February 25, 2026
m9 = 5M a9 = 500 AU e9 = 0.25 i9 = 20 deg
0.4
0.2
0
-0.2
-0.4
-0.6
-1.0 -0.5 0 0.5 1.0
p2 Г cos ∆$
-0.6
-0.4
-0.2 0 0.2
p2 Z cos ∆⌦
0.4
0.6
Figure C.28: Phase space evolution of distant KBOs. This Figure projects the phase-space evolution of the observed long-period KBOs in the same way as in Figure 17. Under the influence of P9’s gravitational potential, the KBOs 2014 SR349, 2010 GB174, 2012 VP113, Sedna, 2004 VN112, 2015 TG387, 2013 SY99,
2013 RF98, 2014 FE72 and 2015 RX245 maintain long-term apsidal confinement and clustering of the orbital poles. Conversely, the KBOs 2013 FT28, 2015 GT50, 2015 KG163, and 2007 TG422 are typically unstable and their depicted long-lived clones derive orbital stability primarily for excitation of extreme orbital inclinations.
that survives over the entire integration time of 4 Gyr is shown in the figure, which depicts the evolution in phase-space, as done in Figure 17. The phase-space trajecto- ries corresponding to individual objects are labeled by color, as shown. In the pres- ence of Planet Nine, the observed distant KBOs display the same type of dynamics as that described in sections 4 and 5. All of the objects that are long-term stable (particularly, 2014 SR349, 2010 GB174, 2012 VP113, Sedna, 2004 VN112, 2015 TG387,
2013 SY99, 2013 RF98, 2014 FE72 and 2015 RX245) execute secular apsidal librations (shown in the left panel), while their orbital poles cluster together as expected (shown in the right panel). The objects 2013 FT28, 2015 GT50, 2015 KG163, and 2007 TG422 are typically unstable. However, their stable clones shown in the figure execute high- inclination dynamics, as shown by the light purple, cyan, yellow, and dark orange paths in the right panel of Figure C.28.
In summary, this appendix has presented simulations of the observed a > 250 AU KBOs in the presence of P9 with revised parameters. The results of these simulations show that this Planet Nine model allows the real object to remain stable over billions of years (Figure C.27) and facilitates sustained clustering of their orbits in a manner that is consistent with observations (Figure C.28).
References
References
Abazajian, K. N., Adshead, P., Ahmed, Z., et al. 2016, CMB-S4 Science Book, First Edition, arXiv:1610.02743
Adams, F. C. 2010, The Birth Environment of the Solar System, N Ann. Rev. Astron. Astrophys., 48, 47
Adams, F. C., Hollenbach, D., Laughlin, G., and Gorti, U. 2004, Photoevaporation of Circumstellar Disks due to External FUV Radiation in Stellar Aggregates, Astro- phys. J., 611, 360
Adams, F. C., and Laughlin, G. 2001, Constraints on the Birth Aggregate of the Solar System, Icarus, 150, 151
Adams, F. C., and Laughlin, G. 2003, Migration and Dynamical Relaxation in Crowded Systems of Giant Planets, Icarus, 163, 290
Adams, F. C., Proszkow, E. M., Fatuzzo, M., and Myers, P. C. 2006, Early Evolution of Stellar Groups and Clusters: Environmental Effects on Forming Planetary Systems, Astrophys. J., 641, 504
Adams, J. C. 1846, Explanation of the observed irregularities in the motion of Uranus, on the hypothesis of disturbance by a more distant planet; with a determination of the mass, orbit, and position of the disturbing body, Mon. Not. R. Astron. Soc., 7, 149
Alexander, A.F.O. 1965, The Planet Uranus: A History of Observation, Theory and Discovery, (American Elsevier)
Alvarez, L. W., Alvarez, W., Asaro, F., and Michel, H. V. 1980, Extraterrestrial cause for the CretaceousTertiary extinction, Science, 208, 1095
Anderson, K. R., Adams, F. C., and Calvet, N. 2013, Viscous Evolution and Photoe- vaporation of Circumstellar Disks Due to External Far Ultraviolet Radiation Fields, Astrophys. J., 774, 9
Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., and Dullemond, C. P. 2009,
Protoplanetary Disk Structures in Ophiuchus, Astrophys. J., 700, 1502
Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., and Dullemond, C. P. 2010, Protoplanetary Disk Structures in Ophiuchus, II: Extension to Fainter Sources, As- trophys. J., 723, 1241
Armitage, P. J. 2010, Astrophysics of Planet Formation, (Cambridge Univ. Press)
Bailey, E., Batygin, K., and Brown, M. E. 2016, Solar Obliquity Induced by Planet Nine, Astron. J., 152, 126
Bailey, E., Brown, M. E., and Batygin, K. 2018, Feasibility of a Resonance-Based Planet Nine Search, submitted to Astron. J.
