The Planet Nine Hypothesis (Part 2)

 February 8, 2026

suggested that these extinction events are periodic, and recur every 26 Myr (Raup and Sepkoski, 1984). One way to achieve a periodic signal in the extinction events is for the Sun to have an eccentric stellar companion, which perturbs comets in the Oort cloud on the necessary time interval (Davis et al., 1984). The envisaged red/brown dwarf companion would therefore have an orbital period of about 26 Myr and hence a semi-major axis of a_nem 88, 000 AU. This hypothetical body became known as Nemesis, named after the Greek goddess of retribution. Although the orbital stability of the proposed companion was inconclusively analyzed by Hills (1984); Hut (1984); Torbett and Smoluchowski (1984), more recent work indicates that the probability of the ejection for Nemesis from the solar system by passing stars is of order unity over the age of the Sun (Li and Adams, 2016).

A number of searches for Nemesis have come up empty, starting with a University of California search (Perlmutter, 1986), and continuing with infrared surveys carried out by IRAS (Beichman, 1987) and 2MASS (Sykes et al., 2002). Moreover, the ev- idence for periodic extinction events itself is tenuous, meaning that the Nemesis hy- pothesis may simply be unnecessary. A more modest proposal, motivated by the dis- tribution of aphelion directions of comets, has been subsequently put forward, where the Sun has a Jovian mass companion (referred to as Tyche) on a distant orbit that perturbs comets in the Oort cloud (Matese et al., 1999; Matese and Whitmire, 2011). However, the Wide-field Infrared Survey Explorer (WISE) has placed stringent limits on the existence of such bodies in the distant solar system. Specifically, objects with the mass of Saturn and Jupiter are ruled out to distances of 28,000 AU and 82,000 AU, respectively (Luhman, 2014). Taken together, these observational surveys leave little parameter space for any putative binary companion to the Sun.

1. Recent Planetary Proposals

Since the discovery of the Kuiper belt (Jewitt & Luu, 1993), the orbital architecture of this population has often been examined in hope that it can provide insight into massive astrophysical objects that may reside beyond the current observational frontier of the solar system. The first suggestion that the observed distribution of objects in the Kuiper belt pointed to the presence of a perturbing planet came from Brunini & Melita (2002), who argued that the dramatic drop-off in the numbers of Kuiper belt

objects (KBOs) with semi-major axes beyond a & 48 AU could be explained by an approximately Mars-sized body with a semi-major axis of a 60 AU. Melita et al.

(2004), however, quickly determined that such an object was incapable of reproducing the observations.

The idea of a sub-Earth-sized outer planet was revisited by Lykawka and Mukai (2008) who suggested that such a body could explain many of the detailed properties of the main region of the Kuiper belt. The next suggestions of a planetary perturber came after the discovery of objects with high eccentricities and with perihelia beyond the immediate reach of strong Neptunian perturbations. Particularly, the KBO 2000 CR₁₀₅ inspired speculation that its large perihelion distance of q = 44.3 AU can most readily be attributed to the current or former presence of an external perturber, although slow chaotic diffusion driven by the known planets also constitutes a viable explanation for this seemingly unusual trajectory

(Gladman et al., 2002; Gladman & Chan, 2006). The orbit of the distant object Sedna (2003 VB₁₂), on the other hand, which has perihelion

 distance of q = 76 AU, can only be explained by perturbations from an external agent. To this end, Brown et al. (2004) suggested that even though an approximately Earth mass object at 70 AU could in principle be responsible, perturbations arising from stars within the birth cluster constitute a more plausible explanation for Sedna’s de- tachment from Neptune (Adams and Laughlin, 2003; Morbidelli and Levison, 2004). Nevertheless, Gomes et al. (2006) carried out an extensive series of numerical simu- lations showing that the orbits of both 2000 CR₁₀₅ and Sedna could be explained by a Neptune-to-Jupiter mass planet with a semi-major axis of 100s to 1000s of AU.

A separate suggestion of a planetary perturber surfaced when Trujillo and Sheppard (2014) discovered an additional outer solar system object, 2012 VP₁₁₃, with a perihe- lion well beyond the planetary region, and noted that all known KBOs in the outer so- lar system with perihelion distance beyond Neptune and semi-major axis greater than a > 150 AU have argument of perihelion⁴, v, clustered around zero. Orbits with v = 0 or v = 180 deg come to perihelion at the heavily observed ecliptic, so observational bias could naturally facilitate a clustering around both of those values, particularly for the highest eccentricity objects. However, no conceivable bias could lead to only ob- serving objects clustered around v = 0, implying that Trujillo and Sheppard (2014)’s result is both statistically robust and not a product of survey strategy.

