The Planet Nine Hypothesis (Part 13)

 February 22, 2026

consider an upper limit to the mass of Planet Nine, the most distant acceptable orbit has a₉ = 800

AU, e₉ = 0.45, and an aphelion of 1160 AU. Such an object would have an aphelion magnitude between 23.0 and 24.0 (perihelion magnitude between 19.9 and 20.8).

Counterintuitively, a lower mass Planet Nine is brighter owing to its requirement for a smaller heliocentric distance to have the same dynamical effect. To this end, a 5 M_⊕ Planet Nine, for example, is bright enough to be detectable by wide-field surveys such as Pan-STARRS throughout most of its orbit. It is not yet known how complete the moving object search for Pan-STARRS is, but with the survey still ongoing a discovery

could in principle happen at any time. An important complication, however, lies in that the inferred aphelion of Planet Nine’s orbit is close to the intersection between P9’s orbital path and the galactic plane, where higher source density can impede detection (see Figure 25).

A higher mass and thus more distant Planet Nine will require a dedicated survey along the predicted orbital path (Brown and Batygin, 2016), but with a lower limit to the brightness of 24th magnitude, such an object is readily observable by the cur- rent generation of telescopes with wide field cameras such as the Dark Energy Camera on the Blanco 4m telescope in Chile and the Hyper-Suprime Camera on the Subaru telescope in Hawaii. Finally, all but the very faintest possible Planet Nine will be ob- servable with the Large Scale Synoptic Telescope (LSST), currently under construction in Chile and scheduled for operations in 2022. Therefore, Planet Nine – if it exists as described here – is likely to be discovered within a decade.

1. Infrared and Microwave Surveys

While detecting sunlight reflected at optical wavelengths might seem like the natu- ral method for searching for Planet Nine, the 1/r⁴ dependency of the flux of reflected sunlight makes the brightness of any object drop precipitously with distance. At long wavelengths, thermal emission, on the other hand, drops as only T /r², where T could be approximately constant with distance (or drop as 1/r² if the planet is in thermal equilibrium with the sun). For sufficiently distant planets, thermal emission constitutes a potentially preferable avenue towards direct detection. While current cosmological experiments at millimeter wavelengths have sufficient sensitivity to detect Planet Nine (Cowan et al., 2016), a systematic search would require millimeter telescopes with both high sensitivity and high angular resolution to robustly detect moving sources. The proposed CMB S-4, a next-generation cosmic microwave background experiment (Abazajian et al., 2016) could fulfill these requirements. Such an observatory would be sensitive not only to Planet Nine, but to putative even more distant bodies that might be present in the solar system.

It is worth noting that Planet Nine could emit more strongly than a blackbody at some wavelengths. Fortney et al. (2016) found that in extreme cases the atmosphere of Planet Nine could be depleted of methane and have order of magnitude more emis- sion in the 3-4 µm range. Meisner et al. (2017b) exploited this possibility to search for Planet Nine in data from the Wide-field Infrared Survey Explorer (WISE) dataset. In particular, they examined 3u steradians and placed a strongly atmospheric-model- dependent constraint on the presence of a high-mass Planet Nine at high galactic lati- tudes.

2. Gravitational Detection

A separate approach towards indirect detection of Planet Nine was explored by Fienga et al. (2016). Employing ranging data from the Cassini spacecraft, these au- thors sought to detect Planet Nine’s direct gravitational signature in the solar system ephemeris (somewhat akin to the technique Le Verrier 1846a,b used to discover Nep- tune; section 1.1). Adopting the P9 parameters from (Batygin and Brown, 2016a), they were able to immediately constrain P9 to the outer ~ 50% of the orbit (in agreementwith observational constraints; Brown and Batygin 2016). Moreover, the calculations of Fienga et al. (2016) point to a small reduction in the residuals of the ranging data if the true anomaly of P9 is taken to be u₉ 118 deg. This line of reasoning was further explored by Holman and Payne (2016a,b), who additionally considered the long base- line ephemerides of Pluto to place additional constraints on the sky-location of Planet Nine.

