first1=Gongjie |last2=Hadden |first2=Samuel |last3=Payne |first3=Matthew |last4=Holman |first4=Mathew J. |title=The Secular Dynamics of TNOs and Planet Nine Interactions |journal=The Astronomical Journal |volume=156 |issue=6 |pages=263 |date=2018 |arxiv=1806.06867|doi=10.3847/1538-3881/aae83b |bibcode=2018AJ....156..263L |s2cid=118898729 |doi-access=free }}</ref><ref name=TAJ201601 /> This is in rough agreement with observations with the differences attributed to distant encounters with the known giant planets.<ref name=TAJ201601 /> Nine high inclination objects with semi-major axes greater than 250 AU and perihelia beyond Jupiter's orbit are currently known:

{| class="wikitable sortable" style="text-align:center"
|+ High-inclination trans-Neptunian objects with a semi-major axis greater than {{val|250|u=AU}}<ref name=TAJ201601 /><ref name="Batygin_Morbidelli_2017" /><ref>{{cite web |title=MPC list of ''q'' > 5.2 and ''a'' > 250, and ''i'' > 60 |url=http://minorplanetcenter.net/db_search/show_by_properties?perihelion_distance_min=5.2&semimajor_axis_min=250&inclination_min=60 |publisher=[[Organization:Minor Planet Center|Minor Planet Center]] |accessdate=19 November 2017}}</ref>
!rowspan=2|Object||colspan=6|Orbit||colspan=2|Body
|-
![[Astronomy:Perihelion and aphelion|Perihelion]]<br />(AU)<br /><small>Figure 9</small><ref name=TAJ201601 />|||Semimaj.<br />(AU)<br /><small>Figure 9</small><ref name=TAJ201601 />||Current<br />distance<br />from Sun<br />(AU)||inc<br />(°)<ref name=mpc-6>{{cite web |title=MPC list of ''a'' > 250, ''i'' > 40, and ''q'' > 6 |url=http://minorplanetcenter.net/db_search/show_by_properties?semimajor_axis_min=250&inclination_min=40&perihelion_distance_min=6 |publisher=[[Organization:Minor Planet Center|Minor Planet Center]]}}</ref>||[[Astronomy:Orbital eccentricity|Eccen.]]||Arg. peri ω<br />(°)||[[Astronomy:Apparent magnitude|Mag.]]|| Diam.<br />(km)
|-
!{{mpl-|336756|2010 NV|1}}
|| 9.4 || 323 || 14 || 141 || 0.97 || 133 || 22 || 20–45
|-
!{{mpl-|418993|2009 MS|9}}
|| 11.1 || 348 || 12 || 68 || 0.97 || 129 || 21 || 30–60
|-
!{{mpl-|523719|2014 LM|28}}
|| 16.8 || 268 || 17 || 85 || 0.94 || 38 || 22 || 46
|-
!{{mpl|2010 BK|118}}
|| 6.3 || 484 || 11 || 144 || 0.99 || 179 || 21 || 20–50
|-
!{{mpl|2013 BL|76}}
|| 8.5 || 1,213 || 11 || 99 || 0.99 || 166 || 21.6 || 15–40
|-
!{{mpl|2012 DR|30}}
|| 14 || 1,404 || 17 || 78 || 0.99 || 195 || 19.6 || 185<ref name=Kiss2013>{{cite journal |last1=Kiss |first1=Cs. |last2=Szabó |first2=Gy. |last3=Horner |first3=J. |last4=Conn |first4=B. C. |last5=Müller |first5=T. G. |last6=Vilenius |first6=E. |last7=Sárneczky |first7=K. |last8=Kiss |first8=L. L. |last9=Bannister |first9=M. |last10=Bayliss |first10=D. |last11=Pál |first11=A. |last12=Góbi |first12=S. |last13=Verebélyi |first13=E. |last14=Lellouch |first14=E. |last15=Santos-Sanz |first15=P. |last16=Ortiz |first16=J. L. |last17=Duffard |first17=R. |last18=Morales |first18=N. |title=A portrait of the extreme solar system object {{mp|2012 DR|30}} |journal=Astronomy and Astrophysics |date=2013 |volume=555 |pages=A3 |doi=10.1051/0004-6361/201321147 |arxiv=1304.7112 |bibcode=2013A&A...555A...3K |s2cid=54021504 }}</ref>
|-
!{{mpl|2015 BP|519}}
|| 35.3 || 449 || 53 || 54 || 0.92 || 348 || 21.5 || 550
|-
!{{mpl-|582301|2015 RM|306}}
|| 11.5 || 255 || 12 || 176 || 0.96 || 44 || 23 || 15–35
|-
!{{mp|2020 YR|3}}
|| 16.5 || 536 || 18 || 169 || 0.97 || 155 || 22 || 35–80
|}