To explain the observations, Trujillo and Sheppard (2014) speculated that a several Earth mass planet at approximately 200 AU could maintain the arguments of perihe- lion alignment through the Kozai-Lidov effect (see section 4.1 for a short discussion). In particular, Trujillo and Sheppard (2014) demonstrated that a 5 M_⊕ body on a circu- lar orbit at a = 210 AU could cause Kozai-Lidov oscillations of 2012 VP₁₁₃, thereby maintaining its argument of perihelion in libration around zero. Nevertheless, they also

pointed out two difficulties with this scenario. First, in their simulations, they failed to find a single planet that can cause all of the KBOs – which have semi-major axes between 150 and 500 AU – to undergo Kozai-Lidov oscillations. This difficultly is not surprising; objects librate about v = 0 or 180 deg only for an interior perturber with a semi-major axis relatively close to the semi-major axis of the object being per- turbed (Thomas and Morbidelli, 1996). Thus, Kozai-Lidov libration of all objects with semi-major axes between 150 and 500 AU would likely require a special configuration of several carefully placed planets (see de la Fuente Marcos and de la Fuente Marcos 2016 for further discussion). Second, internal perturbers can cause affected objects to have Kozai-Lidov oscillations about either v = 0 or v = 180 deg, and as already stated above, the evidence for clustering about only v = 0 is robust. Trujillo and Sheppard (2014) suggested that this dilemma might be overcome if a close stellar en- counter had previously aligned the arguments of perihelia, a process demonstrated by Feng and Bailer-Jones (2015). The Trujillo and Sheppard (2014) planetary proposal thus requires multiple external planets and a close stellar flyby to explain the argument of perihelion clustering, along with some additional mechanism to explain the high perihelia of many of the distant objects.

Even more recently, Volk and Malhotra (2017) examined the observational census

⁴Not to be confused with the longitude of perihelion, the argument of perihelion is an angle made by the vectors pointing to the perihelion and the ascending node (see Figure 3).

of long-period KBOs, and argued that the mean orbital plane of the Kuiper belt in the a 50 80 AU domain is inclined with respect to the ecliptic in an unexpected man- ner. This led the authors to suggest that the observed warping may be facilitated by a small (e.g. Mars-mass) planet, residing in the solar system on an appreciably inclined orbit with a 65 80 AU. The possibility that a body of this type may indeed exist in the solar system is bolstered by the recent simulations of Silsbee and Tremaine (2018), who find a significant probability that sub-Earth-mass planetary embryos can become

trapped on orbits with a . 200 AU and q 40 70 AU early in the solar system’s lifetime. Given that the expected visual magnitude of such an object would be of order

17 or less, the most likely location on the sky where this body could have avoided being discovered to date is the galactic plane, which remains relatively unexplored by solar system surveys.

This brief overview of gravitationally motivated planetary proposals illuminates the fact that over the course of the last 170 years, numerous variants of trans-Neptunian perturbers have been considered (and subsequently abandoned), with the aim to ex- plain a broad range of dynamical phenomena at the outskirts of the solar system. In light of this multiplicity, a natural question emerges: what distinguishes the different planetary proposals and the models that accompany them? A simple answer may be that each proposition of a trans-Neptunian planet is characterized by the unique combi- nation of the anomalous data it seeks to explain, and the specific dynamical mechanism through which the putative planet generates its observational signatures. With an eye towards characterizing the Planet Nine hypothesis specifically within this framework, in the text below we will present an up-to-date account of the orbital architecture of the trans-Neptunian region of the solar system, and outline a theoretical description of the dynamical mechanisms through which Planet Nine sculpts the small body population of the distant solar system.

