User:Agmartin/sandbox

A five-planet Nice model
The following is a version of the five-planet Nice model that results in an early instability and reproduces a number of aspects of the current Solar System. Although in the past the giant planet instability has been linked to the Late Heavy Bombardment, a number of recent studies indicate that the giant planet instability occurred early. The Solar System may have begun with the giant planets in another resonance chain.

The Solar System ends its nebula phase with Jupiter, Saturn, and the three ice giants in a 3:2, 3:2, 2:1, 3:2 resonance chain with semi-major axes ranging from 5.5 – 20 AU. A dense disk of planetesimals orbits beyond these planets, extending from 24 AU to 30 AU. The planetesimals in this disk are stirred due to gravitational interactions between them, increasing the eccentricities and inclinations of their orbits. The disk spreads as this occurs, pushing its inner edge toward the orbits of the giant planets. Collisions between planetesimals in the outer disk also produce debris that is ground to dust in a cascade of collisions. The dust spirals inward toward the planets due to Poynting-Robertson drag and eventually reaches Neptune's orbit. Gravitational interactions with the dust or with the inward scattered planetesimals scattered inward allow the giant planets to escape from the resonance chain roughly ten million years after the dissipation of the gas disk.

The planets then undergo a planetesimal-driven migration as Neptune encounters and exchanges angular momentum with an increasing number of planetesimals. A net inward transfer of planetesimals and outward migration of Neptune occur during these encounters as most of those scattered outward return to be encountered again while some of those scattered inward are prevented from returning after encountering Uranus. A similar process occurs for Uranus, the extra ice giant, and Saturn resulting in their outward migration and a transfer of planetesimals inward from the outer belt to Jupiter. Jupiter, in contrast, ejects most of the planetesimals from the Solar System, and as a result migrates inward. After 10 million years the divergent migration of the planets leads to resonance crossings, exciting the eccentricities of the giant planets and destabilizing the planetary system when Neptune is near 28 AU.

During this instability the extra ice giant enters a Saturn-crossing orbit and is scattered inward by Saturn onto a Jupiter-crossing orbit. Repeated gravitational encounters with the ice giant cause jumps in Jupiter's and Saturn's semi-major axes, driving a step-wise separation of their orbits, leading to a rapid increase of the ratio of their periods until it is greater than 2.3. The ice giant also encounters Uranus and Neptune and crosses parts of the asteroid belt as these encounters increase the eccentricity and semi-major axis of its orbit. After 10,000–100,000 years, the ice giant is ejected from the Solar System following an encounter with Jupiter, becoming a rogue planet. The remaining planets then continue to migrate at a declining rate and slowly approach their final orbits as most of the remaining planetesimal disk is removed.

Planet Nine is a hypothetical planet in the outer region of the Solar System. Its gravity could explain the unlikely clustering of orbits for a group of extreme trans-Neptunian objects (eTNOs), bodies that orbit beyond Neptune with average distances greater than 250 AU. These eTNOs tend to have their points of closest approach to the Sun clustered in one direction, and many of their orbits are similarly tilted. This evidence suggests that the gravity from a large undiscovered object is influencing the orbits of the most distant known Solar System objects.

This undiscovered super-Earth-sized planet would have an estimated mass of ten Earths, a diameter two to four times that of Earth, and an elongated orbit lasting 10,000–20,000 years. Batygin and Brown suggest that Planet Nine could be the core of a primordial giant planet that was ejected from its original orbit by Jupiter during the genesis of the Solar System. Others have proposed that the planet was captured from another star, is a captured rogue planet, or that it formed on a distant orbit and was pulled into an eccentric orbit by a passing star. As of 2019, efforts have failed to directly observe Planet Nine.

History
Following the discovery of the planet Neptune in 1846, there was considerable speculation that another planet might exist beyond its orbit. The Planet Nine hypothesis predicts a specific planet of a certain size and with certain orbital characteristics that are different from past theories.

Attempts to detect planets beyond Neptune by indirect means such as orbital perturbation date back to before the discovery of Pluto. George Forbes was the first to postulate the existence of trans-Neptunian planets in 1880, and his work is considered similar to more recent Planet Nine theories. In Forbes's model the planet had a semi-major axis of ∼300 AU (an orbit where the average radius is three hundred times the distance from Earth to the Sun); locations were based on clustering of the aphelion distances of periodic comets.

The discovery of Sedna with its peculiar orbit in 2004 led to the conclusion that something beyond the known eight planets had perturbed Sedna away from the Kuiper belt. That object could have been an unknown planet on a distant orbit, a member of the open cluster that formed with the Sun, or another star that later passed near the Solar System. The announcement in March 2014 of the discovery of a second sednoid, further raised the possibility of an unseen super-Earth in a large orbit.

At a conference in 2012 Rodney Gomes proposed that an undetected planet was responsible for the orbits of some trans-Neptunian objects with detached orbits and the large semi-major axis centaurs. This Neptune-massed planet in a distant, eccentric, and inclined orbit (a=1500 AU, e=0.4, i=40°), would cause the perihelia of objects with semi-major axes greater than 300 AU to oscillate, delivering some into planet-crossing orbits and others into detached orbits like that of Sedna. In 2015 an article by Gomes, Soares, and Brasser was published detailing their arguments.

In 2014 astronomers Chad Trujillo and Scott S. Sheppard noted the similarities in the orbits of Sedna and and several other extreme trans-Neptunian objects. They proposed that an unknown planet in a circular orbit between 200 and 300 AU was perturbing their orbits. Later, in 2015, Raúl and Carlos de la Fuente Marco argued that two massive planets in orbital resonance were necessary to produce the similarities of so many orbits.

