OBSERVATIONAL CONSTRAINTS ON PLANET NINE: ASTROMETRY OF PLUTO AND OTHER TRANS-NEPTUNIAN OBJECTS

“We use the HEALPix tiling of the sky (Górski et al. 2005) to test a complete set of perturbing planet locations, uniformly distributed on the sky.”

“Solar System. A number of current solar system formation models feature large-scale planet migration (Fernandez and Ip 1996; Malhotra 1993, 1995;´ Levison and Morbidelli 2003; Morbidelli et al. 2005; Tsiganis et al. 2005; Levison et al. 2008), additional giant planets formed ˘5 35 AU from the Sun and then scattered wi…”

“…of current solar system formation models feature largescale planet migration(Malhotra 1993, 1995; Fernández & Ip 1996; Levison & Morbidelli 2003; Morbidelli et al. 2005; Tsiganis et al. 2005; Levison et al. 2008), additional giant planets formed ~5 35 au– from the Sun and then scattered within…”

“Nevertheless, the discovery of the Kuiper Belt (KB; Jewitt & Luu 1993), including its intricate dynamical structure (Malhotra 1995; Gladman et al. 2012), detailed size distribution (Gladman et al. 2001; Bernstein et al. 2004; Fraser et al. 2014), numerous large members(Brown et al. 2004, 2005;…”

“A number of current solar system formation models feature largescale planet migration(Malhotra 1993, 1995; Fernández & Ip 1996; Levison & Morbidelli 2003; Morbidelli et al. 2005; Tsiganis et al. 2005; Levison et al. 2008), additional giant planets formed ~5 35 au– from the Sun and then scattered…”

“In order to guide the trajectory of the New Horizons spacecraft to its encounter with the Pluto system(Stern et al. 2015), a number of groups concentrated on improving the determination of Pluto’s orbit(Assafin et al. 2010; BenedettiRossi et al. 2014; Buie & Folkner 2015; Girdiuk 2015; Pitjeva…”

“…largescale planet migration(Malhotra 1993, 1995; Fernández & Ip 1996; Levison & Morbidelli 2003; Morbidelli et al. 2005; Tsiganis et al. 2005; Levison et al. 2008), additional giant planets formed ~5 35 au– from the Sun and then scattered within or ejected from the solar system(Chiang et al.…”

“de la Fuente Marcos and de la Fuente Marcos (2014) used simulations of observational surveys to confirm that the orbital clustering of extreme scattered disk objects pointed out by Trujillo and Sheppard (2014) is unlikely to be the result of observational bias.”

“…its intricate dynamical structure (Malhotra 1995; Gladman et al. 2012), detailed size distribution (Gladman et al. 2001; Bernstein et al. 2004; Fraser et al. 2014), numerous large members(Brown et al. 2004, 2005; Schwamb et al. 2010), and distant components(Gladman et al. 2002; Brown et al.…”

“993; Quinlan 1993). Nevertheless, the discovery of the Kuiper belt (Jewitt and Luu 1993), including its intricate dynamical structure (Malhotra 1995; Gladman et al. 2012), detailed size distribution (Gladman et al. 2001; Bernstein et al. 2004; Fraser et al. 2014), numerous large members (Brown et al. 2004, 2005; Schwa…”

“A number of current solar system formation models feature largescale planet migration(Malhotra 1993, 1995; Fernández & Ip 1996; Levison & Morbidelli 2003; Morbidelli et al. 2005; Tsiganis et al. 2005; Levison et al. 2008), additional giant planets formed ~5 35 au– from the Sun and then scattered…”

“…al. 2001; Bernstein et al. 2004; Fraser et al. 2014), numerous large members(Brown et al. 2004, 2005; Schwamb et al. 2010), and distant components(Gladman et al. 2002; Brown et al. 2004; Trujillo & Sheppard 2014), rekindled enthusiasm for the possibility of additional planets orbiting undetected…”

“…1995; Gladman et al. 2012), detailed size distribution (Gladman et al. 2001; Bernstein et al. 2004; Fraser et al. 2014), numerous large members(Brown et al. 2004, 2005; Schwamb et al. 2010), and distant components(Gladman et al. 2002; Brown et al. 2004; Trujillo & Sheppard 2014), rekindled…”

“Nevertheless, the discovery of the Kuiper Belt (KB; Jewitt & Luu 1993), including its intricate dynamical structure (Malhotra 1995; Gladman et al. 2012), detailed size distribution (Gladman et al. 2001; Bernstein et al. 2004; Fraser et al. 2014), numerous large members(Brown et al. 2004, 2005;…”

“Lykawka & Mukai (2008) also simulated the dynamical evolution of the outer solar system under the influence of a planet with a mass a few tenths that of the Earth.”