The remainder of this review is structured as follows. In the following section, we sketch out the various sub-categories of objects residing in the trans-Neptunian solar system, and summarize the relevant nomenclature. In section 3, we provide a detailed account of the anomalous structure of the distant solar system, including a brief discus- sion of the characteristic timescales and observational biases. Section 4 outlines a the- oretical description of the dynamical mechanisms through which Planet Nine sculpts the population of small bodies in the distant solar system and thereby accounts for these anomalies. In section 5 we present results from a large ensemble of numerical simulations that fully capture the non-linear and chaotic nature of Planet Nine-induced dynamics. These integrations conform to the expectations of the analytical theory from the previous section and constrain the allowed properties of Planet Nine. The prospects for detecting this as-yet-unseen planet are described in section 6. Given its requisite large distance from the Sun, the formation of Planet Nine poses a challenging problem, and various scenarios are discussed in section 7. The review concludes in section 8 with a summary of results, possible alternative explanations, and a brief outline of questions that remain open within the broader framework of the Planet Nine hypothesis.

1. Inventory and Structure of the Trans-Neptunian Solar System

As astronomical surveys have continued to push to ever greater depth and unveil the population of small bodies beyond Neptune, it has become progressively evident that the trans-Neptunian region of the solar system encompasses a rich diversity of objects that exhibit distinct modes of gravitational coupling with Neptune. Much of this orbital structure is a frozen-in relic of the solar system’s violent dynamical past (Levison et al., 2008; Nesvorny´, 2015a), and plays virtually no role in the formulation of the Planet Nine hypothesis. Meanwhile, other aspects of the distant solar system’s architecture are ceaselessly being sculpted by both known and inferred long-period planets, and are therefore of key importance. Thus, in order to better understand any lines of evidence for external gravitational perturbations, it is of considerable use to first outline the various dynamical classes that make up the Kuiper belt and their respective significance for the analysis that will follow.

The current census of trans-Neptunian objects (TNOs) is comprised of a few thou- sand bodies, the vast majority of which are considerably smaller than 1000 km in di- ameter. The outer solar system also contains a relatively large number of dwarf planets – bodies large enough for gravitational forces to render them quasi-spherical, yet too small to appreciably influence their orbital neighborhoods. In particular, the inventory of currently known objects includes 10 bodies larger than D > 900 km and another 17 bodies with estimated sizes in the range D = 600 – 900 km (see Brown 2008 for a re- view). The number of such objects will continue to grow as the trans-Neptunian region is surveyed to greater depth. Nevertheless, the total mass of the present-day Kuiper belt is estimated to be a small fraction of an Earth-mass (Pitjeva & Pitjev, 2018), meaning that Kuiper belt objects can be essentially thought of as tracers of dynamical evolution facilitated by the outer planets. Accordingly, typical classification of KBOs is based upon their orbital, rather than physical properties (Figure 3), and we will follow this convention here (Figure 4). For more comprehensive discussion of specific attributes of the trans-Neptunian solar system, we direct the reader to reviews of the observational characteristics of the Kuiper belt (Luu and Jewitt 2002; Gladman et al. 2008), planet formation (Armitage, 2010), early dynamical evolution (Nesvorny´, 2018), and the birth environment of the solar system (Adams, 2010), as well as the references therein.

1. Resonant Kuiper Belt

An emblematic sub-population of Kuiper belt objects (that includes Pluto itself) is composed of objects entrained in mean motion resonances with Neptune. Simply put, resonant orbits have periods that can be expressed as rational multiples of Neptune’s orbital period, although we note that having a nearly rational period ratio is a necessary but insufficient condition for resonance. In addition to period commensurability, the angular orbital elements must have the proper form so that the relevant resonance an- gle (a Fourier harmonic of the gravitational potential, also called a “critical argument”) oscillates (or “librates”) around a particular value, instead of steadily increasing or de- creasing its value (a regime known as “circulation”). KBOs residing on resonant orbits generally experience coherent exchange of orbital energy and angular momentum with Neptune, and can be longterm stable even at high eccentricities, thanks to a phase- protection mechanism that allows KBO orbits to overlap the orbit of Neptune without

Figure 3: Definition of Keplerian orbital elements, illustrated by a schematic of an inclined, eccentric orbit in the solar system. The size and ellipticity of the orbit are parameterized by the semi-major axis, a, and the eccentricity, e, as shown in the inset. The longitude of ascending node (denoted Ω) informs the direction into which the orbit is tilted, and is measured by location at which the orbit intersects the ecliptic plane from below. The argument of perihelion (denoted v) describes the angle between the line of nodes and the direction of the planet’s closest approach to the sun (also referred to as the apsidal line). The combined angle, a = v+Ω, defines the overall direction of the apsidal line and is called the longitude of the perihelion. Finally, the tilt of the orbit with respect to the ecliptic is informed by the inclination, i.

being rapidly destabilized by close encounters (Peale, 1976; Nesvorny´ & Roig, 2000, 2001).