Batalha, N. M., Rowe, J., F., Bryson, S. T. et al. 2013, Planetary Candidates Observed by Kepler. III. Analysis of the First 16 Months of Data, Astrophys. J. Suppl., 204, 24
Bate, M. R., Lodato, G., & Pringle, J. E. 2010, Chaotic star formation and the align- ment of stellar rotation with disc and planetary orbital axes, Mon. Not. R. Astron. Soc., 401, 1505
Batygin, K., Brown, M. E., & Fraser, W. C. 2011, Retention of a Primordial Cold Classical Kuiper Belt in an Instability-Driven Model of Solar System Formation, Astrophys. J., 738, 13
Batygin, K., & Adams, F. C. 2013, Magnetic and Gravitational Disk-Star Interactions: An Interdependence of PMS Stellar Rotation Rates and Spin-Orbit Misalignments, Astrophys. J., 778, 169
Batygin, K., & Brown, M. E. 2010, Early Dynamical Evolution of the Solar System: Pinning Down the Initial Conditions of the Nice Model, Astrophys. J., 716, 1323
Batygin, K., and Brown, M. E. 2016a, Evidence for a Distant Giant Planet in the Solar System, Astron. J., 151, 22
Batygin, K., and Brown, M. E. 2016b, Generation of Highly Inclined Trans-Neptunian Objects by Planet Nine, Astrophys. J. Letters, 833, L3
Batygin, K., Brown, M. E., and Betts, H. 2012, Instability-driven Dynamical Evolution Model of a Primordially Five-planet Outer Solar System, Astrophys. J., 744, 3
Batygin, K., and Morbidelli, A. 2017, Dynamical Evolution Induced by Planet Nine,
Astron. J., 154, 229
Becker, J. C., Adams, F. C., Khain, T., Hamilton, S. J., and Gerdes, D. 2017 Evaluating the Dynamical Stability of Outer Solar System Objects in the Presence of Planet Nine, Astron. J., 154, 61
Becker, J. C., Khain, T., Hamilton, S. et al. 2018, Discovery and Dynamical Analysis of an Extreme Trans-Neptunian Object with a High Orbital Inclination, Astron. J., 156, 81
Beichman, C. A. 1987, The IRAS View of the Galaxy and the Solar System, Ann. Rev. Astron. Astrophys., 25, 521
Beust, H. 2016, Orbital Clustering of Distant Kuiper belt Objects by Hypothetical Planet 9: Secular or resonant?, Astron. Astrophys., 590, 2
Binney, J., and Tremaine, S. 2008, Galactic Dynamics: Second Edition, (Princeton Univ. Press)
Borucki, W. J., Koch, D., Basri, G., et al. 2010, Kepler Planet-Detection Mission: Introduction and First Results, Science, 327, 977
Bouvard, A. 1824 Note Relative a´ mes Tables d’Uranus, Astron. Nachrichten, 2, 441
Brasser, R., Duncan, M. J., and Levison, H. F. 2006, Embedded Star Clusters and the Formation of the Oort Cloud, Icarus, 184, 59
Brasser, R., Duncan, M. J., Levison, H. F., Schwamb, M. E., & Brown, M. E. 2012, Re- assessing the formation of the inner Oort cloud in an embedded star cluster, Icarus, 217, 1
Brown, M. E. 2001, The Inclination Distribution of the Kuiper Belt, Astrophys. J., 121, 2804
Brown, M. E. 2008, The Largest Kuiper Belt Objects The Solar System Beyond Nep- tune, 335
Brown, M. E. 2017, Observational Bias and the Clustering of Distant Eccentric Kuiper Belt Objects, Astron. J., 154, 65
Brown, M. E., Trujillo, C., and Rabinowitz, D. 2004, Discovery of a Candidate Inner Oort Cloud Planetoid, Astrophys. J., 617, 645
Brown, M. E., and Batygin, K. 2016, Observational Constraints on the Orbit and Location of Planet Nine in the Outer Solar System, Astrophys. J., 824, 23
Brown, M. E., and Batygin, K. 2019, Orbital Clustering in the Distant Solar System,
Astron. J., 157, 62
Brunini, A., & Melita, M. D. 2002, The Existence of a Planet beyond 50 AU and the Orbital Distribution of the Classical Edgeworth-Kuiper-Belt Objects Icarus, 160, 32
Buie, M. W., Grundy, W. M., Young, E. F., et al. 2006, Orbits and Photometry of Pluto’s Satellites: Charon, S/2005 P1, and S/2005 P2, Astron. J., 132, 290298
Burns, J. A. 1976, Elementary derivation of the perturbation equations of celestial mechanics, American Journal of Physics, 44, 944-949.