“trometry, we adopt 0 00:07 and 0:05 for the RA and Dec, respectively. For 5 Separation Mass M=r3 Mass Designation Name (AU) (M AU) (M 3 ) Reference (136199) Eris 102-128 8:35 10 9 3:3 10 16 6:6 10 16 Brown and Schaller (2007) (134340) Pluto+Charon – 7:33 10 9 - Stern et al. (2015) (136108) Haumea 11-58 2:01 10 9 3:4 1…”

“dynamical structure (Malhotra 1995; Gladman et al. 2012), detailed size distribution (Gladman et al. 2001; Bernstein et al. 2004; Fraser et al. 2014), numerous large members (Brown et al. 2004, 2005; Schwamb et al. 2010), and distant components (Gladman et al. 2002; Brown et al. 2004; Trujillo and Sheppard 2014), reki…”

“Our best fits suggest a planet that is either more massive or closer than argued for by either Batygin & Brown (2016) or Fienga et al. (2016).”

“A number of current solar system formation models feature largescale planet migration(Malhotra 1993, 1995; Fernández & Ip 1996; Levison & Morbidelli 2003; Morbidelli et al. 2005; Tsiganis et al. 2005; Levison et al. 2008), additional giant planets formed ~5 35 au– from the Sun and then scattered…”

“Gomes et al. (2006) examined the long-term, secular influence of a planet in the inner Oort cloud on the orbits of scattered-disk objects with initial perihelion values near Neptune ( <”

“…Planet Nine could account for peculiar features of that distribution, upper limits from dynamical effects that are not observed (Hogg et al. 1991; Iorio 2009, 2012, 2014), nondetections in optical (Brown et al. 2015) and infrared surveys (Luhman 2014), and models of the physical properties such…”

“Some investigations have argued for closer planets, possibly more than one(Brunini & Melita 2002; Lykawka & Mukai 2008; Bromley & Kenyon 2016; Kenyon & Bromley 2016).”

“We further assume that Planet Ninefollows a keplerian orbit and is itself unperturbed by the other planets. We refer to this approach as the “moving planet model.” For our second approach, following Hogg et al. (1991), we assume that the additional planet is stationary and is suciently distant that its gravitational p…”

“…Planet Nine could account for peculiar features of that distribution, upper limits from dynamical effects that are not observed (Hogg et al. 1991; Iorio 2009, 2012, 2014), nondetections in optical (Brown et al. 2015) and infrared surveys (Luhman 2014), and models of the physical properties such…”

“was not suciently massive to account for them. Improved planetary ephemerides, based on more accurate planetary masses and careful vetting of observational data, eliminated most of those residuals (Standish 1993; Quinlan 1993). Nevertheless, the discovery of the Kuiper belt (Jewitt and Luu 1993), including its intrica…”

“haller (2007) (134340) Pluto+Charon – 7:33 10 9 - Stern et al. (2015) (136108) Haumea 11-58 2:01 10 9 3:4 10 15 5:3 10 13 Ragozzine and Brown (2009) (50000) Quaoar 13-39 7:0 10 10 1:2 10 14 3:2 10 13 Fraser et al. (2013) (90377) Sedna 108-130 5:0 1610 10 3:2 10 5:6 10 16 Assumed (90482) Orcus 35-73 3:2 10 10 1:8 10 15…”

“1995); Pluto or Charon positions from recent occultation measurements of Pluto and Charon (Assafin et al. 2010; Benedetti-Rossi et al. 2014); and CCD observations from Pico dos Dias Observatory (Benedetti-Rossi et al. 2014), the USNO’s Flagstaff Station (Stone et al. 2003), and JPL’s Table Mountain Observatory (descri…”

“rbidelli et al. 2005; Tsiganis et al. 2005; Levison et al. 2008), additional giant planets formed ˘5 35 AU from the Sun and then scattered within or ejected from the solar system (Chiang et al. 2007; Bromley and Kenyon 2014, 2016b), or the formation of planets at larger distances (Kenyon and Bromley 2015, 2016b). 1 ar…”

“That celebrated success ensured that scientists would sporadically revisit the possibility of yet undiscovered planets in the solar system (see Tremaine 1990; Hogg et al. 1991 and Gaudi & Bloom 2005 for reviews).”

“…2005; Tsiganis et al. 2005; Levison et al. 2008), additional giant planets formed ~5 35 au– from the Sun and then scattered within or ejected from the solar system(Chiang et al. 2007, p. 895; Bromley & Kenyon 2014, 2016), or the formation of planets at larger distances(Kenyon & Bromley 2015, 2016).”