The reanalysis of the ephemeris carried out by Folkner et al. (2016), however, high- lights the sensitivity of Fienga et al.’s results to the specifics of the underlying dynam- ical model, suggesting that the gravitational determinations of Planet Nine’s on-sky location are in reality considerably less precise than advocated by Fienga et al. (2016); Holman and Payne (2016a,b). An additional complication pertinent to this approach was recently pointed out by Pitjeva & Pitjev (2018), who caution that failure to prop- erly account for the mass contained within the resonant and classical Kuiper belt (which

they determine to be on the order of 2 10^–2 M_⊕) can further obscure P9’s gravitational signal in the solar system’s ephemeris. Particularly, Pitjeva & Pitjev (2018) find that the anomalous acceleration due to a 0.02 M_⊕ Kuiper belt is essentially equivalent to that arising from a m₉ = 10 M_⊕ planet at a heliocentric distance of r = 540 AU (for orbits around Saturn), further discouraging the promise of teasing out Planet Nine’s

gravitational signal from spacecraft data.

1. Formation Scenarios

In terms of both physical and orbital characteristics, the inferred properties of Planet Nine are certainly unlike those of any other planet of the solar system. Re- cent photometric and spectroscopic surveys of planets around other stars (Borucki et al., 2010; Batalha et al., 2013), however, have conclusively demonstrated that m

5 10 M planets are exceedingly common around solar-type stars, and likely repre- sent one of the dominant outcomes of the planet conglomeration process²⁰. A moder- ately excited orbital state (and in particular, a high eccentricity) is also not uncommon among long-period extrasolar planets, and is a relatively well-established byproduct of post-nebular dynamical relaxation of planetary systems (Juric´ & Tremaine, 2008). Nevertheless, the formation of Planet Nine represents a formidable problem, primarily due to its large distance from the sun.

To attack this speculative issue, several different origin scenarios have been pro- posed and are discussed in this section. The first option is for the planet to form in situ, via analogous formation mechanism(s) responsible for the known giant planets (section 7.1). Another option is for Planet Nine to form in the same annular region as the other giant planets, and then be scattered outward into its present orbit (section 7.2). Yet another possibility is for the planet to originate from another planetary sys- tem within the solar birth cluster, and then be captured during the early evolution of the solar system (section 7.3). While all of these scenarios remain in play (Figure 26), each is characterized by non-trivial shortcomings, as discussed below.

²⁰Jovian-class objects like Jupiter and Saturn, on the other hand, are comparatively rare and are believed to reside within 20 AU in only ~ 20% of sun-like stars (Cumming et al., 2008).

1. In Situ Formation

Perhaps the most straightforward model for the origin of Planet Nine is for it to form in situ, at its present orbital location. An attractive feature of this scenario is the fact that it does not require any physical processes beyond conglomeration itself. The advantages, however, stop there. Generally speaking, the timescale over which plan- etary building blocks (pebbles, planetesimals) amass into multi-Earth mass objects²¹ is set by the orbital period at the location of the forming planet (Johansen & Lam- brechts, 2017). With a 10, 000 year orbital period (corresponding to a 500 AU), a forming Planet Nine would only complete 300 revolutions around the sun within the typical lifetime of a protoplanetary disk (Hernandez et al., 2007). The corresponding impedance of growth by the slowness of the orbital clock is illuminated by the calcula- tions of Kenyon and Bromley (2016), who find that even under exceptionally favorable conditions, formation of super-Earths at hundreds of AU requires billions of years.

Another shortcoming of in situ formation concerns the availability of planet-forming material at large heliocentric distances. Various lines of evidence indicate the solar sys- tem did not originate in isolation, and instead formed within a cluster of 10³ 10⁴ stars (Adams and Laughlin 2001; Portegies Zwart 2009; Adams 2010; Pfalzner et al. 2015). Such a cluster environment can be highly disruptive to the outer regions of circum- stellar disks and hence to planet formation. At minimum, a number of authors have shown that over a timescale of 10 Myr, passing stars are expected to truncate the disk down to a radius of 300 AU, about one third of the minimum impact parameter (Heller, 1995; Ostriker, 1994). More importantly, these clusters also produce intense FUV radiation fields that evaporate circumstellar disks, removing all of the material beyond 30 40 AU over a time scale of 10 Myr (Adams et al., 2004). Observational evidence supports this picture and indicates that disks in cluster environments expe- rience some radiation-driven truncation (e.g., Anderson et al. 2013). Moreover, even in regions of distributed star formation, where external photoevaporation is unlikely to play a defining role, observations find that typical disk radii are only of order 100 AU (Haisch et al., 2001; Andrews et al., 2009, 2010). As a result, both observational and theoretical considerations suggest that the early Solar Nebula was unlikely to have

extended much farther than the current orbit of Neptune at a ~ 30 AU (see also Kretke et al. 2012). Forming Planet Nine at a radius of ~ 500 AU is thus strongly disfavored.