Ca´ceres, J., & Gomes, R. 2018, The Influence of Planet Nine on the Orbits of Distant TNOs: The Case for a Low-perihelion Planet, Astron. J., 156, 157
Cameron, A.G.W. 1988, Origin of the Solar System, Ann. Rev. Astron. Astrophys., 26
441
Chambers, J. E. 1999, A Hybrid Symplectic Integrator that Permits Close Encounters Between Massive Bodies, Mon. Not. R. Astron. Soc., 304, 793
Chen, Y.-T.m, Lin, H. W., Holman, M. J, Payne, M. J, et al. 2016, Discovery of A New Retrograde Trans-Neptunian Object: Hint of A Common Orbital Plane for Low Semi-Major Axis, High Inclination TNOs and Centaurs, Astrophys. J. Letters, 827, L24
Contopoulos, G. 1954, Beitrag zur Dynamik der Kugelsternhaufen Mit 1 Textabbil- dung, Z. Astrophys., 35, 67
Cowan, N. B., Holder, G., Kaib, N. A. 2016, Cosmologists in Search of Planet Nine: The Case for CMB Experiments, Astrophys. J., 822, 2
Christy, J. W., and Harrington, R. S. 1978, The Satellite of Pluto, Astron. J., 83, 1005- 1008
Cumming, A., Butler, R. P., Marcy, G. W., et al. 2008, The Keck Planet Search: De- tectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets, Pub. Astron. Soc. Pacific, 120, 531
Curtis, H. 1921, The Scale of the Universe: Part II, Bull. Nat. Res. Coun., 2, 194
Davis, M., Hut, P., and Muller, R. A. 1984, Extinction of Species by Periodic Comet Showers, Nature, 308, 715-717
de la Fuente Marcos, C., and de la Fuente Marcos, R. 2016, Finding Planet Nine: Apsidal Anti-alignment Monte Carlo Results, Mon. Not. R. Astron. Soc., 462, 1972
Duncan, M., Quinn, T., & Tremaine, S. 1988, The origin of short-period comets,Astrophys. J. Letters, 328, L69
Duncan, M. J. 2008, Dynamical Origin of Comets and Their Reservoirs, Space Science Reviews, 138, 109
Einstein, A. 1916, The Foundation of the General Theory of Relativity, Annalen Phys.,
49, 769-822
Eriksson, L. E. J., Mustill, A. J., and Johansen, A. 2018, Circularizing Planet Nine Through Dynamical Friction with an Extended Cold Planetesimal Belt, Mon. Not.
R. Astron. Soc., 475, 4609
Fan, S., and Batygin, K. 2017, Simulations of the Solar System’s Early Dynamical Evolution with a Self-gravitating Planetesimal Disk, Astrophys. J. Letters, 851, L37
Feng, F., Bailer-Jones, C. A. L. 2015, Finding the imprints of stellar encounters in long-period comets, Monthly Notices of the Royal Astronomical Society 454, 3267
Fielding, D. B., McKee, C. F., Socrates, A., Cunningham, A. J., & Klein, R. I. 2015, The turbulent origin of spin-orbit misalignment in planetary systems, Mon. Not. R. Astron. Soc., 450, 3306
Fienga, A., Laskar, J., Manche, H., and Gastineau, M. 2016, Constraints on the Lo- cation of a Possible 9th Planet Derived from the Cassini data, Astron. Astrophys., 587, 8
Flammarion, C. 1884, La Planete Transneptunienne et les Cometes Periodiques., L’Astronomie, 3, 81
Forbes, G. 1880, The Comet 1861 I, Nature, 21, 562
Folkner, W., Jacobson, R. A., Park, R., & Williams, J. G. 2016, Sensitivity of Saturn’s orbit to a hypothetical distant planet, AAS/Division for Planetary Sciences Meeting Abstracts #48, 48, 120.07
Fortney, J. J., Marley, M. S., Laughlin, G., Nettelmann, N., Morley, C. V., Lupu, R. E., Visscher, C., Jeremic, P., Khadder, W. G., and Hargrave, M. 2016, The Hunt for Planet Nine: Atmosphere, Spectra, Evolution, and Detectability, Astrophys. J., 824, 25
Francis, P. J. 2005, The Demographics of Long-Period Comets, Astrophys. J., 635, 1348
Gallardo, T., Hugo, G., and Pais, P. 2012, Survey of Kozai dynamics beyond Neptune,
Icarus, 220, 392
Galle, J. G. 1846, Account of the Discovery of Le Verrier’s Planet Neptune at Berlin, Sept. 23, 1846, Mon. Not. R. Astron. Soc., 7, 153
Gayon, J., Bois, E., Scholl, H. 2009, Dynamics of planets in retrograde mean motion resonance, Celestial Mechanics and Dynamical Astronomy, 103, 267
Ginzburg, S., Sari, R., & Loeb, A. 2016, Blackbody Radiation from Isolated Neptunes,
Astrophys. J. Letters, 822, L11
Gladman, B., Holman, M., Grav, T., et al. 2002, Evidence for an Extended Scattered Disk Icarus, 157, 269
Gladman, B., & Chan, C. 2006, Production of the Extended Scattered Disk by Rogue Planets Astrophys. J. Letters, 643, L135
Gladman, B., Marsden, B. G., and VanLaerhoven, C. 2008, Nomenclature in the Outer Solar System, in The Solar System Beyond Neptune, eds. M. A. Barucci, H. Boehn- hardt, D. P. Cruikshank, and A. Morbidelli (Univ. Arizona Press), pp. 43–57
Gladman, B., Kavelaars, J., Petit, J.-M., Ashby, M. L. N., Parker, J., Coffey, J., Jones, R. L., Rousselot, P., and Mousis, O. 2009, Discovery of the First Retrograde Transnep- tunian Object, Astrophys. J., 697, 91
Goldreich, P., Lithwick, Y., Sari, R. 2004, Final Stages of Planet Formation, The As- trophysical Journal 614, 497
Gomes, R. S., Matese, J. J., & Lissauer, J. J. 2006, A distant planetary-mass solar companion may have produced distant detached objects, Icarus, 184, 589
Gomes, R. S., Ferna´ndez, J. A., Gallardo, T., Brunini, A. 2008, The Scattered Disk: Origins, Dynamics, and End States in The Solar System Beyond Neptune, eds. M.