==Dynamically coherent bodies and disrupted binaries==

The presence of one or more massive perturbers orbiting the Sun well beyond Pluto may lead to the appearance of dynamically coherent minor bodies, i.e. those with similar orbits within a population of otherwise uncorrelated objects, via binary dissociation.<ref name="binary_disruption_paper">{{cite journal |title=Binary stripping as a plausible origin of correlated pairs of extreme trans-Neptunian objects |first1=C. |last1=de la Fuente Marcos |first2=R. |last2=de la Fuente Marcos |first3=S. J. |last3=Aarseth |date=1 November 2017 |journal=[[Physics:Astrophysics and Space Science|Astrophysics and Space Science]] |volume=362 |issue=11 |pages=198 |arxiv=1709.06813 |bibcode=2017Ap&SS.362..198D |doi=10.1007/s10509-017-3181-1 |s2cid=118890903 }}</ref> The fact is that dynamically correlated minor bodies seem to be ubiquitous among those in the outer Solar System.<ref name=pairs>{{cite journal |last1=de la Fuente Marcos |first1=Carlos |last2=de la Fuente Marcos |first2=Raúl |title=Dynamically correlated minor bodies in the outer Solar system |journal=[[Organization:Monthly Notices of the Royal Astronomical Society|Monthly Notices of the Royal Astronomical Society]] |date=11 February 2018 |volume=474 |issue=1 |arxiv=1710.07610 |doi=10.1093/mnras/stx2765 |pages=838–846 |bibcode = 2018MNRAS.474..838D }}</ref> A well-known example is in the Haumea collisional family.<ref name="BrownBarkume2007">{{cite journal |last=Brown |first=Michael E. |author2=Barkume, Kristina M. |author3=Ragozzine, Darin |author4= Schaller, Emily L.  |date=2007 |title=A collisional family of icy objects in the Kuiper belt |journal=Nature |volume=446 |issue=7133 |pages=294–296 |doi=10.1038/nature05619 |pmid=17361177 |bibcode = 2007Natur.446..294B |s2cid=4430027 |url=https://authors.library.caltech.edu/34346/2/nature05619-s1.pdf }}</ref> Another, albeit less-studied case is that of Chiang's collisional family.<ref name=chiang>{{cite journal |last1=Chiang |first1=E.~I. |title=A Collisional Family in the Classical Kuiper Belt |journal=[[Astronomy:The Astrophysical Journal|The Astrophysical Journal]] |date=July 2002 |volume=573 |issue=1 |arxiv=astro-ph/0205275 |doi=10.1086/342089  |pages=L65–L68 |bibcode = 2002ApJ...573L..65C |s2cid=18671789 }}</ref> At least one pair of extreme trans-Neptunian objects, the one made of [[Astronomy:474640 Alicanto|474640 Alicanto]] and {{mpl|2013 RF|98}}, exhibit both similar dynamics and physical properties.<ref name="spectroscopy">{{Cite journal |first1=Julia |last1=de León |first2=Carlos |last2=de la Fuente Marcos |last3=de la Fuente Marcos |first3=Raúl |year=2017 |title=Visible spectra of (474640) 2004 VN112-2013 RF98 with OSIRIS at the 10.4 m GTC: evidence for binary dissociation near aphelion among the extreme trans-Neptunian objects |journal=Monthly Notices of the Royal Astronomical Society: Letters |volume=467 |issue=1 |pages=L66–L70 |arxiv=1701.02534 |bibcode=2017MNRAS.467L..66D |doi=10.1093/mnrasl/slx003}}</ref> If there are no massive planets beyond Pluto, the orbits of the ETNOs must be randomized and the statistical distributions of some of their angular elements should be compatible with a uniform distribution. This has interesting implications on what it should and should not be observed when exploring the relationships between the orbits of the ETNOs. Favorable evidence is now mounting on the statistically significant deviations of the distribution of mutual nodal distances for this population.<ref name=nodes-2021>{{cite journal |last1=de la Fuente Marcos |first1=Carlos |last2=de la Fuente Marcos |first2=Raúl |year=2021 |title=Peculiar orbits and asymmetries in extreme trans-Neptunian space |journal=[[Organization:Monthly Notices of the Royal Astronomical Society|Monthly Notices of the Royal Astronomical Society]] |url=https://academic.oup.com/mnras/article-abstract/506/1/633/6307523|volume=506 |issue=1 |pages=633–649 |arxiv=2106.08369 |bibcode=2021MNRAS.506..633D |doi=10.1093/mnras/stab1756|date=1 September 2021  }}</ref><ref name=nodes-2022>{{cite journal |last1=de la Fuente Marcos |first1=Carlos |last2=de la Fuente Marcos |first2=Raúl |title=Twisted extreme trans-Neptunian orbital parameter space: statistically significant asymmetries confirmed |journal=Monthly Notices of the Royal Astronomical Society Letters |url=https://academic.oup.com/mnrasl/article-abstract/512/1/L6/6524836 |volume=512 |issue=1 |pages=L6–L10 |arxiv=2202.01693 |bibcode=2022MNRAS.512L...6D |doi=10.1093/mnrasl/slac012 |date=1 May 2022}}</ref> Such asymmetries are expected if massive perturbers (one or more) are present.