In early 2016, Caltech's Konstantin Batygin and Michael E. Brown described how the similar orbits of six TNOs could be explained by Planet Nine and proposed a possible orbit for the planet. This hypothesis could also explain TNOs with orbits perpendicular to the inner planets and others with extreme inclinations, as well as the tilt of the Sun's axis.

Orbit
Planet Nine is hypothesized to follow a highly elliptical orbit around the Sun with a period lasting 10,000–20,000 years. The planet's semi-major axis is estimated to be $1,200 AU$, roughly 20 times the distance from Neptune to the Sun, and its inclination to the ecliptic, the plane of the Earth's orbit, to be about $200 AU$. The high eccentricity of Planet Nine's orbit could bring it as close as $700 AU$ to the Sun at its perihelion and take it as far away as $0.6$ at its aphelion.

The aphelion, or farthest point from the Sun, would be in the general direction of the constellation of Taurus, whereas the perihelion, the nearest point to the Sun, would be in the general direction of the southerly areas of Serpens (Caput), Ophiuchus, and Libra.

Brown thinks that if Planet Nine is confirmed to exist, a probe could fly by it in as little as 20 years with a powered slingshot around the Sun.

Size and composition


The planet is estimated to have 10 times the mass of Earth, and a diameter of 26,000 to 52,000 km, or two to four times that of Earth. An object with the same diameter as Neptune has not been excluded by previous surveys in visible light. Infrared surveys by the Wide-field Infrared Survey Explorer (WISE) may have the capabilities to detect Planet Nine, depending upon its location and characteristics. Past surveys by WISE have not excluded the existence of Planet Nine, and a new survey ongoing since 2017 may yet find it.

Brown thinks that if Planet Nine exists, its mass is sufficient to clear its orbit of large bodies in 4.6 billion years (with possible exceptions for some combinations of semi-major axis and mass) and that its gravity dominates the outer edge of the Solar System, which is sufficient to make it a planet by current definitions. Jean-Luc Margot has also stated that Planet Nine satisfies his criteria and would qualify as a planet if and when it is detected.

Brown speculates that the predicted planet is most probably an ejected ice giant, similar in composition to Uranus and Neptune: a mixture of rock and ice with a small envelope of gas. In fact, if it once orbited the region of the gas/ice giants, the planet probably acquired an atmosphere of hydrogen and helium.

Origin
A number of possible origins for Planet Nine have been examined including its ejection from the neighborhood of the current giant planets, capture from another star, and in situ formation.

In their initial article, Batygin and Brown proposed that Planet Nine formed closer to the Sun and was ejected into a distant eccentric orbit following a close encounter with Jupiter or Saturn during the nebular epoch. The gravity of a nearby star, or drag from the gaseous remnants of the Solar nebula, then reduced the eccentricity of its orbit. This raised its perihelion, leaving it in a very wide but stable orbit beyond the influence of the other planets. Had it not been flung into the Solar System's farthest reaches, Planet Nine could have accreted more mass from the proto-planetary disk and developed into the core of a gas giant. Instead, its growth was halted early, leaving it with a mass lower, or somewhat lower, than that of Uranus and Neptune.

Dynamical friction from a massive belt of planetesimals could also enable Planet Nine's capture in a stable orbit. Recent models propose that a 60–130 Earth mass disk of planetesimals could have formed as the gas was cleared from the outer parts of the proto-planetary disk. As Planet Nine passed through this disk its gravity would alter the paths of the individual objects in a way that reduced Planet Nine's velocity relative to it. This would lower the eccentricity of Planet Nine and stablize its orbit. If this disk had a distant inner edge, 100–200 AU, a planet encountering Neptune would have a 20% chance of being captured in an orbit similar to that proposed for Planet Nine, with the observed clustering more likely if the inner edge is at 200 AU. Unlike the gas nebula the planetesimal disk is likely to be long lived, potentially allowing a later capture.

Planet Nine could have been captured from outside the Solar System during a close encounter between the Sun and another star. If a planet was in a distant orbit around this star, three-body interactions during the encounter could alter the planet's path, leaving it in a stable orbit around the Sun. A planet originating in a system without Jupiter-massed planets could remain in a distant eccentric orbit for a longer time, increasing its chances of capture. Although the odds of capture can be higher, a wider variety of orbits are possible, reducing the probability of a planet being captured in a relatively low inclination orbit to 1–2 percent. This process could also occur with rogue planets, but the likelihood of their capture is much smaller, with only 0.05% - 0.10% being captured in orbits similar to that proposed for Planet Nine.

An encounter with another star could also alter the orbit of a distant planet, shifting it from a circular to an eccentric orbit. The in situ formation of a planet at this distance would require a very massive and extensive disk, or the outward drift of solids in a dissipating disk forming a narrow ring from which the planet accreted over a billion years. If a planet formed at such a great distance while the Sun was in its original cluster, the probability of it remaining bound to the Sun in a highly eccentric orbit is roughly 10%. A previous article, however, reported that if the massive disk extended beyond 80 AU some objects scattered outward by Jupiter and Saturn would have been left in high inclination (inc > 50°), low eccentricity orbits which have not been observed.