A. Barucci, H. Boehnhardt, D. P. Cruikshank, and A. Morbidelli, (Tuscon: Univ. Arizona Press), 259
Gomes, R. S., Soares, J. S., and Brasser, R. 2015, The Observation of Large Semi- major Axis Centaurs: Testing for the signature of a planetary-mass solar companion Icarus, 258, 37
Gomes, R., Deienno, R., and Morbidelli, A. 2016, The Inclination of the Planetary System Relative to the Solar Equator May be Explained by the Presence of Planet 9, Astron. J., 153, 27
Gronchi, G. F. 2005, An Algebraic Method to Compute the Critical Points of the Dis- tance Function Between Two Keplerian Orbits, Celest. Mech. Dynam. Astron., 93, 295
Grosser, M. 1964, The Search for a Planet beyond Neptune, Isis, 55, 2, 163-183
Hadden, S., Li, G., Payne, M. J., and Holman, M. J. 2018, Chaotic Dynamics of Trans- Neptunian Objects Perturbed by Planet Nine, Astron. J., 155, 249, arXiv:1712.06547
Haisch, K. E., Lada, E. A., and Lada, C. J. 2001, Disk Frequencies and Lifetimes in Young Clusters, Astrophys. J., 553, L153
Heisler, J., and Tremaine, S. 1986, The Influence of the Galactic Tidal Field on the Oort Comet Cloud, Icarus, 65, 13
Heller, C. 1995, Encounters with Protostellar Disks II: Disruption and Binary Forma- tion, Astrophys. J., 455, 252
Herna´ndez, J., Hartmann, L., Megeath, T., Gutermuth, R., Muzerolle, J., Calvet, N., Vivas, A. K., Bricen˜o, C., Allen, L., Stauffer, J., Young, E., and Fazio, G. 2007, A Spitzer Space Telescope Study of Disks in the Young σ Orionis Cluster, Astrophys. J., 662, 1067
Hills, J. G. 1981, Comet Showers and the Steady-State Infall of Comets from the Oort cloud, Astron. J., 86, 1730
Hills, J. G. 1984, Dynamical Constraints on the Mass and Perihelion Distance of Nemesis and the Stability of its Orbit, Nature, 311, 636
Holman, M. J., and Payne, M. J. 2016, Observational Constraints on Planet Nine: Astrometry of Pluto and Other Trans-Neptunian Objects, Astron. J., 152, 80
Holman, M. J., and Payne, M. J. 2016, Observational Constraints on Planet Nine: Cassini Range Observations, Astron. J., 152, 94
Hoyt, W.G. 1976, W. H. Pickering’s Planetary Predictions and the Discovery of Pluto, Isis, 67, 4, 551-564
Hubble, E. 1929, A Relation between Distance and Radial Velocity among Extra- Galactic Nebulae, Pub. Nat. Acad. Sci., 15, 168
Hut, P. 1984, How Stable is an Astronomical Clock that can Trigger Mass Extinctions on Earth? Nature, 311, 638
Hut, P., and Tremaine, S. 1981, Have Interstellar Clouds Disrupted the Oort Comet Cloud?, Astron. J., 90, 1548
Izidoro, A., Raymond, S. N., Morbidelli, A., Hersant, F., and Pierens, A. 2015, Gas Giant Planets as Dynamical Barriers to Inward-Migrating Super-Earths, Astrophys. J., 800, L22
Jewitt, D., & Luu, J. 1993, Discovery of the candidate Kuiper belt object 1992 QB1
Nautre, 362, 730
Johansen, A., & Lambrechts, M. 2017, Forming Planets via Pebble Accretion, Annual Review of Earth and Planetary Sciences, 45, 359
Johnson, M. C., Cochran, W. D., Addison, B. C., Tinney, C. G., & Wright, D. J. 2017, Spin-Orbit Misalignments of Three Jovian Planets via Doppler Tomography, Astron. J., 154, 137
Juric´, M., & Tremaine, S. 2008, Dynamical Origin of Extrasolar Planet Eccentricity Distribution, Astrophys. J., 686, 603
Kenyon, S. J., and Bromley, B. C. 2016, Making Planet Nine: Pebble Accretion at 250–750 AU in a Gravitationally Unstable Ring, Astrophys. J., 825, 33
Khain, T., Batygin, K., and Brown, M. E. 2018a, The Generation of the Distant Kuiper Belt by Planet Nine from an Initially Broad Perihelion Distribution, Astron. J., 155, 250
Khain, T., Becker, J. C., Gerdes, D. W. et al. 2018b, Dynamical Analysis of Three Distant Trans-Neptunian Objects with Similar Orbits, accepted to Astron. J.