2. Formation Among the Giant Planets

A somewhat more natural origin scenario is for Planet Nine to form within the region that produces the known giant planets (i.e., the annulus defined roughly by

5 AU _~^< a _~^< 30 AU), and to be scattered out later. The physics of the planet forma-

tion process is notoriously stochastic, and the number of planets produced in a given planet-forming region cannot be calculated in a deterministic manner (Morbidelli & Raymond, 2016), meaning that additional ice giants other than Uranus and Neptune

²¹While gravitational instability of the early solar nebula provides an alternate means of forming planets, it is irrelevant to the problem at hand, since the mass scale for objects generated through this channel is of order 10 M_J (or higher, e.g., Rafikov 2005)

Figure 26: Above, we show not-to-scale schematics for the three possible mechanisms by which Planet Nine could have been formed and placed in its current orbit in the solar system. (top panel) In in situ formation, Planet Nine forms in its current distant orbit while the protoplanetary disk is still present, and resides there throughout the history of the solar system. (middle panel) If Planet Nine forms among the outer planets in the solar system, it could subsequently be scattered outwards onto a high-eccentricity orbit through interactions with the other solar system planets. Then, its orbit could be circularized through interactions with passing stars. (bottom panel) If Planet Nine originally formed around a host star other than the sun, a subsequent close encounter between this other star and the sun could result in Planet Nine being captured into its current- day long-period orbit around the sun.

 may have occupied the outer solar system during its infancy. To this end, analytic ar- guments put forth by Goldreich et al. (2004) suggest that the outer solar system could have started out with as many as five ice giants. Along similar lines, numerical models for the agglomeration of Neptune and Uranus through collisions among large plane- tary embryos find that 5 M_⊕ objects routinely scatter away from the primary planet

forming region (Izidoro et al., 2015). Calculations of ancillary ice giant ejection during

the outer solar system’s transient epoch of dynamical instability are also presented in Nesvorny´ (2011); Batygin et al. (2012); Nesvorny´ & Morbidelli (2012).

It is important to recognize that this model of Planet Nine formation must neces- sarily involve a two-step process. This is because outward scattering of Planet Nine facilitated by the giant planets places it onto a temporary, high-eccentricity (q 5 AU) orbit, which must subsequently be circularized (thus lifting its perihelion out of the planet-forming region) by additional gravitational perturbations arising from the clus- ter. The difficulty with this scenario, however, is that the likelihood of producing the required orbit for Planet Nine is low. Li and Adams (2016) estimated the scattering probability for this process by initializing Planet Nine on orbits with zero eccentricity and semi-major axis a 100 200 AU, and found that stellar fly-by encounters pro- duce final states with orbital elements a = 400 1500 AU, e = 0.4 0.9, and i < 60 deg only a few percent of the time. We note however, that the calculations of Brasser et al. (2006, 2012) obtain considerably more favorable odds of decoupling a scattered plan- etary embryo from the canonical giant planets and trapping it in the outer solar system, with reported probability of success as high as 15%, depending on the specifics of the adopted cluster model.

As an alternative to invoking cluster dynamics, Ericksson et al. (2018) considered the circularization of a freshly scattered Planet Nine through dynamical friction arising from a massive disk of planetesimals, extending far beyond the orbit of Neptune. Un- like the aforementioned cluster calculations, in this scenario the chances of producing a favorable Planet Nine orbit can be as high as 30%. An important drawback of this model, however, is that it suffers from the same issues of disk truncation outlined in the previous sub-section. Moreover, simulations of the Nice model (Tsiganis et al., 2005) require the massive component of the solar system’s primordial planetesimal disk to end at a 30 AU, to prevent Neptune from radially migrating beyond its current orbit. Therefore, within the framework of Ericksson et al. (2018), some additional physical process would be required to create an immense gap ranging from 30 AU to 100 AU in the solar system’s primordial planetesimal disk.