Evidence
The gravitational influence of Planet Nine would explain five peculiarities of the Solar System:
 * the clustering of the orbits of extreme trans-Neptunian objects (eTNOs);
 * the high perihelia of objects like 90377 Sedna that are detached from Neptune's influence;
 * the high inclinations of extreme trans-Neptunian objects with orbits roughly perpendicular to the orbits of the eight known planets,
 * high-inclination trans-Neptunian objects with semi-major axis less than 100 AU;
 * and the obliquity, or tilt, of the Sun's axis six degrees relative to the orbital planes of the major planets.

Planet Nine was initially proposed to explain the clustering of orbits, via a mechanism that would also explain the high perihelia of objects like Sedna. Of Planet Nine's other effects, one was unexpected, the perpendicular objects, and the other two were found after further analysis. While other mechanisms have been offered for many of these peculiarities, the gravitational influence of Planet Nine is the only one that explains all five. However, the gravity of Planet Nine would also increase the inclinations of other objects that cross its orbit, leaving the short-period comets with a broader inclination distribution than is observed.

Observations: Orbital clustering among high perihelion objects
The clustering of the orbits of extreme trans-Neptunian objects was first described by Trujillo and Sheppard, who noted similarities between the orbits of Sedna and. Without the presence of Planet Nine, these orbits should be distributed randomly, without preference for any direction. Upon further analysis, Trujillo and Sheppard observed that the arguments of perihelion of 12 eTNOs with perihelia greater than $30 °$ and semi-major axes greater than $150 °$ were clustered near zero degrees, meaning that they rise through the ecliptic when they are closest to the sun. Trujillo and Sheppard proposed that this alignment was caused by a massive unknown planet beyond Neptune via the Kozai mechanism. For objects with similar semi-major axes the Kozai mechanism would confine their arguments of perihelion to near 0 or 180 degrees. This confinement allows objects with eccentric and inclined orbits to avoid close approaches to the planet because they would cross the plane of the planet's orbit at their closest and farthest points from the Sun, and cross the planet's orbit when they are well above or below its orbit. However, Trujillo and Sheppard's hypothesis about how the objects would be aligned by the Kozai mechanism has been supplanted by further analysis and evidence.

Batygin and Brown, looking to refute the mechanism proposed by Trujillo and Sheppard, also examined the orbits of the extreme trans-Neptunian objects. After eliminating the objects in Trujillo and Sheppard's original analysis that were unstable due to close approaches to Neptune or were affected by Neptune's mean-motion resonances, Batygin and Brown determined that the arguments of perihelion for the remaining six objects (namely Sedna,, , , , and ) were clustered around $6 kg$. This finding did not agree with how the Kozai mechanism would tend to align orbits with arguments of perihelion at 0° or 180°.

Batygin and Brown also found that the orbits of the six objects with semi-major axes greater than 250 AU and perihelia beyond 30 AU (namely Sedna,, , , , and ) were aligned in space with their perihelia in roughly the same direction, resulting in a clustering of their longitudes of perihelion, the location where they make their closest approaches to the Sun. The orbits of the six objects were also tilted with respect to that of the ecliptic and approximately coplanar, producing a clustering of their longitudes of ascending nodes, the directions where they each rise through the ecliptic. They determined that there was only a 0.007% likelihood that this combination of alignments was due to chance. These six objects had been discovered by six different surveys on six different telescopes. That made it less likely that the clumping might be due to an observation bias such as pointing a telescope at a particular part of the sky. The observed clustering should be smeared out in a few hundred million years due to the locations of the perihelia and the ascending nodes changing, or precessing, at differing rates due to their varied semi-major axes and eccentricities. This indicates that it could not be due to an event in the distant past, like a passing star, and is most likely being maintained by an object orbiting the Sun.

In a later article Trujillo and Sheppard noted a correlation between the longitude of perihelion and the argument of perihelion of the eTNOs with semi-major axes greater than 150 AU. Those with a longitude of perihelion of 0–120° have arguments of perihelion between 280–360°, and those with longitude of perihelion between 180&deg; and 340&deg; have arguments of perihelion between 0&deg; and 40&deg;. The statistical significance of this correlation was 99.99%. They suggested that the correlation is due to the orbits of these objects avoiding close approaches to a massive planet by passing above or below its orbit.

Simulations: Observed clustering reproduced, inference on Planet Nine orbit and mass
The clustering of the orbits of extreme trans-Neptunian objects and raising of their perihelia is reproduced in simulations that include Planet Nine. In simulations conducted by Batygin and Brown, swarms of objects with large semi-major axes that began with random orientations were sculpted into roughly collinear and coplanar groups of spatially confined orbits by a massive distant planet in a highly eccentric orbit. The objects perihelia tended to point in the same direction and the objects orbits tended to align in the same plane. Many of these objects entered high perihelion orbits like Sedna and, unexpectedly, some entered perpendicular orbits that Batygin and Brown later noticed had been previously observed.

Batygin and Brown found that the distribution of the orbits of the first six extreme trans-Neptunian objects was best reproduced in simulations using a planet in the following orbit:
 * semi-major axis a ≈ $700 AU$ (orbital period 7001.5=18,520 years)
 * eccentricity e ≈ 0.6, (perihelion ≈ $30 °$, aphelion ≈ $200 AU$)
 * inclination i ≈ 30° to the ecliptic
 * longitude of the ascending node Ω ≈ $1,200 AU$.
 * argument of perihelion ω ≈ 141° and longitude of perihelion ϖ = $30 AU$

These parameters for Planet Nine produce different simulated effects on trans-Neptunian objects. Objects with semi-major axis greater than 250 AU are strongly anti-aligned with Planet Nine, with perihelia opposite Planet Nine's perihelion. Objects with semi-major axes between 150 AU and 250 AU are weakly aligned with Planet Nine, with perihelia in the same direction as Planet Nine's perihelion. Little effect is found on objects with semi-major axes less than 150 AU.