“That celebrated success ensured that scientists would sporadically revisit the possibility of yet undiscovered planets in the solar system (see Tremaine 1990; Hogg et al. 1991 and Gaudi & Bloom 2005 for reviews).”

“Based on those residuals, Le Verrier & Adams(Adams 1846; Le Verrier 1846a, 1846b) predicted the existence of Neptune, which was discovered shortly thereafter(Galle 1846).”

“Some investigations have argued for closer planets, possibly more than one(Brunini & Melita 2002; Lykawka & Mukai 2008; Bromley & Kenyon 2016; Kenyon & Bromley 2016).”

“ow Planet Ninecould account for peculiar features of that distribution; upper limits from dynamical eects that are not observed (Hogg et al. 1991; Iorio 2009, 2012, 2014); non-detections in optical (Brown et al. 2015) and infrared surveys (Luhman 2014); and models of the physical properties such a planet might have (G…”

“Some investigations have argued for closer planets, possibly more than one(Brunini & Melita 2002; Lykawka & Mukai 2008; Bromley & Kenyon 2016; Kenyon & Bromley 2016).”

“centric unit vector directed from the observatory to the observed location. However, when comparing the calculated sky position with those observed, we resolve the diflocal tangent plane projections (Herget 1965). 2.We replaced Orbfit’s analytic but approximate expressions for the derivatives of the observable properti…”

“…occultation measurements of Pluto and Charon(Assafin et al. 2010; Benedetti-Rossi et al. 2014); and CCD observations from Pico dos Dias Observatory(Benedetti-Rossi et al. 2014), the USNO’s Flagstaff Station(Stone et al. 2003), and JPL’s Table Mountain Observatory (described in Buie & Folkner…”

“…measurements of Pluto and Charon(Assafin et al. 2010; Benedetti-Rossi et al. 2014); and CCD observations from Pico dos Dias Observatory(Benedetti-Rossi et al. 2014), the USNO’s Flagstaff Station(Stone et al. 2003), and JPL’s Table Mountain Observatory (described in Buie & Folkner 2015).”

“…object embedded in the KB region, proposing that such an object could naturally explain the observed “edge” in the KB distribution at ∼50 au, although later work found that such a body would be inconsistent with other features of the observed orbital distribution of TNOs (Melita et al. 2004).”

“Buie and Folkner (2015) took great care to develop a reliable astrometric data set with which to better determine Pluto’s orbit.”

“from the observed orbital distribution of TNOs and how Planet Ninecould account for peculiar features of that distribution; upper limits from dynamical eects that are not observed (Hogg et al. 1991; Iorio 2009, 2012, 2014); non-detections in optical (Brown et al. 2015) and infrared surveys (Luhman 2014); and models of…”

“ntly massive to account for them. Improved planetary ephemerides, based on more accurate planetary masses and careful vetting of observational data, eliminated most of those residuals (Standish 1993; Quinlan 1993). Nevertheless, the discovery of the Kuiper belt (Jewitt and Luu 1993), including its intricate dynamical…”

“Fienga et al. (2016) and Holman & Payne (2016a, 2016b) have looked further into the Cassini tracking and planetary ephemerides to put limits on the size and distance of an unseen massive planet in the outer solar system.”

“It is also pertinent to note that Holman & Payne (2016a) recently identified ranges of mass and distance combinations for an unseen planet whose perturbations could improve the orbit-fit residuals for Pluto and other KBOs.”

“Note that P9’s existence and hence its orbit is entirely speculative at this point (Trujillo & Sheppard 2014; Brown & Batygin 2016; Batygin & Brown 2016; Fienga et al. 2016; Malhotra et al. 2016; Holman & Payne 2016; Shankman et al. 2017; Millholland & Laughlin 2017).”

“…prospects for the direct detection of Planet Nine either through ongoing or future surveys are quite promising (Brown & 19 Batygin 2016; Holman & Payne 2016a,b; Fortney et al. 2016; Millholland & Laughlin 2017), and it is likely that the concluding assessment of the theoretical model…”

“…and observational perspectives (Batygin & Brown 2016b; Bromley & Kenyon 2016; Chen et al. 2016; de la Fuente Marcos & de la Fuente Marcos 2016; Holman & Payne 2016a, 2016b; Kenyon & Bromley 2016; Li & Adams 2016; Malhotra et al. 2016; Mustill et al. 2016; Sheppard & Trujillo 2016; Batygin &…”

“Fienga et al. (2016) and Holman & Payne (2016b) derived similar constraints using the precise measurements of the Earth-Saturn distance obtained by the Cassini spacecraft.”