==Oort cloud and comets==

Numerical simulations of the migration of the giant planets show that the number of objects captured in the Oort cloud is reduced if Planet Nine was in its predicted orbit at that time.<ref name="Nesvorny_etal_2017" /> This reduction of objects captured in the [[Astronomy:Oort cloud|Oort cloud]] also occurred in simulations with the giant planets on their current orbits.<ref name="Lawler_etal_2016" />

The inclination distribution of Jupiter-family (or ecliptic) [[Astronomy:Comet|comet]]s would become broader under the influence of Planet Nine. [[Astronomy:Comet#Short period|Jupiter-family comets]] originate primarily from the scattering objects, trans-Neptunian objects with semi-major axes that vary over time due to distant encounters with Neptune. In a model including Planet Nine, the scattering objects that reach large semi-major axes dynamically interact with Planet Nine, increasing their inclinations. As a result, the population of the scattering objects, and the population of comets derived from it, is left with a broader inclination distribution. This inclination distribution is broader than is observed, in contrast to a five-planet Nice model without a Planet Nine that can closely match the observed inclination distribution.<ref name="Nesvorny_etal_2017" /><ref name="Gibbs_IEEE" />

In a model including Planet Nine, part of the population of [[Astronomy:Comet#Short period|Halley-type comets]] is derived from the cloud of objects that Planet Nine dynamically controls. This Planet Nine cloud is made up of objects with semi-major axes centered on that of Planet Nine that have had their perihelia raised by the gravitational influence of Planet Nine. The continued dynamical effects of Planet Nine drive oscillations of the perihelia of these objects, delivering some of them into planet-crossing orbits. Encounters with the other planets can then alter their orbits, placing them in low-perihelion orbits where they are observed as comets. The first step of this process is slow, requiring more than 100 million years, compared to comets from the Oort cloud, which can be dropped into low-perihelion orbits in one period. The Planet Nine cloud contributes roughly one-third of the total population of comets, which is similar to that without Planet Nine due to a reduced number of Oort cloud comets.<ref name="Nesvorny_etal_2017" />

==Notes==
{{notelist-ua}}

==References==
{{reflist|30em|refs=
