Abstract
Four small moons (Styx, Nix, Kerberos and Hydra) are at present known to orbit around the barycenter of Pluto and Charon, which are themselves considered a binary dwarf planet due to their relatively high mass ratio. The central, non-axisymmetric potential induces moon orbits inconvenient to be described by Keplerian osculating elements. Here, we report that observed orbital variations may not be the result of orbital eccentricities or observational uncertainties, but may be due to forced oscillations caused by the central binary. We show, using numerical integration and analytical considerations, that the differences reported on their orbital elements may well arise from this intrinsic behavior rather than limitations on our instruments.
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Bromley, B.C., Kenyon, S.J.: A Pluto-Charon concerto: an impact on Charon as the origin of the small satellites. Astron. J. 160(2), 85 (2020). https://doi.org/10.3847/1538-3881/ab9e6c
Bromley, B.C., Kenyon, S.J.: On the estimation of circumbinary orbital properties. Astron. J. 161(1), 25 (2021). https://doi.org/10.3847/1538-3881/abcbfb
Brozović, M., Showalter, M.R., Jacobson, R.A., Buie, M.W.: The orbits and masses of satellites of Pluto. Icarus 246, 317–329 (2015). https://doi.org/10.1016/j.icarus.2014.03.015
Buie, M.W., Tholen, D.J., Grundy, W.M.: The orbit of Charon is circular. Astron. J. 144(1), 15 (2012). https://doi.org/10.1088/0004-6256/144/1/15
Burns, J.A., Lamy, P.L., Soter, S.: Radiation forces on small particles in the solar system. Icarus 40(1), 1–48 (1979). https://doi.org/10.1016/0019-1035(79)90050-2
Christy, J.W., Harrington, R.S.: The satellite of Pluto. Astron. J. 83, 1005 (1978). https://doi.org/10.1086/112284
Doolin, S., Blundell, K.M.: The dynamics and stability of circumbinary orbits. Mon. Not. R. Astron. Soc. 418(4), 2656–2668 (2011). https://doi.org/10.1111/j.1365-2966.2011.19657.x
Dvorak, R.: Critical orbits in the elliptic restricted three-body problem. Astron. Astrophys. 167, 379–386 (1986)
Georgakarakos, N., Eggl, S.: Analytic orbit propagation for transiting circumbinary planets. Astrophys. J. 802(2), 94 (2015). https://doi.org/10.1088/0004-637X/802/2/94
Hamilton, D.P., Krivov, A.V.: Circumplanetary dust dynamics: effects of solar gravity, radiation pressure, planetary oblateness, and electromagnetism. Icarus 123(2), 503–523 (1996). https://doi.org/10.1006/icar.1996.0175
Holman, M.J., Wiegert, P.A.: Long-term stability of planets in binary systems. Astron. J. 117(1), 621–628 (1999). https://doi.org/10.1086/300695
Kenyon, S.J., Bromley, B.C.: A Pluto-Charon sonata: dynamical limits on the masses of the small satellites. Astron. J. 158(2), 69 (2019). https://doi.org/10.3847/1538-3881/ab2890
Kenyon, S.J., Bromley, B.C.: A Pluto-Charon concerto. II. Formation of a circumbinary disk of debris after the giant impact. Astron. J. 161(5), 211 (2021). https://doi.org/10.3847/1538-3881/abe858
Lee, M.H., Peale, S.J.: On the orbits and masses of the satellites of the Pluto Charon system. Icarus 184(2), 573–583 (2006). https://doi.org/10.1016/j.icarus.2006.04.017
Leung, G.C.K., Lee, M.H.: An analytic theory for the orbits of circumbinary planets. Astrophys. J. 763(2), 107 (2013). https://doi.org/10.1088/0004-637X/763/2/107
Michaely, E., Perets, H.B., Grishin, E.: On the existence of regular and irregular outer moons orbiting the Pluto-Charon system. Astrophys. J. 836(1), 27 (2017). https://doi.org/10.3847/1538-4357/aa52b2
Murray, C.D., Dermott, S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999)
Pires dos Santos, P.M., Giuliatti Winter, S.M., Sfair, R., Mourão, D.C.: Small particles in Pluto’s environment: effects of the solar radiation pressure. arXiv e-prints, art. arXiv:1108.0712 (Aug. 2011)
Porter, S., Spencer, J.R., Showalter, M., J. Weaver, H. A., McKinnon, W.B., Olkin, C., et al.: Shapes and Densities of the small satellites of Pluto. In: AGU Fall Meeting Abstracts, p. P42A-06