Kozai, Y. 1962, Secular Perturbations of Asteroids with High Inclination and Eccen- tricity, Astron. J., 67, 591
Krajnovic´, D. 2016, Astronomy and Geophysics, 57, 5.28
Kretke, K. A., Levison, H. F., Buie, M. W., Morbidelli, A. 2012, A Method to Constrain the Size of the Protosolar Nebula, Astron. J., 143, 91
Lai, D., Foucart, F., Lin, D. N. C. 2011, Evolution of spin direction of accreting mag- netic protostars and spin-orbit misalignment in exoplanetary systems , Monthly No- tices of the Royal Astronomical Society 412, 2790
Lai, D. 2014, Star-disc-binary interactions in protoplanetary disc systems and primor- dial spin-orbit misalignments, Mon. Not. R. Astron. Soc., 440, 3532
Lai, D. 2016, Solar Obliquity Induced by Planet Nine: Simple Calculation, Astron. J.,
152, 215
Laskar, J. 1997 Large Scale Chaos and the Spacing of the Inner Planets, å, 317, 75
Lawler, S. M., Shankman, C., Kaib, N., Bannister, M. T., Gladman, B., and Kavelaars,
J. J. 2017, Observational Signatures of a Massive Distant Planet on the Scattering Disk, Astron. J., 153, 33
Le Verrier, U. J. 1843, Recherches sur l?orbite de Mercure et sur ses perturbations.
Journal de mathematiques pures et appliquees, 1, 8:273?359
Le Verrier, U. J. 1846, Recherches sur les mouvements d’Uranus par U. J. Le Verrier (Fortsetzung), Astron. Nachrichten, 25, 65
Le Verrier, U. J. 1846, Recherches sur les mouvements d’Uranus par U. J. Le Verrier (Beschluß), Astron. Nachrichten, 25, 85
Le Verrier, U. J. 1859, Theorie du mouvement de Mercure par U. J. Le Verrier, Ann. Obs. Paris, 76, 51-103
Levison, H. F., Dones, L., Duncan, M. J. 2001, The Origin of Halley-Type Comets: Probing the Inner Oort Cloud, Astron. J., 121, 2253.
Levison, H. F., Morbidelli, A., Van Laerhoven, C., Gomes, R., and Tsiganis, K., 2008, Late Orbital Instabilities in the Outer Planets Induced by Interaction with a Self- gravitating Planetesimal Disk, Icarus, 196, 258
Levy, D. H. 1991, Clyde Tombaugh: Discoverer of Planet Pluto, (Univ. Arizona Press)
Li, G., and Adams, F. C. 2015, Cross-sections for Planetary Systems Interacting with Passing Stars and Binaries, Mon. Not. R. Astron. Soc., 448, 344-363
Li, G., and Adams, F. C. 2016, Interaction Cross Sections and Survival Rates for Pro- posed Solar System Member Planet Nine, Astrophys. J. Letters, 823, L3
Li, G., Naoz, S., Kocsis, B., Loeb, A. 2014, Eccentricity Growth and Orbit Flip in Near-coplanar Hierarchical Three-body Systems, Astrophys. J., 785, 116
Li, G., Naoz, S., Valsecchi, F., Johnson, J. A., & Rasio, F. A. 2014, The Dynamics of the Multi-planet System Orbiting Kepler-56, Astrophys. J., 794, 131
Li, G., & Winn, J. N. 2016, Are Tidal Effects Responsible for Exoplanetary Spin &
Orbit Alignment?, Astrophys. J., 818, 5
Li, G., Hadden, S., Payne, M., and Holman, M. J. The Secular Dynamics of TNOs and Planet Nine Interactions, arXiv:1806.06867
Lidov, M. L. 1962, The Evolution of Orbits of Artificial Satellites of Planets under the Action of Gravitational Perturbations of External Bodies, Plan. Space Sci., 9, 719