Other possible orbits for Planet Nine were also examined, with semi-major axes between $150 AU$ and $318 °$, eccentricites up to 0.8, and a wide range of inclinations. These orbits yield varied results. Batygin and Brown found that orbits of the eTNOs were more likely have similar tilts if Planet Nine had a higher inclination, but anti-alignment also decreased. Simulations by Becker et al. showed that their orbits were more stable if Planet Nine had a smaller eccentricity, but that anti-alignment was more likely at higher eccentricities. Lawler et al. found that the population captured in orbital resonances with Planet Nine was smaller if it had a circular orbit, and that fewer objects reached high inclination orbits. Investigations by Cáceres et al. showed that the orbits of the eTNOs were better aligned if Planet Nine had a lower perihelion orbit, but its perihelion would need to be higher than 90 AU. While there are many possible combinations of orbital parameters and masses for Planet Nine, none of the alternative simulations have been better at predicting the observed alignment of objects in the Solar System. The discovery of additional distant Solar System objects may provide further support for, or refutation of, the Planet Nine hypothesis.

Dynamics: How Planet Nine modifies the orbits of extreme trans-Neptunian objects


Planet Nine modifies the orbits of extreme trans-Neptunian objects via a combination of effects. On very long timescales Planet Nine exerts a torque on the orbits of the eTNOs that varies with the alignment of their orbits with Planet Nine's. The resulting exchanges of angular momentum cause the perihelia to rise, placing them in Sedna-like orbits, and later fall, returning them to their original orbits after several hundred million years. The motion of their directions of perihelion also reverses when their eccentricities are small, keeping the objects anti-aligned, see blue curves on diagram, or aligned, red curves. 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 gravity of Neptune and the other giant planets, and the inclination of Planet Nine's orbit, weaken this protection. This results in a chaotic variation of semi-major axes as objects hop between resonances, including high order resonances such as 27:17, on million-year timescales. The mean-motion resonances may not be necessary for the survival of eTNOs if they and Planet Nine are both on inclined orbits, however. The orbital poles of the objects precess around, or circle, the pole of the Solar System's Laplace plane. At large semi-major axes the Laplace plane is warped toward the plane of Planet Nine's orbit. This causes orbital poles of the eTNOs on average to be tilted toward one side and their longitudes of ascending nodes to be clustered.

Objects in perpendicular orbits with large semi-major axis


Planet Nine can deliver extreme trans-Neptunian objects into orbits roughly perpendicular to the ecliptic. Several objects with high inclinations, greater than 50°, and large semi-major axes, above 250 AU, have been observed. These orbits are produced when some low inclination eTNOs enter a secular resonance with Planet Nine upon reaching low eccentricity orbits. The resonance causes their eccentricities and inclinations to increase, delivering the eTNOs into perpendicular orbits with low perihelia where they are more readily observed. The eTNOs then evolve into retrograde orbits with lower eccentricities, after which they pass through a second phase of high eccentricity perpendicular orbits, before returning to low eccentricity and inclination orbits. The secular resonance with Planet Nine involves a linear combination of the orbit's arguments and longitudes of perihelion: Δϖ - 2ω. Unlike the Kozai mechanism this resonance causes objects to reach their maximum eccentricities when in nearly perpendicular orbits. In simulations conducted by Batygin and Morbidelli this evolution was relatively common, with 38% of stable objects undergoing it at least once. The arguments of perihelion of these objects 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 when they reach low perihelia. This is in rough agreement with observations with the differences attributed to distant encounters with the known giant planets.

Orbits of high inclination objects
A population of high inclination trans-Neptunian objects with semi-major axes less than 100 AU may be generated by the combined effects of Planet Nine and the other giant planets. The extreme trans-Neptunian objects that enter perpendicular orbits have perihelia low enough for their orbits to intersect those of Neptune or the other giant planets. An encounter with one of these planets can lower an eTNO's semi-major axis to below 100 AU, where the object's orbits is no longer controlled by Planet Nine, leaving it on orbits like. The orbital distribution of the longest lived of these objects is nonuniform. Most have orbits with perihelia ranging from 5 AU to 35 AU and inclinations below 110 degree; beyond a gap with few objects are others with inclinations near 150 degrees and perihelia near 10 AU. Previously it was proposed that these objects originated in the Oort cloud.

Oort cloud and comets
Planet Nine alters the source regions and the inclination distribution of comets. In simulations of the migration of the giant planets described by the Nice model fewer objects are captured in the Oort cloud when Plane Nine is included. Other objects are captured in the Planet Nine cloud. This Planet Nine cloud, estimated to contain 0.3-0.4 Earth masses, is made up of the objects dynamically controlled by Planet Nine. It includes the eTNOs and the perpendicular objects and extends from semimajor axes of 250 AU to 3000 AU. When the perihelia of objects in this cloud drop low enough for them to encounter the other planets some are scattered into orbits the enter the inner Solar System where they are observed as comets. If Planet Nine exists these would make up roughly one third of the Halley-type comets. Planet Nine also alters the orbits of the scattering disk objects, those with semi-major axes greater than 50 AU and perihelia near Neptune's orbit, that cross its orbit, increasing their inclinations. This also increases the inclinations of the Jupiter-family comets derived from that population leaving them with a broader inclination distribution than is observed.

