Antognini, Francesco; Biasco, Luca; Chierchia, Luigi The spin-orbit resonances of the solar system: a mathematical treatment matching physical data. (English) Zbl 1302.70034 J. Nonlinear Sci. 24, No. 3, 473-492 (2014). Summary: In the mathematical framework of a restricted, slightly dissipative spin-orbit model, we prove the existence of periodic orbits for astronomical parameter values corresponding to all satellites of the Solar System observed in exact spin-orbit resonance. Cited in 2 Documents MSC: 70F15 Celestial mechanics 70F40 Problems involving a system of particles with friction 70E20 Perturbation methods for rigid body dynamics 70G70 Functional analytic methods for problems in mechanics 70H09 Perturbation theories for problems in Hamiltonian and Lagrangian mechanics 70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics 34C23 Bifurcation theory for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 34D10 Perturbations of ordinary differential equations Keywords:periodic orbits; celestial mechanics; spin-orbit resonances; moons in the solar system; Mercury; dissipative systems PDF BibTeX XML Cite \textit{F. Antognini} et al., J. Nonlinear Sci. 24, No. 3, 473--492 (2014; Zbl 1302.70034) Full Text: DOI arXiv References: [1] Bambusi, D., Haus, E.: Asymptotic stability of synchronous orbits for a gravitating viscoelastic sphere. Celest. Mech. Dyn. Astron. 114(3), 255-277 (2012) · Zbl 1266.70022 [2] Biasco, L; Chierchia, L, Low-order resonances in weakly dissipative spin-orbit models, J. Differ. Equ., 246, 4345-4370, (2009) · Zbl 1178.34043 [3] Castillo-Rogez, JC; Efroimsky, M; Lainey, V, The tidal history of iapetus: spin dynamics in the light of a refined dissipation mode, J. Geophys. Res., 116, e09008, (2011) [4] Celletti, A, Analysis of resonances in the spin-orbit problem in celestial mechanics: the synchronous resonance (part I), J. Appl. Math. Phys., 41, 174-204, (1990) · Zbl 0699.70014 [5] Celletti, A.: Stability and Chaos in Celestial Mechanics. Springer-Praxis, Providence (2010) · Zbl 1203.70001 [6] Celletti, A; Chierchia, L, Quasi-periodic attractors in celestial mechanics, Arch. Ration. Mech. Anal., 191, 311-345, (2009) · Zbl 1161.70012 [7] Correia, ACM; Laskar, J, Mercury’s capture into the 3/2 spin-orbit resonance as a result of its chaotic dynamics, Nature, 429, 848-850, (2004) [8] Danby, J.M.A.: Fundamentals of Celestial Mechanics. Macmillan, New York (1962) [9] Dougherty, M.K., et al. (eds.): Saturn from Cassini-Huygens. Springer, Netherlands (2009). doi:10.1007/978-1-4020-9217-6 [10] Goldreich, P; Peale, S, Spin-orbit coupling in the solar system, Astron. J., 71, 425, (1967) [11] Hussmann, H; Sohl, F; Spohn, T, Subsurface oceans and deep interiors of medium-sized outer planet satellites and large trans-Neptunian objects, Icarus, 185, 258-273, (2006) [12] Iess, L; etal., Gravity field, shape, and moment of inertia of Titan, Science, 327, 1367-1369, (2010) [13] Iess, L; etal., The tides of Titan, Science, 337, 457-459, (2012) [14] Lainey, V; etal., Strong tidal dissipation in saturn and constraints on enceladus’ thermal state from astrometry, Astrophys. J., 752, 14-19, (2012) [15] MacDonald, GJF, Tidal friction, Rev. Geophys., 2, 467-541, (1964) [16] Peale, SJ, The free precession and libration of Mercury, Icarus, 178, 4-18, (2005) [17] Porco, CC; etal., Saturn’s small inner satellites: clues to their origins, Science, 318, 1602-1607, (2007) [18] Runcorn, S.K., Hofmann, S.: The Moon. In: Proceedings from IAU Symposium no. 47. Reidel, Dordrecht (1972) [19] Sicardy, B; etal., Charon’s size and an upper limit on its atmosphere from a stellar occultation, Nature, 439, 52-54, (2006) [20] Thomas, PC, Radii, shapes, and topography of the satellites of uranus from limb coordinates, Icarus, 73, 427-441, (1988) [21] Thomas, PC, The shapes of small satellites, Icarus, 77, 248-274, (1989) [22] Thomas, P.C., et al.: The small inner satellites of Jupiter. Icarus 135, 360-371 (1998) [23] Wintner, A.: The Analytic Foundations of Celestial Mechanics. Princeton University Press, Princeton (1941) · JFM 67.0785.01 [24] Wisdom, J, Rotational dynamics of irregularly shaped natural satellites, Astron. J., 94, 1350-1360, (1987) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.