February 9, 2026
where the distinction is based on their orbital inclinations, which show a bimodal dis- tribution (Brown, 2001). The dividing point between the cold and hot populations is often taken to be i 5 deg, but the boundary is not sharp. Ca´ceres & Gomes (2018) recently considered the gravitational constraints upon Planet Nine’s orbit and mass that may ensue from the lack of orbital excitation of the cold belt, and demonstrated that no strong limits arise within this framework. Thus, like the resonant Kuiper belt, the classical belt is largely inconsequential for the Planet Nine hypothesis.
Scattered Disk
If the resonant and classical populations were the only constituents of the Kuiper belt, gravitational evidence for any distant, massive perturber is unlikely to have sur- faced. Thankfully, this is not the case, and the Kuiper belt hosts a third dynamical class of icy objects that spans a much more extended range of orbital elements – the so- called scattered disk. The vast majority of scattered disk objects reside on dynamically metastable orbits, and have perihelion distances in the vicinity of Neptune’s orbit i.e., q 30 38 AU. While the relatively confined perihelion range exhibited by scattered disk objects necessitates persistent orbital diffusion facilitated by Neptune’s chaotic perturbations, the semi-major axes of scattered disk objects range from the neighbor- hood of Neptune’s orbit (a q) to thousands of AU, connecting this population to the much more distant Oort cloud (Gomes et al., 2008). Because the orbits of long-period scattered disk objects sample a broad range of heliocentric distances, they are keenly relevant to the Planet Nine hypothesis, and provide some primary lines of evidence for the existence of Planet Nine.
Although comparatively rare, some members of the scattered disk have perihelia well outside of the immediate gravitational reach of Neptune (typically q & 40 AU). Placed within the framework of the currently known eight-planet solar system, this sub-class of “detached” Kuiper belt objects exhibits dynamically stable evolution. The
existence of such objects is important for two reasons. First, such objects cannot be generated simply through interactions with Neptune, and require an additional source of external gravitational perturbations (Morbidelli and Levison, 2004). Second, be- cause the orbital evolution of such objects is not contaminated by chaotic interactions with Neptune, they provide a particularly intelligible probe of dynamical evolution that unfolds in the far reaches of the solar system. We will return to the characterization of the distant scattered disk in sections 3.1 and 3.2.
Centaurs
Facilitated by short-periodic interactions with Neptune, some KBOs get scattered inwards, attaining perihelion distances below q ≤ 30 AU. For the purposes of this review, we will refer to the population of objects with q ≤ 30 AU and a ≥ 30 AU as Centaurs, although we note that a more general definition also includes objects withsemi-major axes in between the giant planets (Gladman et al., 2008). Because the orbits of Centaurs veer into the inter-planetary space, their orbital evolution is chaotic, with typical dynamical lifetimes measured in tens to hundreds of millions of years (Tiscareno & Malhotra, 2003, 2009; Lykawka and Mukai, 2008). Despite having small perihelion distances, however, like the scattered disk, the Centaur population spans a
Figure 4: Main dynamical classes of trans-Neptunian objects. This diagram shows the current observational census of the Kuiper belt in the a-e plane (black points), and outlines the primary sub-populations of Kuiper belt objects. Resonant Kuiper belt objects have orbital periods that are commensurate with that of Neptune. The classical Kuiper belt is primarily composed of comparatively low-eccentricity objects that reside be- tween the 3:2 and the 2:1 mean motion resonances, extending out to 48 AU. The scattered disk contains objects with higher eccentricity and perihelion distance in the range q 30 38 AU. The few objects with higher perihelia and large semi-major axes represent the detached population, and are keenly relevant to the Planet Nine hypothesis. Objects with perihelion distance smaller than the semi-major axis of Neptune are referred to as Centaurs.
broad range of orbital periods with some known objects having semi-major axes in excess of 2000 AU. Therefore, in spite of dynamical contamination from the known giant planets, long-period Centaurs may still be strongly influenced by Planet Nine’s gravity.