Solar obliquity
Planet Nine may be responsible for the Sun's obliquity, the tilt of its axis of rotation relative to the orbits of the planets. Models of the formation of the Solar System predict that the planets and the Sun should rotate in the same plane. However, the Sun's axis of rotation is tilted approximately six degrees from the orbital plane of the giant planets. Planet Nine could have produced the Sun's obliquity by exerting a torque on the orbits of the planets, causing their orbital planes to precess like spinning tops through short arcs. Planet Nine would be able to produce this precession because its orbit is tilted with respect to those of the other planets and because it has more angular momentum than the rest of the Solar System's planets combined due to its large semi-major axis. Analyses using analytical models and computer simulations conducted contemporaneously and independently by Bailey, Batygin and Brown; by Gomes, Deienno and Morbidelli; and later by Lai find that both the magnitude and direction of the tilt of the Sun's axis can be explained by the gravitational torques exerted by Planet Nine. These observations are consistent with the Planet Nine hypothesis but do not prove that Planet Nine exists as there are other potential explanations for the spin–orbit misalignment of the Solar System.

Reception
Batygin was cautious in interpreting the results of the simulation developed for his and Brown's research article, saying, "Until Planet Nine is caught on camera it does not count as being real. All we have now is an echo." Brown put the odds for the existence of Planet Nine at about 90%. Greg Laughlin, one of the few researchers who knew in advance about this article, gives an estimate of 68.3%. Other skeptical scientists demand more data in terms of additional KBOs to be analyzed or final evidence through photographic confirmation. Brown, though conceding the skeptics' point, still thinks that there is enough data to mount a search for a new planet.

Brown is supported by Jim Green, director of NASA's Planetary Science Division, who said, "the evidence is stronger now than it's been before". But Green also cautioned about the possibility of other explanations for the observed motion of distant TNOs and, quoting Carl Sagan, he said, "extraordinary claims require extraordinary evidence."

Tom Levenson concluded that, for now, Planet Nine seems the only satisfactory explanation for everything now known about the outer regions of the Solar System. Alessandro Morbidelli, who reviewed the research article for The Astronomical Journal, concurred, saying, "I don't see any alternative explanation to that offered by Batygin and Brown."

Renu Malhotra remains agnostic about Planet Nine, but noted that she and her colleagues have found that the orbits of extremely distant KBOs seem tilted in a way that is difficult to otherwise explain. "The amount of warp we see is just crazy," she said. "To me, it's the most intriguing evidence for Planet Nine I've run across so far."

American astrophysicist Ethan Siegel, who is deeply skeptical of the existence of an undiscovered planet in the Solar System, nevertheless speculates that at least one super-Earth, which have been commonly discovered in other planetary systems but have not been discovered in the Solar System, might have been ejected from the Solar System during a dynamical instability in the early Solar System. Planetary scientist Hal Levison thinks that the chance of an ejected object ending up in the inner Oort cloud is only about 2%, and speculates that many objects must have been thrown past the Oort cloud if one has entered a stable orbit.

Astronomers expect that the discovery of Planet Nine would aid in understanding the processes behind the formation of the Solar System and other planetary systems, as well as how unusual the Solar System is, with a lack of planets with masses between that of Earth and that of Neptune, compared to other planetary systems.

Temporary or coincidental nature of clustering
The results of the Outer Solar System Survey (OSSOS) suggest that the observed clustering is the result of a combination of observing bias and small number statistics. OSSOS, a well-characterized survey of the outer Solar System with known biases, observed eight trans-Neptunian objects with semi-major axis > 150 AU with orbits oriented on a wide range of directions. After accounting for the observational biases of the survey, no evidence for the arguments of perihelion (ω) clustering identified by Trujillo and Sheppard was seen, and the orientation of the orbits of the objects with the largest semi-major axis was statistically consistent with random. This result differs from an analysis of discovery biases in the previously observed eccentric trans-Neptunian objects by Mike Brown. He found that after observing biases were accounted for the clustering of longitudes of perihelion of the known objects would be observed only 1.2% of the time if their actual distribution was uniform. When combined with the odds of the observer of clustering of the arguments of perihelion the probability was 0.025%.

Simulations of 15 known extreme trans-Neptunian objects evolving under the influence of Planet Nine also revealed a number of differences with observations. Cory Shankman and his colleagues included Planet Nine in a simulation of a large number of clones (objects with similar orbits) of 15 objects with semi-major axis > 150 AU and perihelion > 30 AU. While they observed alignment of the orbits opposite that of Planet Nine's for the objects with semi-major axis greater than 250 AU, clustering of the arguments of perihelion was not seen. Their simulations also showed that the perihelia of the eTNOs rose and fell smoothly, leaving many with perihelion distances between 50 AU and 70 AU where none had been observed, and predicted that there would be many other unobserved objects. These included a large reservoir of high-inclination objects that would have been missed due to most observations being at small inclinations, and a large population of objects with perihelia so distant that they would be too faint to observe. Many of the objects were also ejected from the Solar System after encountering the other giant planets. The large unobserved populations and the loss of many objects led Shankman et al. to estimate that the mass of the original population was tens of Earth masses, requiring that a much larger mass had been ejected during the early Solar System. Shankman et al. concluded that the existence of Planet Nine is unlikely and that the currently observed alignment of the existing TNOs is a temporary phenomenon that will disappear as more objects are detected.