Linder, E. F., and Mordasini, C. 2016, Evolution and Magnitudes of Candidate Planet Nine, Astron. Astrophys., 589, 134
Luhman, K. L. 2014, A Search for a Distant Companion to the Sun with the Wide-field Infrared Survey Explorer, Astrophys. J., 781, 4
Luu, J. X., and Jewitt, D. C. 2002, Kuiper Belt Objects: Relics from the Accretion Disk of the Sun, Ann. Rev. Astron. Astrophys., 40, 63
Lykawka, P. S., and Mukai, T. 2008, An Outer Planet Beyond Pluto and the Origin of the Trans-Neptunian Belt Architecture, Astron. J., 135, 1161
Lyttleton, R. A. 1958, A Short Method for the Discovery of Neptune, Mon. Not. R. Astron. Soc., 118, 551
Madigan, A.-M., and McCourt, M. 2016, A New Inclination Instability Reshapes Ke- plerian Discs into Cones: Application to the Outer Solar System, Mon. Not. R. Astron. Soc., 457, L8993
Madigan, A.-M., Zderic, A., McCourt, M., & Fleisig, J. 2018, On the Dynamics of the Inclination Instability, Astron. J., 156, 141
Malhotra, R. 1995, The Origin of Pluto’s Orbit: Implications for the Solar System Beyond Neptune, Astron. J., 110, 420
Malhotra, R., Volk, K., and Wang, X. 2016, Corralling a Distant Planet with Extreme Resonant Kuiper Belt Objects, Astrophys. J., 824, L22
Malmberg, D., Davies, M. B., and Heggie, D. C. 2011, The Effects of Fly-bys on Plan- etary Systems, Mon. Not. R. Astron. Soc., 411, 859-877
Mardling, R. 2010, The Determination of Planetary Structure in Tidally Relaxed In- clined Systems, Mon. Not. R. Astron. Soc., 407, 1048
Margot, J.-L, 2015, A Quantitative Criterion for Defining Planets, Astron. J., 150, 185
Marsh, T. R. 2001, Doppler Tomography, Astrotomography, Indirect Imaging Methods in Observational Astronomy, 573, 1
Matese, J. J., Whitman, P. G., and Whitmire, D. P. 1999, Cometary Evidence of a Massive Body in the Outer Oort Cloud, Icarus, 141, 354
Matese, J. J., and Whitmire, D. P. 2011, Persistent Evidence of a Jovian Mass Solar Companion in the Oort cloud, Icarus, 211, 926-938
Meisner, A. M., Bromley, B. C., Nugent, P. E., Schlegel, D. J. Kenyon, S. J., Schlafly,
E. F., and Dawson, K. S. 2017, Searching for Planet Nine with Coadded WISE and NEOWISE-Reactivation Images, Astron. J., 153, 65
Meisner, A. M., Bromley, C. D., Kenyon, S. J., and Anderson, T. E. 2017, A 3u Search for Planet Nine at 3.4µm with WISE and NEOWISE, aj, 155, 166, arXiv:1712.04950
Melita, M. D., Williams, I. P., Collander-Brown, S. J., & Fitzsimmons, A. 2004, The edge of the Kuiper belt: the Planet X scenario Icarus, 171, 516
Millholland, S., and Laughlin, G. 2017, Constraints on Planet Nine’s Orbit and Sky Position within a Framework of Mean Motion Resonances, Astron. J., 153, 91
Miner, E. D. 1998, Uranus: The Planet, Rings and Satellites, (John Wiley and Sons)
Morbidelli, A., and Levison, H. F. 2004, Scenarios for the Origin of the Orbits of the Trans-Neptunian Objects 2000 CR105 and 2003 VB12 (Sedna), Astron. J., 128, 2564
Morbidelli, A., Levison, H. F., and Gomes, R. 2008, The Dynamical Structure of the Kuiper Belt and Its Primordial Origin, in The Solar System Beyond Neptune, eds.