Showalter, M.R., Hamilton, D.P.: Resonant interactions and chaotic rotation of Pluto’s small moons. Nature 522(7554), 45–49 (2015). https://doi.org/10.1038/nature14469
Showalter, M.R., Hamilton, D.P., Stern, S.A., Weaver, H.A., Steffl, A.J., Young, L.A.: New Satellite of (134340) Pluto:S/2011 (134340) 1. IAUC 9221, 1 (2011)
Showalter, M.R., Weaver, H.A., Stern, S.A., Steffl, A.J., Buie, M.W., Merline, W.J., Mutchler, M.J., Soummer, R., Throop, H.B.: New Satellite of (134340) Pluto: S/2012 (134340) 1. IAUC 9253, 1 (2012)
Springel, V., Pakmor, R., Zier, O., Reinecke, M.: Simulating cosmic structure formation with the GADGET-4 code. Mon. Not. R. Astron. Soc. 506(2), 2871–2949 (2021). https://doi.org/10.1093/mnras/stab1855
Steffl, A.J., Mutchler, M.J., Weaver, H.A., Stern, S.A., Durda, D.D., Terrell, D., Merline, W.J., Young, L.A., Young, E.F., Buie, M.W., Spencer, J.R.: New constraints on additional satellites of the Pluto system. Astron. J. 132(2), 614–619 (2006). https://doi.org/10.1086/505424
Stern, S.A., Fesen, R.A., Barker, E.S., Parker, J.W., Trafton, L.M.: A search for distant satellites of Pluto. Icarus 94(1), 246–249 (1991). https://doi.org/10.1016/0019-1035(91)90154-L
Stern, S.A., Bagenal, F., Ennico, K., Gladstone, G.R., Grundy, W.M., McKinnon, W.B., et al.: The Pluto system: initial results from its exploration by new horizons. Science 350(6258), aad1815 (2015). https://doi.org/10.1126/science.aad1815
Szebehely, V.: Theory of orbits. The restricted problem of three bodies (1967)
Szebehely, V.: Stability of artificial and natural satellites. Celestial Mech. 18(4), 383–389 (1978). https://doi.org/10.1007/BF01230350
Weaver, H.A., Stern, S.A., Mutchler, M.J., Steffl, A.J., Buie, M.W., Merline, W.J., Spencer, J.R., Young, E.F., Young, L.A.: Discovery of two new satellites of Pluto. Nature 439(7079), 943–945 (2006). https://doi.org/10.1038/nature04547
Weaver, H.A., Buie, M.W., Buratti, B.J., Grundy, W.M., Lauer, T.R., Olkin, C.B., et al.: The small satellites of Pluto as observed by New Horizons. Science 351(6279), aae0030 (2016). https://doi.org/10.1126/science.aae0030
Winter, S.M.G., Winter, O.C., Guimarães, A.H.F., Silva, M.R.: Exploring S-type orbits in the Pluto-Charon binary system. Mon. Not. R. Astron. Soc. 404(1), 442–450 (2010). https://doi.org/10.1111/j.1365-2966.2010.16302.x
Woo, J.M.Y., Lee, M.H.: On the Early In Situ Formation of Pluto’s Small Satellites. Astron. J. 155(4), 175 (2018). https://doi.org/10.3847/1538-3881/aab367
Woo, J.M.Y., Lee, M.H.: A numerical method for determining the elements of circumbinary orbits and its application to circumbinary planets and the satellites of Pluto-Charon. Astron. J. 159(6), 277 (2020). https://doi.org/10.3847/1538-3881/ab8dc1
Youdin, A.N., Kratter, K.M., Kenyon, S.J.: Circumbinary chaos: using Pluto’s newest moon to constrain the masses of Nix and Hydra. Astrophys. J. 755(1), 17 (2012). https://doi.org/10.1088/0004-637X/755/1/17
Acknowledgements
We thank an anonymous referee for a thorough and insightful review that has improved this paper. The numerical code used in this work was branched from an n-body code (https://github.com/pmocz/nbody-python) created by Philip Mocz, that was based on the second-order leapfrog integration method (see, e.g., Springel et al. 2021). KNG acknowledges funding from grant FK 81641 “Theoretical and Computational Astrophysics,” ELKE. The authors thank Apostolos Christou for insightful comments on this manuscript. Part of this paper was written on Mountain Aroania in Greece, within a short distance from the mythological dwelling of the deity Styx, and the Styx spring.
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FK 8161, Theoretical and Computational Astrophysics, University of Patras.
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Gakis, D., Gourgouliatos, K.N. Orbit determination of the moons of the Pluto–Charon system. Celest Mech Dyn Astr 134, 14 (2022). https://doi.org/10.1007/s10569-022-10071-x
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DOI: https://doi.org/10.1007/s10569-022-10071-x