A point of greater importance is that Centaurs exhibit a very broad dispersion of orbital inclinations, with a significant number of bodies occupying strongly retrograde orbits. Such a wide scatter of inclinations cannot be accounted for by interactions with the known giant planets alone, and requires some additional dynamics to explain the observations. As discussed further below, a radically excited distribution of Centaur inclinations is a natural outcome of Planet Nine induced evolution, and constitutes a tantalizing line of evidence that points to Planet Nine’s existence (Batygin and Brown 2016b; Batygin and Morbidelli 2017; Becker et al. 2018; see also Gomes et al. 2015). In other words, if Planet Nine exists, highly inclined Centaurs almost certainly repre- sent an outcome of dynamical evolution sculpted by an interplay between P9 and the canonical giant planets.
At heliocentric distances more than one thousand times that of Neptune, resides yet another, nearly spherical reservoir of debris known as the Oort cloud. Distinct from the Kuiper belt, the Oort Cloud is a collection of icy bodies that provides the source for long-period comets (O¨ pik, 1932; Oort, 1950). The region is thought to have a radial extent from about 20,000 to 200,000 AU, where the outer distance scale correspondsto the effective gravitational boundary to the solar system and is roughly given by the Hill Sphere of the Sun (as dictated by the potential of the Galaxy).
It is noteworthy that although its existence is seemingly well established (Hills, 1981), the only concrete evidence for the Oort Cloud stems from the observations of comets with semi-major axes in excess of a ≥ 20, 000. The observed cometary flux
yields a cumulative mass estimate for the Oort cloud of approximately 1 2 M⊕, al-
though this value is highly uncertain (Francis, 2005). With its large outer boundary, the
Oort Cloud is subject to disruption by passing stars (Hut and Tremaine, 1985; Heisler and Tremaine, 1986). The continued existence of the Oort Cloud thus puts constraints on the severity of such interactions, and also constrains how disruptive such events would be for distant Kuiper belt objects as well as Planet Nine itself (Duncan 2008, see also section 7).
The overview of TNOs outlined above delineates the main dynamical classes of the observable Kuiper belt. Before leaving this section, however, let us remark on the un- charted domain of the distant solar system, with a specific focus on generic constraints that restrict the properties of any putative trans-Neptunian planets. Intriguingly, inde- pendent of any particular model, reasonably tight observational and gravitational limits can be placed on the permissible parameters for any as-yet-undiscovered major bodies.
In principle, new planets could orbit with semi-major axes ranging from just outside Neptune (tens of AU) out to the boundary specified by galactic tides (~ 104–5 AU). In terms of mass, new planets could be as small as Mars ( 0.1 M⊕; smaller entities are not considered to be major bodies) or as large as a few thousand Earth masses (due to Deuterium fusion that ensues in objects more massive than ~ 13 Jupiter masses, entities larger than 4100 M⊕ are considered brown dwarfs). This initial parameter space, spanning four decades in both semi-major axis and mass, is strongly restricted by
considerations of both dynamics and observational surveys, as outlined in this section. These results are summarized in Figure 5, which delineates the available parameter space in the (a, m) plane for possible new planets.
The orbits of the known planets are well determined, so that any additional bodies must be small and far away in order to avoid contradicting the working ephemerides. For example, a hypothetical planet with mass m = 10 M⊕ would produce perturba- tions to Saturn’s orbit that would be detectable via telemetry of the Cassini spacecraft, if it were currently closer to the Sun than about r . 370 AU (Fienga et al., 2016).
In general, distant planets interact primarily through their stationary tidal effects over
timescales of modern observations (which are short compared to the orbital period of such distant orbits). As a result, the bound on additional planets from the orbits of known giant planets scales as m/r3 (see the discussion of Silsbee and Tremaine 2018). This constraint requires planets to fall below the purple line in Figure 5, although we note that such determinations are sensitive to the specifics of the employed dynamical model (Folkner et al., 2016; Pitjeva & Pitjev, 2018).
On the other end of parameter space, solar system bodies cannot have overly large orbits and remain bound to the Sun. Passing stars can disrupt wide orbitsover the age of the solar system. This outer boundary is not sharp, and this process must be addressed statistically (Li and Adams, 2015). As a working estimate, orbiting bodies
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Figure 5: Available parameter space for yet-undiscovered planetary members of the solar system. Planets that are massive enough to gravitationally clear their orbits must lie above the green line. In order to survive the stochastic perturbations within the solar birth cluster, planets must have sufficiently tight orbits, with semi-major axes to the left of the red line. To avoid producing anomalously large perturbations of giant planet orbits, new planets must fall below the purple line. Finally, infrared surveys require planets to fall below the yellow line. The resulting admissible portion of parameter space is shown as the hatched region.
with semi-major axis a > 30, 000 AU are likely to be stripped from the sun by passing stars in the field (or at least have their orbital elements drastically altered), as marked by the dashed line in the Figure. The corresponding limits from the solar birth cluster are much more restrictive, so that surviving planets must have semi-major axes a < 1000 AU (Li and Adams 2016; see also section 7 for more detail). This limit requires planets to lie to the left of the red line in Figure 5.