M. A. Barucci, H. Boehnhardt, D. P. Cruikshank, and A. Morbidelli, (Tuscon: Univ. Arizona Press), pp. 275-292
Morbidelli, A. 2002, Modern celestial mechanics : aspects of solar system dynamics, London: Taylor & Francis, 2002, ISBN 0415279399
Morbidelli, A., & Raymond, S. N. 2016, Challenges in planet formation, Journal of Geophysical Research (Planets), 121, 1962
Murray, C. D. 1986, Structure of the 2:1 and 3:2 Jovian resonances, Icarus, 65, 70
Murray, C. D., and Dermott, S. F. 1999, Solar System Dynamics, (Cambridge Univ. Press)
Mustill, A. J., Raymond, S. N., and Davies, M. B. 2016, Is there an Exoplanet in the Solar system? Mon. Not. R. Astron. Soc., 460, L109-L113
Nesvorny´, D., & Roig, F. 2000, Mean Motion Resonances in the Trans-neptunian Re- gion. I. The 2:3 Resonance with Neptune, Icarus, 148, 282
Nesvorny´, D., & Roig, F. 2001, Mean Motion Resonances in the Transneptunian Re- gion. Part II: The 1 : 2, 3 : 4, and Weaker Resonances, Icarus, 150, 104
Nesvorny´, D. 2011, Young Solar System’s Fifth Giant Planet? Astrophys. J., 742, 22
Nesvorny´, D. 2015, Jumping Neptune Can Explain the Kuiper Belt Kernel, Astron. J.,
150, 68
Nesvorny´, D. 2551b,Evidence for Slow Migration of Neptune from the Inclination Dis- tribution of Kuiper Belt Objects, Astron. J., 150, 73
Nesvorny´, D., Vokrouhlicky´, D., Dones, L., et al. 2017, Origin and Evolution of Short- period Comets, Astrophys. J., 845, 27
Nesvorny´, D. 2018, Dynamical Evolution of the Early Solar System, Ann. Rev. Astron. Astrophys., in press, arXiv:1807.06647
Nesvorny´, D., & Morbidelli, A. 2012, Statistical Study of the Early Solar System’s Instability with Four, Five, and Six Giant Planets, Astron. J., 144, 117
Nicholson, S. B., and Mayall, N. U. 1931, Positions, Orbit, and Mass of Pluto, Astro- phys. J., 73, 1
Oort, J. 1950, The Structure of the Cloud of Comets Surrounding the Solar System and a Hypothesis Concerning its Origin, Bull. Astron. Inst. Netherlands, 11, 91110
O¨ pik, E. J. 1932, Note on Stellar Perturbations of Nearby Parabolic Orbits. Proc. Amer. Acad., Arts Sci., 67, 169182
Ostriker, E. C. 1994, Capture and Induced Disk Accretion in Young Etar Encounters,
Astrophys. J., 424, 292O
Parker, R. J.., Lichtenberg, T., and Quanz, S. P. 2017, Was Planet 9 Captured in the Sun’s Natal Star-forming Region? Mon. Not. R. Astron. Soc., 472, L75-L79
Peale, S. J. 1976, Orbital resonances in the solar system Ann. Rev. Astron. Astrophys., 14, 215
Perlmutter, S. 1986, An Astrometric Search for a Stellar Companion to the Sun, PhD Thesis, Univ. California, Berkeley
Petigura, E. A., Sinukoff, E., Lopez, E. D., et al. 2017, Four Sub-Saturns with Dis- similar Densities: Windows into Planetary Cores and Envelopes, Astron. J., 153, 142
Pitjeva, E. V., & Pitjev, N. P. 2018, Mass of the Kuiper belt, Celestial Mechanics and Dynamical Astronomy, 130, 57
Pfalzner, S. 2013, Early Evolution of the Birth Cluster of the Solar System, Astron. Astrophys., 549, A82
Pfalzner, S., Davies, M. B., Gounelle, M., Johansen, A., Mu¨nker, C., Lacerda, P., Portegies Zwart, S., Testi, L., Trieloff, M., and Veras, D. 2015, The Formation of the Solar System, Phys. Scripta, 90, 068001
Pfalzner, S., Bhandare, A., Vincke, K., and Lacerda, P. 2018, Outer Solar System Pos- sibly Shaped by a Stellar Fly-by, Astrophys. J., in press, arXiv:1807.02960
Pollack, J. B., Hubickyj, O., Bodenheimer, P., Lissauer, J. J., Podolak, M., and Green- zweig, Y. 1996, Formation of the Giant Planets by Concurrent Accretion of Solids and Gas, Icarus, 124, 62
Portegies Zwart, S. F. 2009, The Lost Siblings of the Sun, Astrophys. J. Letters, 696, L13-L16
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. 1992, Numeri- cal Recipes in FORTRAN. The Art of Scientific Computing (2nd ed.; Cambridge: Cambridge Univ. Press)
Proszkow, E.-M., and Adams, F. C. 2009, Dynamical Evolution of Young Embedded Clusters: A Parameter Space Survey, Astrophys. J. Suppl., 185, 486-510
Rafikov, R. 2005, Can Giant Planets Form by Direct Gravitational Instability? Astro- phys. J., 621, L69
Raup, D. M., and Sepkoski, J. J. 1984, Periodicity of Extinctions in the Geologic Past,
Pub. Nat. Acad. Sci., 81, 801
Sefilian, A. A., & Touma, J. R. 2018, Shepherding in a Self-Gravitating Disk of Trans- Neptunian Objects, arXiv:1804.06859
Shankman, C., Kavelaars, J. J., Lawler, S. M., Gladman, B. J., and Bannister, M.