Inclination instability due to mass of undetected objects
Ann-Marie Madigan and Michael McCourt postulate that an inclination instability in a distant massive belt is responsible for the alignment of the arguments of perihelion of the eTNOs. An inclination instability could occur in a disk of particles with eccentric orbits around a central body, such as the Sun. The self-gravity of this disk would cause its spontaneous organization, increasing the inclinations of the objects and aligning the arguments of perihelion, forming it into a cone above or below the original plane. This process would require an extended time and significant mass of the disk, on the order of a billion years for a 1–10 Earth-mass disk. While an inclination instability could align the arguments of perihelion and raise perihelia, producing detached objects, it would not align the longitudes of perihelion. Mike Brown considers Planet Nine a more probable explanation, noting that current surveys have not revealed a large enough scattered-disk to produce an "inclination instability". In Nice model simulations of the Solar System that included the self-gravity of the planetesimal disk an inclination instability did not occur. Instead, the simulation produced a rapid precession of the objects' orbits and most of the objects were ejected on too short of a timescale for an inclination instability to occur.

Object in lower-eccentricity orbit
The Planet Nine hypothesis includes a set of predictions about the mass and orbit of the planet. An alternative theory predicts a planet with different orbital parameters. Malhotra, Kathryn Volk, and Xianyu Wang have proposed that the four detached objects with the longest orbital periods, those with perihelia beyond $700 AU$ and semi-major axes greater than $280 AU$, are in n:1 or n:2 mean-motion resonances with a hypothetical planet. Two other objects with semi-major axes greater than $1,120 AU$ are also potentially in resonance with this planet. Their proposed planet could be on a lower eccentricity, low inclination orbit, with eccentricity e < 0.18 and inclination i ≈ 11°. The eccentricity is limited in this case by the requirement that close approaches of to the planet are avoided. If the eTNOs are in periodic orbits of the third kind, with their stability enhanced by the libration of their arguments of perihelion, the planet could be in a higher inclination orbit, with i ≈ 48°. Unlike Batygin and Brown, Malhotra, Volk and Wang do not specify that most of the distant detached objects would have orbits anti-aligned with the massive planet.

Alignment due to the Kozai mechanism
Trujillo and Sheppard argued in 2014 that a massive planet in a distant, circular orbit was responsible for the clustering of the arguments of perihelion of twelve extreme trans-Neptunian objects. Trujillo and Sheppard identified a clustering near zero degrees of the arguments of perihelion of the orbits of twelve trans-Neptunian objects with perihelia greater than $94 °$ and semi-major axes greater than $94 °$. After numerical simulations showed that after billions of years the varied rates of precession should leave their perihelia randomized they suggested that a massive planet in a circular orbit at a few hundred astronomical units was responsible for this clustering. This massive planet would cause the arguments of perihelion of the eTNOs to librate about 0° or 180° via the Kozai mechanism so that their orbits crossed the plane of the planet's orbit near perihelion and aphelion, the closest and farthest points from the planet. In numerical simulations including a 2–15 Earth mass body in a circular low-inclination orbit between $235 °$ and $400 AU$ the arguments of perihelia of Sedna and librated around 0° for billions of years (although the lower perihelion objects did not) and underwent periods of libration with a Neptune mass object in a high inclination orbit at 1,500 AU. An additional process such as a passing star would be required to account for the absence of objects with arguments of perihelion near 180°.

These simulations showed the basic idea of how a single large planet can shepherd the smaller extreme trans-Neptunian objects into similar types of orbits. It was a basic proof of concept simulation that did not obtain a unique orbit for the planet as they state there are many possible orbital configurations the planet could have. Thus they did not fully formulate a model that successfully incorporated all the clustering of the extreme objects with an orbit for the planet. But they were the first to notice there was a clustering in the orbits of extremely distant objects and that the most likely reason was from an unknown massive distant planet. Their work is very similar to how Alexis Bouvard noticed Uranus' motion was peculiar and suggested that it was likely gravitational forces from an unknown 8th planet, which led to the discovery of Neptune.

Raúl and Carlos de la Fuente Marcos proposed a similar model but with two distant planets in resonance. An analysis by Carlos and Raúl de la Fuente Marcos with Sverre J. Aarseth confirmed that the observed alignment of the arguments of perihelion could not be due to observational bias. They speculated that instead it was caused by an object with a mass between that of Mars and Saturn that orbited at some $1,500 AU$ from the Sun. Like Trujillo and Sheppard they theorized that the eTNOs are kept bunched together by a Kozai mechanism and compared their behavior to that of Comet 96P/Machholz under the influence of Jupiter. However, they also struggled to explain the orbital alignment using a model with only one unknown planet. They therefore suggested that this planet is itself in resonance with a more-massive world about $40 AU$ from the Sun. In their article, Brown and Batygin noted that alignment of arguments of perihelion near 0° or 180° via the Kozai mechanism requires a ratio of the semi-major axes nearly equal to one, indicating that multiple planets with orbits tuned to the data set would be required, making this explanation too unwieldy.

Visibility and location
Due to its extreme distance from the Sun, Planet Nine would reflect little sunlight, potentially evading telescope sightings. It is expected to have an apparent magnitude fainter than 22, making it at least 600 times fainter than Pluto. If Planet Nine exists and is close to perihelion, astronomers could identify it based on existing images. At aphelion, the largest telescopes would be required. However, if the planet is currently located in between, many observatories could spot Planet Nine. Statistically, the planet is more likely to be closer to its aphelion at a distance greater than 500 AU. This is because objects move more slowly when near their aphelion, in accordance with Kepler's second law.