“…and physical properties of P9 (Brown & Batygin 2016; de la Fuente Marcos & de la Fuente Marcos 2016a,b; Fienga et al. 2016; Fortney et al. 2016; Holman & Payne 2016b,a; Linder & Mordasini 2016; Philippov & Chobanu 2016; Toth 2016), the dynamical implications of P9 in the Solar System (de la…”

“…Brown & Batygin 2016; de la Fuente Marcos & de la Fuente Marcos 2016a,b; de la Fuente Marcos, de la Fuente Marcos & Aarseth 2016; Fienga et al. 2016; Holman & Payne 2016a,b; Lawler et al. 2016; Malhotra, Volk & Wang 2016) and intrinsic physical properties (Cowan, Holder & Kaib 2016; Fortney et…”

“A recent body of research (e.g. Trujillo & Sheppard 2014; Batygin & Brown 2016a,b; Brown & Batygin 2016; Holman & Payne 2016a,b) has suggested that the unusual orbital characteristics of several Edgeworth–Kuiper Belt Objects could be explained by the presence of an unseen/undiscovered ∼20M⊕ planet – the so-called ‘Pla…”

“Since then, many attempts to locate the elusive planet have followed (Fienga et al. 2016a, 2020; Folkner et al. 2016; Holman & Payne 2016a,b).”

“…of Planet Nine (Brown & Batygin 2016; de la Fuente Marcos & de la Fuente Marcos 2016) and by simulations of the tidal perturbation induced by Planet Nine on the relative distance between the Earth and the Cassini spacecraft (Holman & Payne 2016b) and Pluto and other TNOs (Holman & Payne 2016a).”

“The possibility of using the ongoing telemetry of New Horizons, a further complementary feature of this work with respect to Fienga et al. (2016a); Holman & Payne (2016b), is discussed in Section 7.”

“…by this suggestion, leading to a wide range of related topics being investigated, including: constraining its location (Brown & Batygin 2016; Holman & Payne 2016a,b); formation mechanisms (Bromley & Kenyon 2016; Kenyon & Bromley 2016; Li & Adams 2016; Mustill et al. 2016), atmospheric…”

“The uncertain orbital path of Pluto across the sky is the main limitation in these predictions (e.g., Benedetti-Rossi et al. 2014; Holman & Payne 2016, and references therein).”

“A closer perturber is also advocated by Holman & Payne (2016).”

“…is more distant and more massive than the one thought to be sculpting the Kuiper Cliff, but its existence has not been ruled out by recent analyses carried out by e.g. Brown and Batygin (2016), Fienga et al. (2016), Holman and Payne (2016a, 2016b), Sheppard and Trujillo (2016), and Brown (2017).”

“Fienga et al. (2020) reprised the investigation using the INPOP19a model, which includes the gravitational influence of the Kuiper Belt, and a tidal model as in Holman & Payne (2016b).”

“…not result of an observational bias and/or smallness of the sample, and the quest of finding P9 was prompted (Brown & Batygin 2016; Cowan et al. 2016; de la Fuente Marcos & de la Fuente Marcos 2016; de la Fuente Marcos et al. 2016; Fortney et al. 2016; Fienga et al. 2016; Holman & Payne 2016b,a).”

“…the location of Planet 9 on its orbit from the reduction of the residuals in Saturn’s orbital motion based on Cassini data (Fienga et al. 2016; Holman & Payne 2016a), or in Pluto’s orbit (Holman & Payne 2016b), or assuming that several of the distant TNOs are in mean motion resonance (MMR)…”

“Numerical simulations by Holman & Payne (2016b), Millholland & Laughlin (2017), Becker et al. (2017), and Batygin & Morbidelli (2017) (among others) have steadily refined the dynamical evidence and now point toward a planet with m ∼ 5− 10M⊕ with semimajor axis a ∼ 400− 800 AU.”

“Several authors provide restrictions on the location of Planet Nine based on Cassini data (Fienga et al. 2016; Holman & Payne 2016b), motion of comets (Medvedev et al. 2017), a Monte Carlo approach (de la Fuente Marcos & de la Fuente Marcos 2016), astrometry of Trans-Neptunian Objects (TNOs)…”

“From the definition of Θ µν and using equation (2), we have In other words, Θ µν will depend on the Lagrangian of matter, that is, this can refer to the case of the electromagnetic field, the massless scalar field, the case of the perfect fluid, among others.”