The most prominent orbital commensurabilities in the Kuiper belt correspond to the 3:2 and 2:1 mean motion resonances. Drawing on the fact that these resonances are densely populated, Malhotra (1995) demonstrated that Neptune likely formed much closer to the sun, and must have experienced long-range outward migration, capturing resonant KBOs along the way. Subsequent characterization of resonant dynamics in the Kuiper belt further revealed that Neptune’s migration must have had a stochastic component, and likely occurred during a transient period of dynamical instability ex- perienced by the outer solar system (Tsiganis et al. 2005; Levison et al. 2008; see also Nesvorny´ 2015a for a recent study). Despite the constraints that the structure of the resonant Kuiper belt places on the early evolution of the solar system, it plays no role within the context of the Planet Nine hypothesis, and its existence can be safely ignored for the purpose of the calculations that will follow.

1. Classical Kuiper Belt

The Classical Kuiper Belt is primarily comprised of icy bodies that have semi- major axes in between the 3:2 and 2:1 mean motion resonances, correspondingto a 42 48 AU. By virtue of not being locked into resonances with Neptune, clas- sical KBOs dominantly experience phase-averaged (so-called “secular”) interactions that are considerably more subdued than their resonant counterparts. The broader class of classical KBOs is often divided into dynamically ‘cold’ and ‘hot’ sub-populations,

The Planet Nine Hypothesis (Part 1)

 

July 29, 2021

Constantin Batygin,¹ Fred C. Adams,^2,3 Michael E. Brown,¹ and Juliette C. Becker³¹Division of Geological and Planetary Sciences California Institute of Technology, Pasadena, CA 91125, USA

²Physics Department, University of Michigan, Ann Arbor, MI 48109, USA

³Astronomy Department, University of Michigan, Ann Arbor, MI 48109, USA

 Abstract

Over the course of the past two decades, observational surveys have unveiled the intri- cate orbital structure of the Kuiper Belt, a field of icy bodies orbiting the Sun beyond Neptune. In addition to a host of readily-predictable orbital behavior, the emerging census of trans-Neptunian objects displays dynamical phenomena that cannot be ac- counted for by interactions with the known eight-planet solar system alone. Specifi- cally, explanations for the observed physical clustering of orbits with semi-major axes in excess of 250 AU, the detachment of perihelia of select Kuiper belt objects from Neptune, as well as the dynamical origin of highly inclined/retrograde long-period or- bits remain elusive within the context of the classical view of the solar system. This

newly outlined dynamical architecture of the distant solar system points to the exis- tence of a new planet with mass of m₉ 5 10 M_⊕, residing on a moderately inclined orbit (i₉ 15 25 deg) with semi-major axis a₉ 400 800 AU and eccentricity between e₉ 0.2 0.5. This paper reviews the observational motivation, dynamical constraints, and prospects for detection of this proposed object known as Planet Nine.

Introduction

Understanding the solar system’s large-scale architecture embodies one of human- ity’s oldest pursuits and ranks among the grand challenges of natural science. Histor- ically, the first attempts to astronomically map the imperceptible structure of the solar system trace back to Galileo himself, and his adoption of the telescope as a scientific instrument some four centuries ago. In terms of sheer numbers, however, the quest to unveil new planets in the solar system has been strikingly inefficient: only two large objects that were not already known to ancient civilizations – Uranus and Neptune – have been discovered to date, with no significant updates to the solar system’s planetary catalogue since 1930.

While countless astronomical surveys aimed at discovering new solar system plan- ets have consistently resulted in non-detections, the solar system’s vast collection of minor bodies has slowly come into sharper focus. Particularly, the past quarter-century witnessed the discovery and characterization of a diverse collection of small icy objects residing in the outer reaches of our solar system, extending from the immediate vicinity

Preprint submitted to Physics Reports February 27, 2019

of Neptune’s orbit to far beyond the heliosphere¹ (Jewitt & Luu, 1993). Intriguingly, rather than the planets themselves, it is this population of scattered debris that holds the key to further illuminating the solar system’s intricate dynamical structure and to unraveling its dramatic evolutionary history.