Searches of existing data
The search in databases of stellar objects performed by Batygin and Brown has already excluded much of the sky the predicted planet could be in, save the direction of its aphelion, or in the difficult to spot backgrounds where the orbit crosses the plane of the Milky Way, where most stars lie. This search included the archival data from the Catalina Sky Survey to magnitude c. 19, Pan-STARRS to magnitude 21.5, and infrared data from the WISE satellite.

David Gerdes who helped develop the camera used in the Dark Energy Survey claims that it is quite possible that one of the images taken for his galaxy map may actually contain a picture of Planet Nine, and if so, purpose-built software, which was used to identify objects such as, can help to find it.

Michael Medford and Danny Goldstein, graduate students at the University of California, Berkeley, are also examining archived data using a technique that combines multiple images, taken at different times. Using a supercomputer they will offset the images to account for the calculated motion of Planet Nine, allowing many faint images of a faint moving object to be combined to produce a brighter image.

A search combining multiple images collected by WISE and NEOWISE data has also been conducted without detecting Planet Nine. This search covered regions of the sky away from the galactic plane at the "W1" wavelength (the 3.4 μm wavelength used by WISE) and is estimated to be able to detect a 10 Earth mass object out to 800–900 AU.

Ongoing searches
Because the planet is predicted to be visible in the Northern Hemisphere, the primary search is expected to be carried out using the Subaru Telescope, which has both an aperture large enough to see faint objects and a wide field of view to shorten the search. Two teams of astronomers—Batygin and Brown, as well as Trujillo and Sheppard—are undertaking this search together, and both teams cooperatively expect the search to take up to five years. Brown and Batygin initially narrowed the search for Planet Nine down to roughly 2,000 square degrees of sky near Orion, a swath of space, that in Batygin's opinion, could be covered in about 20 nights by the Subaru Telescope. Subsequent refinements by Batygin and Brown have reduced the search space to 600–800 square degrees of sky. In December 2018, they spent 7 nights observing with the Subaru Telescope.

A zone around the constellation Cetus, where Cassini data suggest Planet Nine may be located, is being searched by the Dark Energy Survey—a project in the Southern Hemisphere designed to probe the acceleration of the Universe. DES observes about 105 nights per season, lasting from August to February.

Radiation
Although a distant planet such as Planet Nine would reflect little light, it would still be radiating the heat from its formation as it cools due to its large mass. At its estimated temperature of 47 K, the peak of its emissions would be at infrared wavelengths. This radiation signature could be detected by Earth-based submillimeter telescopes, such as ALMA, and a search could be conducted by cosmic microwave background experiments operating at mm wavelengths. Additionally, Jim Green of NASA's Science Mission Directorate is optimistic that it could be observed by the James Webb Space Telescope, the successor to the Hubble Space Telescope, that is expected to be launched in 2021.

Citizen science
The Zooniverse Backyard Worlds project, started in February 2017, is using archival data from the WISE spacecraft to search for Planet Nine. The project will additionally search for substellar objects like brown dwarfs in the neighborhood of the Solar System. 32,000 animations of four images each, which constitute 3 per cent of the WISE data has been uploaded to the Backyard World's website. By looking for moving objects in the animations, citizen scientists might find Planet Nine. In April 2017, using data from the SkyMapper telescope at Siding Spring Observatory, citizen scientists on the Zooniverse platform reported four candidates for Planet Nine. These candidates will be followed up on by astronomers to determine their viability. The project, which started on 28 March 2017, completed their goals in less than three days with around five million classifications by more than 60,000 individuals.

Search for additional extreme trans-Neptunian objects
Finding more eTNO's would allow astronomers to make more accurate predictions about the orbit of the hypothesized planet. The Large Synoptic Survey Telescope, when it is completed in 2023, will be able to map the entire sky in just a few nights, providing more data on distant Kuiper belt objects that could both bolster evidence for Planet Nine and help pinpoint its current location.

Batygin and Brown also predict a yet-to-be-discovered population of distant objects. These objects would have semi-major axes greater than $250 AU$, but they would have lower eccentricities and orbits that would be aligned with that of Planet Nine. The larger perihelia of these objects would make them fainter and more difficult to detect than the anti-aligned objects.

Cassini measurements of perturbations of Saturn
An analysis of Cassini data on Saturn's orbital residuals was inconsistent with Planet Nine being located with a true anomaly of −130° to −110° or −65° to 85°. The analysis, using Batygin and Brown's orbital parameters for Planet Nine, suggests that the lack of perturbations to Saturn's orbit is best explained if Planet Nine is located at a true anomaly of $150 AU$. At this location, Planet Nine would be approximately $221.59$ from the Sun, with right ascension close to 2h and declination close to −20°, in Cetus. In contrast, if the putative planet is near aphelion it could be moving projected towards the area of the sky with boundaries: right ascension 3.0h to 5.5h and declination −1° to 6°.

An improved mathematical analysis of Cassini data by astrophysicists Matthew Holman and Matthew Payne tightened the constraints on possible locations of Planet Nine. Holman and Payne developed a more efficient model that allowed them to explore a broader range of parameters than the previous analysis. The parameters identified using this technique to analyze the Cassini data was then intersected with Batygin and Brown's dynamical constraints on Planet Nine's orbit. Holman and Payne concluded that Planet Nine is most likely to be located within 20° of RA = 40°, Dec = −15°, in an area of the sky near the constellation Cetus.