A lower limit on the mass arises from the definition of a planet. One of the charac- teristics of planets specified by the International Astronomical Union is that the body must be massive enough to clear its orbit over the age of the solar system. This require- ment can be written in several different forms, and implies that the minimum planetary mass is an increasing function of orbital distance. Here we use the constraint advocated by Margot (2015), which can be written in the form
m > a 9/8
This lower limit on the planetary mass is shown as the green line in Figure 5 (see Soter 2006 for an alternate treatment of this criterion).
An upper limit to the mass of any possible new planets is provided by WISE ob- servations, which rule out bodies larger than Saturn out to distances 3 104AU (see Luhman 2014 for further details). This upper limit is shown as the yellow line in Figure5. Note that stronger limits can be derived for smaller distances, but such results are model-specific (Meisner et al., 2017a,b). This is because infrared emission is domi- nated by the internal energy sources of the planet, rendering its observational signature (surface emission in the WISE bands) dependent on the detailed interior structure of the planet (Ginzburg et al., 2016; Linder and Mordasini, 2016).
In light of the constraints delineated above, we can speculate that generically, planetary semi-major axes must be measured in hundreds of AU, but cannot exceed 1000 AU. Meanwhile, the allowed masses range from the mass of Earth to that of a sub-Saturn5. As we will see below, the P9 parameters necessary to explain the dynam- ical anomalies in the orbits of distant TNOs requires the hypothetical planet to have
semi-major axis and mass that reside precisely within the allowed region.
Observational characterization of the orbital architecture of the classical (a < 100 AU) domain of the Kuiper belt discussed in the previous section has had a profound effect on reshaping our understanding of the outer solar system’s evolutionary history (Lev- ison et al., 2008; Batygin et al., 2011). Indeed, as the structure of the trans-Neptunian region came into sharper focus a little over a decade ago, the hitherto conventional, in-situ formation narrative of the solar system (e.g. Cameron 1988; Pollack et al. 1996) was gradually replaced with a strikingly dynamic evolution model, wherein the giant planets are envisioned to have formed closer to the sun and subsequently scattered onto their current orbits during a transient period of instability (Malhotra, 1995; Tsiganis et al., 2005; Batygin & Brown, 2010; Nesvorny´, 2011, 2015a). As illuminating as map- ping of the a < 100 AU domain of Kuiper belt may have been, an important aspect of its architecture is that very little of it is anomalous – that is, the vast majority of the ob- servations can be readily understood as being a consequence of gravitational sculpting facilitated by the known giant planets of the solar system. Remarkably, the same state- ment does not hold true for trans-Neptunian objects with semi-major axes in excess of
a & 250 AU.
A diagram depicting the fourteen presently known6 long-period KBOs with a ≥ 250 AU, q ≥ 30 AU, and i ≤ 40 deg is presented in Figure 6. The orbits are shown from the perspective of the north ecliptic pole, and have their apsidal lines (vectors point-
ing into the perihelion direction from the sun) marked by arrows, which are 250 AU in length. Additionally, the inset on the top left corner of the diagram shows a polar pro- jection of the angular momentum vectors of the individual KBOs, and thus informs the magnitude, and the direction of the orbital tilts. By and large, these objects have (ap- parently) randomly distributed semi-major axes ranging from hundreds to thousands of astronomical units, and large eccentricities that typically equate to perihelion distances that approximately cradle Neptune’s orbit, with q ~ 35 – 45 AU. Notable exceptions to
5See e.g., Petigura et al. (2017) for an extrasolar characterization of such an object.6In this review, we consider the census of trans-Neptunian objects to be comprised of all objects listed in the minor planet center database, as of October 10th, 2018.
VP113 TG422 GB174
Sedna
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