T. 2017, Consequences of a Distant Massive Planet on the Large Semimajor Axis Trans-Neptunian Objects, Astron. J., 153, 63
Shankman, C., Kavelaars, J. J., Bannister, M. T., et al. 2017, OSSOS. VI. Striking Biases in the Detection of Large Semimajor Axis Trans-Neptunian Objects, Astron. J., 154, 50
Shapley, H. 1921, The Scale of the Universe: Part I, Bull. Nat. Res. Coun., 2, 171
Sheppard, S. S., and Trujillo, C. 2016, New Extreme Trans-Neptunian Objects: Toward a Super-Earth in the Outer Solar System, Astron. J., 152, 221
Sheppard, S., Trujillo, C., Tholen, D., & Kaib, N. 2018, A New High Perihelion Inner Oort Cloud Object,arXiv:1810.00013
Silsbee, K., and Tremaine, S. 2018, Producing Distant Planets by Mutual Scattering of Planetary Embryos, Astron. J., 155, 75
Slipher, V. M. 1917a, The Spectrum and Velocity of the Nebula N.G.C. 1068 (M77),
Lowell Obs. Bulletin, 3, 59-62
Slipher, V. M. 1917b, Nebulae, Proc. American Phil. Soc., 56, 403-409
Slipher, V. M. 1930, Planet X – Lowell Observatory Observation Circular, J. Royal. Astron. Soc. Canada, 24, 282
Soter, S. 2006, What Is a Planet? Astron. J., 132, 2513
Souami, D., & Souchay, J. 2012, The solar system’s invariable plane, Astron. Astro- phys., 543, A133
Spalding, C., & Batygin, K. 2014, Early Excitation of Spin-Orbit Misalignments in Close-in Planetary Systems, Astrophys. J., 790, 42
Spalding, C., & Batygin, K. 2015, Magnetic Origins of the Stellar Mass-Obliquity Correlation in Planetary Systems, Astrophys. J., 811, 82
Spalding, C., Batygin, K., & Adams, F. C. 2014, Alignment of Protostars and Circum- stellar Disks during the Embedded Phase, Astrophys. J. Letters, 797, L29
Standish, E. M. 1993, Astron. J., 105, 2000
Sykes, M. V., Cutri, R. M., Fowler, J. M., Nelson, B., Tholen, D. J., Skrutskie, M. F., and Price, S. 2002, 2MASS Observations of the Solar System, in Proceedings of Asteroids, Comets, Meteors – ACM 2002, ed. B.Warmbein (ESA Publications), pp. 481-484
Thomas, F., and Morbidelli, A. 1996, The Kozai Resonance in the Outer Solar System and the Dynamics of Long-Period Comets, Celest. Mech. Dynam. Astron., 64, 209
Tiscareno, M. S., & Malhotra, R. 2003, The Dynamics of Known Centaurs, Astron. J., 126, 3122
Tiscareno, M. S., & Malhotra, R. 2009, Chaotic Diffusion of Resonant Kuiper Belt Objects, Astron. J., 138, 827
Tombaugh, C. W. 1946, The Search for the Ninth Planet Pluto, Astron. Soc. Pacific Leaflets, 5, 7380
Tombaugh, C. W. 1996, Completing the Inventory of the Solar System, ASP Conf. Series 107, 157
Torbett, M. V., and Smoluchowski, R. 1984, Orbital Stability of the Unseen Solar Companion linked to Periodic Extinction Events, Nature, 311, 641
Touma, J. R., Tremaine, S., & Kazandjian, M. V. 2009, Gauss’s method for secular dynamics, softened, Mon. Not. R. Astron. Soc., 394, 1085
Triaud, A. H. M. J. 2017, Handbook of Exoplanets, Edited by Hans J. Deeg and Juan Antonio Belmonte. Springer Living Reference Work, ISBN: 978-3-319-30648-3, 2017, id.2, 2
Trujillo, C. A., and Sheppard, S. S. 2014, A Sedna-like Body with a Perihelion of 80 Astronomical Units, Nature, 507, 471-474
Tsiganis, K., Gomes, R., Morbidelli, A., and Levison, H. F. 2005, Origin of the Cat- aclysmic Late Heavy Bombardment Period of the Terrestrial Planets, Nature, 435, 459
Volk, K., and Malhotra, R. 2017, The Curiously Warped Mean Plane of the Kuiper Belt, Astron. J., 154, 62
Weiss, L. M. and Marcy, G. W. 2014, The Mass-Radius Relation for 65 Exoplanets Smaller than 4 Earth Radii, Astrophys. J., 783, L6
Wisdom, J. 1980, The Resonance Overlap Criterion and the Onset of Stochastic Be- havior in the Restricted Three-Body Problem, Astron. J., 85, 1122
Wisdom, J., and Holman, M. 1992, Symplectic Maps for the N-body Problem – Stability Analysis, Astron. J., 104, 2022
Winn, J. N., Johnson, J. A., Howard, A. W., et al. 2010, The Oblique Orbit of the Super-Neptune HAT-P-11b, Astrophys. J. Letters, 723, L223
https://www.iau.org/static/resolutions/Resolution_GA26-5-6.pdf
No comments:
Post a Comment