The vast majority of trans-Neptunian small bodies, collectively known as the Kuiper belt, reside on orbits that are consistent with known dynamical properties of the so- lar system. The most extreme members of this population, however, trace out highly elongated orbits with periods measured in millennia, and display a number of curious orbital patterns. These anomalies include the striking alignment in the orientations of eccentric orbits in physical space, a common tilt of the orbital planes, perihelion dis- tances that stretch far beyond the gravitational reach of Neptune, as well as excursions of trans-Neptunian objects into highly inclined, and even retrograde orbits. All of these otherwise mysterious orbital features can be readily understood if the solar system con- tains an additional – as yet undetected – large planet, residing hundreds of astronomical units away from the sun.

The existence of this particular solar system object, colloquially known as Planet Nine, has only recently been proposed (Batygin and Brown, 2016a). Nonetheless, the discoveries in the outer solar system that ultimately led to the Planet Nine Hypothesis (Brown et al. 2004; Trujillo and Sheppard 2014 and the references therein) represent a veritable revolution in the scientific understanding of our home planetary system. This review will explore these developments, and will provide a status update on the Planet Nine hypothesis. Before delving into specifics, however, we note that despite being characterized by a unique combination of observational evidence and dynamical mechanisms, the Planet Nine hypothesis is by no means the first inference of a new solar system member that is based upon anomalous orbital behavior of known objects. Moreover, it is important to recognize that this general class of scientific proposals has a long and uneven history, with results varying from the stunning success of Neptune (Le Verrier, 1846a; Galle, 1846; Adams, 1846) to the regrettable failure of Nemesis (Davis et al., 1984). Accordingly, it is instructive to begin this manuscript with a brief historical review of past claims.

The Discovery of Neptune

The mathematical determination of the existence of Neptune represents the only successful example of a new planetary discovery motivated by dynamical evidence within the solar system, and epitomizes one of the most sensational stories in the his- tory of astronomy (see Krajnovic´ 2016 for a recent review). The saga begins with the official discovery of the planet Uranus (then called Georgium Sidus) in 1781 by William Herschel. Although Herschel was the first to record the proper motion of the object and present his results to the Royal Astronomical Society (for further details, see the historical accounts of Alexander 1965; Miner 1998), numerous recorded obser- vations of Uranus already existed, which mistook the planet for a background star.

¹Data collected by the Voyager 1 and 2 spacecraft suggest that the heliosphere nominally extends to a heliocentric distance of approximately 120 AU.

Figure 1: Predicted orbit of Neptune. This diagram shows the outer solar system viewed from the north ecliptic pole, including the orbits of Uranus (gray) and Neptune (black), as well as the predicted Neptunian orbits (purple) from Le Verrier (1846a) and Adams (1846). Note that although the predicted physical location of Neptune was in close agreement with the actual location of Neptune in 1846, the derived orbits are considerably wider and more eccentric than Neptune’s true orbit.

Over the next six decades, astronomers continued to monitor the motion of Uranus along its 84 year orbit and computed ephemerides of its position over time based on the then-known properties of the giant planets (e.g., Bouvard 1824). The calculations and the observations were not in perfect agreement, with thedifferences between the theoretical longitudes and the observed longitudes of the orbit growing by approxi- mately 2^jj per year (see page 150 of Adams 1846). These data led Le Verrier (1846a,b)

and then Adams (1846)² to propose an additional planet to account for the differences.

It is worth noting that the inferred physical and orbital properties of Le Verrier’s and Adams’ putative planet differ considerably from those of the real Neptune (Figure 1). Specifically, instead of the modern value a₈ ≈ 30 AU, the orbit of the proposed planet

had a semi-major axis (reported as the ‘assumed mean distance’) of ~ 36 AU (Le

Verrier, 1846b) and ~ 37 AU (Adams, 1846). Meanwhile, the estimated orbital eccen- tricity was e₈ ~ 0.11 (Le Verrier, 1846b) and e₈ ~ 0.12 (Adams, 1846), significantly larger than the modern value of e₈ ≈ 0.008. Finally, the mass estimate for the new planet was reported as m₈ ~ 36 M_⊕ (Le Verrier, 1846b) and m₈ ~ 50 M_⊕ (Adams, 1846), two to three times larger than Neptune’s actual mass of m₈ 17 M_⊕. The pre- dicted properties of Neptune were thus somewhat larger in both mass and semi-major

²Although Le Verrier’s calculations famously predate Galle & d’Arrest’s astronomical detection of Nep- tune, Adams’s orbital predictions were only published after Neptune’s location was already known.axis than the observed body.