1. Ejection and Capture Within the Solar Birth Cluster

Although gravitational perturbations arising from passing stars can act to alter the orbital properties of Planet Nine, as discussed above, the possibilities do not end there – the birth environment of the solar system can also lead to the disruption of Planet Nine from its wide orbit. Several groups have worked to quantify the effects of scattering encounters in young stellar clusters using N-body methods over the last decade (e.g., Portegies Zwart 2009; Malmberg et al. 2011; Pfalzner 2013; Pfalzner et al. 2015, 2018). Another way to study this class of disruption events is to separately calculate the cross sections for fly-by encounters to ionize the solar system,  

The Planet Nine Hypothesis (Part 12)

 February 21, 2026

employ a color-scale that is solely a measure of the perihelion distance, with blue points

¹⁹Equivalent i ∆Ω plots for the favorable m₉ = 10 M_⊕ solutions look quite similar to the top right panel of Figure 23, so we omit them to avoid redundancy.

^m9 ^{= 5M a}9 ^{= 500 AU e}9 ^{= 0.25 i}9 ^{= 20 deg} ₁₈₀ ^m9 ^{= 5M a}9 ^{= 500 AU e}9 ^{= 0.25 i}9 ^{= 20 deg}

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^{2⌦ — $ — $}9 ^(deg)

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^{distance (AU)} 30 40 50 60 70 80 90 100 +

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Figure 23: High-inclination dynamics induced by a m₉ = 5 M_⊕ Planet Nine. Akin to plots illustrated in Figure 11, the right panels show the orbital footprints of simulated KBOs on the (i, ∆Ω) plane for the two optimal P9 orbital solutions emphasized in Figure 20. Note that the a₉ = 500 AU, e₉ = 0.25 solution produces high-inclination objects more readily than its lower eccentricity counterpart. The panel on the left

shows a density histogram of particles footprints, projected into (θ, Θ) phase-space (see equation 11 and Figure 12). Unlike the color-scheme employed in Figures 14 and 17, here we adopt a blue-gray gradient to exclusively represent perihelion distance.

 corresponding to q = 30 AU, and gray points signifying q ≥ 100 AU. The full census of observed a ≥ 250 AU TNOs is also shown on the panels, with high-inclination (i > 40 deg) Centaurs plotted as large orange points, and the KBO 2015 BP₅₁₉ shown

with a pink dot, as in Figure 9.

Because we are showing only long-term stable particles in Figure 23, simulated orbits that achieve q < 30 AU are essentially absent from the plot. This renders the comparison between the numerical experiments and the present-day orbits of high- inclination Centaurs inexact, leaving 2015 BP₅₁₉ as the only high-inclination TNO which conforms strictly to the depicted numerical results (recall that severe observa- tional biases exist against detecting high-inclination, high-perihelion KBOs). Nev- ertheless, it is very likely that the observed Centaurs originate as strongly inclined q > 30 AU Kuiper belt objects that are scattered inwards by Neptune, meaning that the numerical data depicted in Figure 23 represents the simulated source population of high-i KBOs from which the observed Centaurs are derived.

As can be deduced from examination of Figure 23, the simulation with e = 0.25 produces retrograde TNOs in much greater proportions than its lower eccentricity counterpart. Qualitatively, this can be attributed to the fact that the harmonic term responsible for orbit-flipping behavior is octupolar in nature (section 4.1) and thus ne- cessitates a significant eccentricity to drive high-inclination dynamics. In light of the strong observational biases that act against the detection of high-inclination TNOs, the 

 true occurrence ratio of distant high-i objects to low-i objects is not known. Unfor- tunately, this means that at present, we cannot observationally favor either of the two shown simulations, since they both produce strongly inclined TNOs in some propor- tion. To complement the discussion presented in section 4.4, the panel on the left-hand- side of Figure 23 presents the simulation results as a density histogram in phase-space, where the transparency of the cells corresponds to a logarithmic measure of the num- ber of orbital footprints contained within each cell and the color corresponds to typical values q of the constituent points. The regions of phase-space occupied by real TNOs is also heavily populated by simulated particles, suggesting that the agreement between the observed and synthetic populations of distant TNOs is satisfactory.

Although highly inclined long-period Centaurs embody an unexpected consequence of P9-induced dynamics, TNOs residing on nearly orthogonal and retrograde orbits are not confined to the distant edges of the Kuiper belt, and are observed on shorter- period orbits as well (Figure 9). As with the large semi-major axis Centaurs them- selves, these objects are envisioned to have acquired large inclinations through in- teractions with Planet Nine at large semi-major axes, and to have subsequently been scattered inwards by Neptune. N-body simulations that elucidate this process for a

m₉ = 10 M_⊕, a₉ = 600 AU, e₉ = 0.5 Planet Nine were reported in Batygin and Brown (2016b). Accordingly, let us now examine the generation of high-inclination TNOs with a ≤ 100 AU by a lower mass, lower eccentricity Planet Nine derived from the preceding analysis.