<ref name="TAJ201601">{{cite journal |last1=Batygin |first1=Konstantin |last2=Brown |first2=Michael E. |author-link2=Michael E. Brown |date=2016 |title=Evidence for a distant giant planet in the Solar system |journal=[[Astronomy:The Astronomical Journal|The Astronomical Journal]] |volume=151 |issue=2 |page=22 |arxiv=1601.05438 |bibcode=2016AJ....151...22B |doi=10.3847/0004-6256/151/2/22 |s2cid=2701020 |doi-access=free }}</ref>

<ref name="Siegel">{{cite web |last1=Siegel |first1=Ethan |date=20 January 2016 |title=Not So Fast: Why There Likely Isn't A Large Planet Beyond Pluto |url=https://www.forbes.com/sites/startswithabang/2016/01/20/not-so-fast-why-there-likely-isnt-a-large-planet-beyond-pluto/#749e30245af4 |website={{wipe|Forbes}} |accessdate=22 January 2016}}</ref>

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<ref>{{cite news |last1=Siegel |first1=Ethan |date=3 November 2015 |title=Jupiter May Have Ejected A Planet From Our Solar System |url=https://www.forbes.com/sites/startswithabang/2015/11/03/leading-theory-for-how-the-solar-system-formed-just-disproved/ |work={{wipe|Forbes}} |accessdate=22 January 2016}}</ref>-->

<ref name="Nesvorny_etal_2017">{{cite journal |last1=Nesvorny |first1=D. |last2=Vokrouhlicky |first2=D. |last3=Dones |first3=L. |last4=Levison |first4=H. F. |last5=Kaib |first5=N. |last6=Morbidelli |first6=A. |journal=The Astrophysical Journal |volume=845 |issue=1 |pages=27 |title=Origin and Evolution of Short-Period Comets |arxiv=1706.07447 |date=2017 |doi=10.3847/1538-4357/aa7cf6 |bibcode=2017ApJ...845...27N|s2cid=119399322 |doi-access=free }}</ref>

<ref name="Lawler_etal_2016">{{cite journal |last1=Lawler |first1=S. M. |last2=Shankman |first2=C. |last3=Kaib |first3=N. |last4=Bannister |first4=M. T. |last5=Gladman |first5=B. |last6=Kavelaars |first6=J. J. |origyear=21 May 2016 |title=Observational Signatures of a Massive Distant Planet on the Scattering Disk |journal=The Astronomical Journal |date=29 December 2016 |volume=153 |issue=1 |pages=33 |bibcode=2017AJ....153...33L |doi=10.3847/1538-3881/153/1/33 |arxiv=1605.06575|s2cid=54854087 |doi-access=free }}</ref>

<ref name="Gibbs_IEEE">{{cite web |last1=Gibbs |first1=W. Wayt |title=Is There a Giant Planet Lurking Beyond Pluto? |url=https://spectrum.ieee.org/aerospace/satellites/is-there-a-giant-planet-lurking-beyond-pluto |website=IEEE Spectrum |accessdate=1 August 2017}}</ref>
}}



[[Category:Solar System]]
[[Category:Hypothetical planets]]
[[Category:Hypothetical trans-Neptunian objects]]

{{Sourceattribution|Effects of Planet Nine on trans-Neptunian objects}}