We note that resolution of the irregularities found in the orbit of Uranus required rather extensive calculations (Le Verrier, 1846a; Adams, 1846). The analysis had to include perturbations of all the previously known planets, the error budget for the es- timated orbital elements of Uranus, and the assumed orbital elements (and mass) of the proposed new planet (an overview of the difficulties is outlined in Lyttleton 1958). The discrepancies between Le Verrier’s and Adams’ theoretical expectations and the observed properties of Neptune therefore constitutes a gold standard for dynamically motivated planetary predictions. Moreover, it is worth pointing out that the most sig- nificant quantity in perturbing the orbit of Uranus was the anomalous acceleration in the radial direction produced by the new body, m₈/r² – a ratio that was predicted with much higher accuracy than the individual values of mass and semi-major axis. As we discuss below, comparable degeneracies between mass and orbital parameters exist within the framework of the Planet Nine hypothesis as well.

1. Planet X and the Discovery of Pluto

Following Le Verrier’s triumphant mathematical discovery of Neptune, unexplained behavior in the motions of objects in the solar system continued to inspire predictions of the existence, and sometimes locations of new planets beyond the boundaries of the known solar system. Some of the early trans-Neptunian planetary proposals include Jacques Babinet’s 1848 claim of a 12 M_⊕ planet beyond Neptune (Grosser, 1964),

David P. Todd’s 1877 speculation about a planet at 52 AU (Hoyt, 1976), Camille Flam-

marion’s inference of a planet at 48 AU (Flammarion, 1884), as well as the prediction of two planets at 100 and 300 AU by George Forbes, whose calculations were mo- tivated by an apparent grouping of orbital elements of long-period comets (Forbes, 1880). An expansive set of planetary hypotheses was later put forth by W. H. Picker- ing, who predicted seven different planets between 1909 and 1932, with masses rang-

ing from 0.045 M_⊕ to 20, 000 M_⊕ (see Hoyt 1976 for an excellent historical overview). Arguably, the most emblematic planetary prediction, however, can be attributed to Per-

cival Lowell, who championed the search for what he called “Planet X” and founded Lowell Observatory in Arizona in hopes of finding it.

The story of the search for Planet X is well documented in the literature (e.g., Levy 1991). Briefly: despite the addition of Neptune to the solar system’s ledger of planets, small apparent discrepancies in the orbits of the giant planets remained. With the ob- servations and analysis available at the time, the inferred orbital anomalies in the orbit of Uranus implied a planetary object with a mass of m_X 7 M_⊕, about half the mass

of Neptune. Lowell died suddenly in 1916, without having found the elusive planet.

Nevertheless, the search continued. The new director, Vesto Slipher (who used the ob- servatory to measure the recession velocities of galaxies; see Appendix A), handed off the search for Planet X to Clyde Tombaugh. By 1930, Tombaugh had examined countless photographic plates containing millions of point sources for possible plane- tary motion and finally discovered a moving object (Tombaugh,1946, 1996). Because it was found in the approximate location on the sky where Planet X was envisioned to be, and because Planet X was the object of the original search, the newly found body was initially considered to be the long-sought-after Planet X (Slipher, 1930).

1

₁₀-1

₁₀-2

₁₀-3

1920 1940 1960 1980 2000 2020

Year

Figure 2: Estimated mass of Pluto as a function of time. The first (and largest) estimate is from the dynamical calculations that inpired the initial search. The subsequent estimates are based on observations (as labeled) and show a steady downward trend until relatively recently. The particularly steep decline of Pluto’s mass in 1978 is marked by the discovery of its largest moon, Charon.

Immediately there was a problem. An object with physical size comparable to Nep- tune should have been resolved with the observational facilities of the era, but the new planet appeared point-like. It was also dim, coming in about six times fainter than the estimates. It soon became clear that the newly found member of the solar system was not the Planet X, as it was not massive enough to account for the perceived perturba- tions in the orbit of Uranus. The new body was subsequently named Pluto, after the Greek god of the underworld³. In the end, the observed irregularities in Uranus’ and Neptune’s motion turned out to be spurious, and were fully resolved by a 0.5% revision of Neptune’s mass, following the Voyager 2 flyby (Standish, 1993).

