page_title: Effects of Planet Nine on trans-Neptunian objects
section_title: Apsidal anti-alignment
hierarchical_section_title: Effects of Planet Nine on trans-Neptunian objects / Apsidal anti-alignment
caption_attribution_description: English: The secular evolution of extreme transneptunian objects with semi-major axes of 250 AU under the influence of hypothetical Planet Nine. Green curves for meta-stable objects, red curves for aligned objects, blue curves for anti-aligned objects, orange curve for circulating objects. Arrows shows direction of evolution with time. Above black curve orbits intercept that of Planet Nine.
context_page_description: The hypothetical 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 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.
context_section_description: 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 torques on each other, causing exchanges of angular momentum but not energy. Thus secular effects can alter the eccentricities, inclinations and orientations of orbits but not the semi-major axes.
  Exchanges of angular momentum with Planet Nine cause the perihelia of the anti-aligned objects to rise and fall while their longitudes of perihelion librate, or 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 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.
  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. Aligned objects with lower perihelia are only temporarily stable, their orbits precess until parts of the orbits are tangent to that of Planet Nine, leading to frequent close encounters. After crossing this region the perihelia of their orbits decline, causing them to encounter the other planets, leading to their ejection.
  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. 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. 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, is maintained by a similar evolution inside the mean-motion resonances. 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 secular resonances.
caption: Secular evolution of eTNOs induced by Planet Nine for objects with semi-major axis of 250 AU.[2][1] Blue:anti-aligned, Red:aligned, Green:metastable, Orange:circulating. Crossing orbits above black line.[A]
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