In order to populate the inner trans-Neptunian region with a sufficient number of synthetic KBOs, we re-ran the m₉ = 5 M_⊕, a₉ = 500 AU, e₉ = 0.25, i₉ = 20 deg numer- ical experiment, increasing the particle count to N = 20, 000. The simulated orbital dis- tribution of particles that attain a ≤ 100 AU throughout any point in the simulations is shown in Figure 24 as a density histogram, where once again transparency represents a

logarithmic measure of the density of points. Recalling that all initial conditions of our numerical experiments (including this one) are drawn from the a (100 AU, 800 AU) range, every particle that comprises the density histogram shown in Figure 24 has been emplaced into the a ≤ 100 AU region from a more distant orbital domain. The current

a ≤ 100 AU observational sample of TNOs is over-plotted on the Figure, and objects

with i ≥ 60 deg are emphasized.

Upon examination of Figure 24, two qualitative features are immediately evident.

First, P9-induced dynamics significantly boosts the inclination dispersion of compar- atively short-period TNOs, providing a natural explanation for the existence of nearly orthogonal orbits, such as those of Drac (Gladman et al., 2009) and Niku (Chen et al., 2016). Second, a distinct population of strongly retrograde particles with perihelion

distances in the 6 AU . q . 12 AU range is also produced. These synthetic objects seamlessly explain the almost planar, but backward orbits of the TNOs 2016 NM₅₆ and 2017 KZ₃₁. Comprehensively, the union of the two panels shown on Figure 24 demon- strates that the observed data is in excellent agreement with synthetic population of TNOs produced within the simulation.

More generally, the inability of standard Nice model simulations to produce KBOs with inclinations in excess of i & 40 deg has long been recognized as a shortcoming of the instability-driven scenario of outer solar system evolution (Levison et al., 2008; Nesvorny´, 2015b). Although the conflict between the observed aggregate of KBOs and

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Figure 24: Generation of a ≤ 100 AU high-inclination Centaurs by inward scattering of P9-perturbed distant objects. The current census of TNOs is shown with black points, and the i ≥ 60 deg objects that cannot be explained within the standard model of solar system evolution are emphasized. The underlying density

histogram delineates the regions of parameter space onto which long-period, P9-influenced particles are emplaced when they are scattered inwards by Neptune. The specific domains of a q i space most heavily populated by Planet Nine signal a strong consistency with the observational dataset.

the Nice model can in principle be resolved either by P9-facilitated pollution of the Kuiper belt with high-inclination objects that originate further out, or by inward deliv- ery of Oort cloud objects, the two hypotheses make distinct predictions regarding the orbital structure of the resulting high-inclination Kuiper belt. That is, while dynamical emplacement driven by Planet Nine generates a rather specific orbital architecture (as detailed in Figures 23 and 24), high-inclinations objects sourced from the Oort cloud should stem from a more uniform distribution of orbital elements. Continued map- ping of the high-i component of the Kuiper belt thus offers a direct avenue towards observational differentiation between these two hypotheses.

Solar Obliquity

A final piece of information that is readily informed by our aggregate of JSUNP9 simulations concerns the interactions between Planet Nine and the mean plane of the known eight-planet solar system (often referred to as the “invariable plane”; Souami & Souchay 2012). Shortly after the initial formulation of the Planet Nine hypothesis, it was pointed out by Bailey et al. (2016); Gomes et al. (2016); Lai (2016) that the sec- ular gravitational torque exerted by P9 upon the canonical giant planets would slowly perturb the orbital plane of the planets away from its initial state, thereby exciting a spin-orbit misalignment between the total angular momentum vector of the canonical giant planets and the spin-axis of the sun. Moreover, these authors found that given plausible P9 parameters (e.g., m₉ = 15 M_⊕, a₉ = 500 AU, e₉ = 0.5, i = 20 deg; Bai- ley et al. 2016), the entire 6-degree obliquity of the sun could be accounted for by P9 perturbations alone. 