Figure 2 shows the estimated mass of Pluto as a function of time. The initial es- timate (m_X 7 M_⊕) is the mass required to account for the perceived perturbations of the giant planet orbits (Tombaugh, 1946). The first observational estimate for the mass of Pluto (Nicholson and Mayall, 1931) was already down toM_LP 1 M_⊕, and subsequent observations led to steadily lower values as shown in the Figure. Note that

a precipitous drop in the mass estimate that came in 1978, with the discovery of the moon Charon and the first clean measurement of Pluto’s mass (Christy and Harring- ton, 1978). The current mass estimate is only M_LP 0.00218 M_⊕ (Buie et al., 2006), roughly 3200 times smaller than the original mass estimate that inspired the search. In spite of its diminutive size, Pluto was considered as the ninth planet of the solar system

until 2006, when it was demoted to the status of a dwarf planet (IAU Resolution B5, 2006).

³As a bonus, the first two letters of the planet’s name were coincident with the initials of Percival Lowell, although W. H. Pickering was evidently under the impression that it stood for Pickering-Lowell (Hoyt, 1976).

1. The False Alarm of Vulcan

By the mid 19th century, observations of the planet Mercury became precise enough to detect variations in its orbital parameters, lending a handle on the gravitational per- turbations exerted by the terrestrial planets upon one-another. By making precise mea- surements of transits of Mercury across the Sun, 19th century astronomers thus realized that the orbit of Mercury was precessing forward at a rate that could not be fully ac- counted for by known bodies. This determination inspired Le Verrier (1843, 1859) to propose that an additional planet interior to Mercury is responsible for the extra perihe- lion precession necessary to fit the observations. This hypothetical new planet become known as Vulcan, the god of fire, volcanoes, and metal working in Roman mythology. In order to generate the anomalous (da/dt) = 43”/century perihelion advance of Mercury, the parameters of the unseen planet (m_v, a_v) would have been constrained by

(see section 3.1)_da

3 ^, G M_s 1

m_v a²

_da

^, G M_s G M_s 3

 where G is the gravitational constant and c is the speed of light. Coincidentally, the above expression is satisfied by a m_v 3 M_⊕ Super-Earth type planet with an orbital period of approximately 3 days, analogues of which are now known to be very com-

mon around sun-like stars (Borucki et al., 2010; Batalha et al., 2013). In the early 20th century, however, Einstein developed his theory of General Relativity, which self- consistently resolved the ancillary precession problem (yielding a rate of apsidal ad- vance given by the RHS of the above equation; Einstein 1916). This alleviated the need for intra-Mercurian planets within the solar system. Accordingly, unlike the case of Uranus (discussed in section 1.1), dynamical anomalies in the inner solar system paved the way to the discovery of fundamentally new physics rather than a planet.

1. The Nemesis Affair

The 1980s witnessed the proposal that the Sun was actually part of a binary star system. This time, the motivation for the proposed stellar companion stemmed from paleontology: approximately 65 Myr ago, a mass extinction event wiped out three quar- ters of the species then living on Earth. This cataclysm, which famously included the removal of (non-avian) dinosaurs from the biosphere, occurred at what is known as the Cretaceous-Tertiary (K-T) boundary. At the layer of rock corresponding to this geological age, sediments are observed to contain high levels of iridium, an element that is relatively rare in crustal rocks on Earth, but is much more plentiful in asteroids. The association of the iridium layer with the extinction boundary led to the hypothesis that the event was caused by a collision of a large ( 10 15 km) asteroid with Earth (Alvarez et al., 1980). The resulting impact would have catastrophic consequences on the climate, and would, in turn, explain the mass extinction event.

Although the K-T extinction event is often seen as being the most dramatic, it is far from unique: the geologic record unequivocally shows that the biosphere of Earth has experienced a series of mass extinction events. Moreover, although the data are sparse, with 12 events distributed over a time span of ~ 250 Myr, some analyses have

Figure 1: Predicted orbit of Neptune. This diagram shows the outer solar system viewed from the north ecliptic pole, including the orbits of Uranus (gray) and Neptune (black), as well as the predicted Neptunian orbits (purple) from Le Verrier (1846a) and Adams (1846). Note that although the predicted physical location of Neptune was in close agreement with the actual location of Neptune in 1846, the derived orbits are considerably wider and more eccentric than Neptune’s true orbit.

Over the next six decades, astronomers continued to monitor the motion of Uranus along its 84 year orbit and computed ephemerides of its position over time based on the then-known properties of the giant planets (e.g., Bouvard 1824). The calculations and the observations were not in perfect agreement, with the