The Jet Propulsion Laboratory has stated that according to their mission managers and orbit determination experts, the Cassini spacecraft is not experiencing unexplained deviations in its orbit around Saturn. William Folkner, a planetary scientist at JPL stated, "An undiscovered planet outside the orbit of Neptune, 10 times the mass of Earth, would affect the orbit of Saturn, not Cassini ... This could produce a signature in the measurements of Cassini while in orbit about Saturn if the planet was close enough to the Sun. But we do not see any unexplained signature above the level of the measurement noise in Cassini data taken from 2004 to 2016." Observations of Saturn's orbit neither prove nor disprove that Planet Nine exists. Rather, they suggest that Planet Nine could not be in certain sections of its proposed orbit because its gravity would cause a noticeable effect on Saturn's position, inconsistent with actual observations.

Analysis of Pluto's orbit
An analysis of Pluto's orbit by Matthew J. Holman and Matthew J. Payne found perturbations much larger than predicted by Batygin and Brown's proposed orbit for Planet Nine. Holman and Payne suggested three possible explanations: systematic errors in the measurements of Pluto's orbit; an unmodeled mass in the Solar System, such as a small planet in the range of 60–$4,268$ (potentially explaining the Kuiper cliff); or a planet more massive or closer to the Sun instead of the planet predicted by Batygin and Brown.

Optimal orbit if objects are in strong resonances
An analysis by Sarah Millholland and Gregory Laughlin indicates that the commensurabilities (period ratios consistent with pairs of objects in resonance with each other) of the extreme TNOs are most likely to occur if Planet Nine has a semi-major axis of 654 AU. They used 11 then-known extreme TNOs with their semi-major axis over 200, and perihelion over 30 AU, with five bodies close to four simple ratios (5:1, 4:1, 3:1, 3:2) with a 654 AU distance: , (5:1),  (5:1),  (4:1), , ,  (3:1), , , , and Sedna (3:2). Beginning with this semi-major axis they determine that Planet Nine best maintains the anti-alignment of their orbits and a strong clustering of arguments of perihelion if it is near aphelion and has an eccentricity e ≈ 0.5, inclination i ≈ 30°, argument of perihelion ω ≈ 150°, and longitude of ascending node Ω ≈ 50° (the last differs from Brown and Batygin's value of 90°). The favored location of Planet Nine is a right ascension of 30° to 50° and a declination of −20° to 20°. They also note that in their simulations the clustering of arguments of perihelion is almost always smaller than has been observed.

A previous analysis by Carlos and Raul de la Fuente Marcos of commensurabilities among the known eTNOs using Monte Carlo techniques revealed a pattern similar to that of the Kuiper belt, where accidental commensurabilities occur due to objects in resonances with Neptune. They find that this pattern would be best explained if the eTNOs were in resonance with an additional planetary-sized object beyond Pluto and note that a number of these objects may be in 5:3 and 3:1 resonances if that object had semi-major axis of ≈700 AU.

A later analysis by Elizabeth Bailey, Michael Brown and Konstantin Batygin found that if Planet Nine is in an eccentric and inclined orbit the capture of many of the eTNOs in higher order resonances and their chaotic transfer between resonances prevent the identification of Planet Nine's semi-major axis using current observations. They also determined that the odds of the first six objects observed being in N/1 or N/2 period ratios with Planet Nine are less than 5% if it is in an eccentric orbit.

Ascending nodes of objects with large semi-major axes
In an article by Carlos and Raul de la Fuente Marcos evidence is shown for a possible bimodal distribution of the distances to the ascending nodes of the extreme TNOs. This correlation is unlikely to be the result of observational bias since it also appears in the nodal distribution of centaurs and comets with large semi-major axes. If it is due to the extreme TNOs experiencing close approaches to Planet Nine, it is consistent with a planet with a semi-major axis of 300–400 AU.

Orbits of nearly parabolic comets
An analysis of the orbits of comets with nearly parabolic orbits identifies five new comets with hyperbolic orbits that approach the nominal orbit of Planet Nine described in Batygin and Brown's initial article. If these orbits are hyperbolic due to close encounters with Planet Nine the analysis estimates that Planet Nine is currently near aphelion with a right ascension of 83°–90° and a declination of 8°–10°. Scott Sheppard, who is skeptical of this analysis, notes that many different forces influence the orbits of comets.

Possible disrupted binary
Similarities between the orbits of and  have led to the suggestion that they were a binary object disrupted near aphelion during an encounter with a distant object. The visible spectra of and  are also similar but very different from that of Sedna. The value of their spectral slopes suggests that the surfaces of and  can have pure methane ices (like in the case of Pluto) and highly processed carbons, including some amorphous silicates. The disruption of a binary would require a relatively close encounter with Planet Nine, however, which becomes less likely at large distances from the Sun.

Naming
Planet Nine does not have an official name and will not receive one unless its existence is confirmed, typically through optical imaging. Once confirmed, the International Astronomical Union will certify a name, with priority usually given to a name proposed by its discoverers. It is likely to be a name chosen from Roman or Greek mythology.

In their original article, Batygin and Brown simply referred to the object as "perturber", and only in later press releases did they use "Planet Nine". They have also used the names "Jehoshaphat" and "George" for Planet Nine. Brown has stated: "We actually call it Phattie when we're just talking to each other."

In 2018, planetary scientist Alan Stern objected to the name Planet Nine, saying, "It is an effort to erase Clyde Tombaugh's legacy [the discovery of Pluto] and it's frankly insulting", suggesting the name Planet X until its discovery. A statement was signed by 35 scientists saying, "We further believe the use of this term [Planet Nine] should be discontinued in favor of culturally and taxonomically neutral terms for such planets, such as Planet X, Planet Next, or Giant Planet Five."