 This effect is self-consistently captured in our simulations, and it is worthwhile to examine if the revised orbital properties of Planet Nine derived above remain consistent with a scenario where Planet Nine plays a dominant role in the excitation of solar obliquity. For the two best-fit P9 parameters combinations shown in Figures 17 and 18, the answer is a resounding ’no.’ Specifically, for m₉ = 5 M_⊕, a₉ = 500 AU, e₉ = 0.25,

i₉ = 20 deg, P9’s secular torque only leads to a ψ = 1.1 deg change in the inclination

of the solar system’s invariable plane over 4 Gyr. For a m₉ = 10 M_⊕ perturber on a a₉ = 800 AU, e₉ = 0.45, i₉ = 15 deg orbit, the induced solar obliquity is similarly small, evaluating to only ψ = 0.7 deg. This implies that some other process, unrelated

to the existence of Planet Nine, must be responsible the present-day obliquity of the sun.

To elaborate on this result further, it is useful to contextualize the sun’s spin-orbit misalignment within its broader, galactic context. Over the last decade, observations of the Rossiter-McLaughlin effect (see for example Winn et al. 2010; Triaud 2017) and doppler tomography (e.g., Marsh 2001; Johnson et al. 2017) have revealed that exo- planetary systems around sun-like stars generically exhibit a very broad range of spin- orbit misalignments, with projected stellar obliquities ranging from 0 to 180 deg. Importantly, this finding applies both to singly-transiting planets as well as to multi- transiting systems wherein the planets themselves are almost exactly coplanar, but are cumulatively inclined with respect to the spin-axis of their host star (e.g., the inner planets of Kepler-56, Li et al. 2014; Li & Winn 2016). Although the exact mechanism through which extrasolar spin-orbit misalignments are excited remains an active area of research, viable theories for the generation of planet-star misalignments include tur- bulence within the protostellar core (Bate et al., 2010; Spalding et al., 2014; Fielding et al., 2015), gravitational torques arising from primordial stellar companions (Batygin et al., 2012; Batygin & Adams, 2013; Lai, 2014; Spalding & Batygin, 2014, 2015), as well as magnetohydrodynamic interactions between the stellar magnetospheres and the inner edges of their circumstellar disks (Lai et al., 2011). In light of these results, we can comfortably attribute the 6-degree obliquity of the sun to the same primordial pro- cess that shapes the broad distribution of spin-orbit misalignments of generic sun-like stars throughout the Galaxy, decoupling it from the Planet Nine hypothesis.

Prospects for Detection 

Optical Surveys

An important aspect of the Planet Nine hypothesis is that all of its theoretical at- tributes are directly testable, through the astronomical detection, and characterization of P9 itself. Arguably, the most straightforward approach towards direct detection of Planet Nine is via conventional observations in reflected visible light. The reference Planet Nine envisioned by Batygin and Brown (2016a,b) and (Brown and Batygin, 2016) had a moderately high semi-major axis, eccentricity, and mass, making Planet Nine potentially as faint as 25th magnitude. The more detailed model comparisons shown here suggest a Planet Nine that is lower in all of these parameters. Let us exam- ine the effect of this refinement on the expected brightness.

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Figure 25: On-sky properties of a typical P9 orbital fit. The top panel depicts an example path of Planet Nine, along with the RA-DEC projection of the ecliptic and galactic planes. The bottom panel reports the expected range of the visual magnitude of Planet Nine as a function of the right ascension. While ongoing observational surveys such as Pan-STARRS yield important limits on the location of P9 along its orbit, such constraints are absent from the galactic plane, which remains scarcely explored by solar system surveys.

The brightness of Planet Nine depends on its size, albedo, and distance. For a mass range between 5 and 10 M_⊕, exoplanets follow an approximate power law where R R_⊕(M/M_⊕)^0.55, suggesting radii of 2.4 and 3.5R_⊕, respectively (Weiss and Marcy, 2014). Such estimates are further consistent with the interior modeling efforts of Linder and Mordasini (2016) who compute physical radii of ~ 1.9 – 3.7R_⊕ for an isolated 10 M_⊕ object (see also Ginzburg et al. 2016). The albedo of Planet Nine is unknown, but modeling by Fortney et al. (2016) suggests that at the inferred heliocentric distance,

the planetary H/He envelope will be free of all potential condensibles, rendering the atmosphere an essentially pure Rayleigh scatterer with a V-band albedo of almost unity. Neptune, in contrast, has an albedo of approximately 40%, which we take as a plausible lower limit.

As discussed above, for 5 M_⊕, the best-fit orbital solution is characterized by a₉ = 500 AU and e₉ = 0.25 which corresponds to an aphelion distance of 625 AU, where it would be between magnitude V ≈ 21.2 and 22.2 (it would be between magnitude 19.0 and 20.0 at perihelion), depending on the albedo. For 10 M_⊕, which we Part