Abstract
Possible rotation states of two satellites of Saturn, Prometheus (S16) and Pandora (S17), are studied by means of numerical experiments. The attitude stability of all possible modes of synchronous rotation and the motion close to these modes is analyzed by means of computation of the Lyapunov spectra of the motion. The stability analysis confirms that the rotation of Prometheus and Pandora might be chaotic, though the possibility of regular behaviour is not excluded. For the both satellites, the attitude instability zones form series of concentric belts enclosing the main synchronous resonance center in the phase space sections. A hypothesis is put forward that these belts might form “barriers” for capturing the satellites in synchronous rotation. The satellites in chaotic rotation can mimic ordinary regular synchronous behaviour: they preserve preferred orientation for long periods of time, the largest axis of satellite’s figure being directed approximately towards Saturn.
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References
Beletsky V.V. (1965). The Motion of an Artificial Satellite about its Mass Center. Nauka Publishers, Moscow
Black G.J., Nicholson P.D. and Thomas P.C. (1995). Hyperion: rotational dynamics. Icarus 117: 149–161
Cooper N.J. and Murray C.D. (2004). Dynamical influences on the orbits of Prometheus and Pandora. Astron. J. 127: 1204–1217
Devyatkin A.V., Gorshanov D.L., Gritsuk A.N., Melnikov A.V., Sidorov M.Yu. and Shevchenko I.I. (2002). Observations and theoretical analysis of light curves of natural planetary satellites. Sol. Sys. Res. 36: 248–259 [Astron. Vestnik 36, 269–281]
Éphémérides Astronomiques (Annuaire du Bureau des Longitudes). Masson, Paris (1999)
Farmer A.J. and Goldreich P. (2006). Understanding the behavior of Prometheus and Pandora. Icarus 180: 403–411
French R.G., McGhee C.A. and Dones L. et al. (2003). Saturn’s wayward shepherds: the peregrinations of Prometheus and Pandora. Icarus 162: 143–170
Goldreich P. and Rappaport N. (2003a). Chaotic motions of Prometheus and Pandora. Icarus 162: 391–399
Goldreich P. and Rappaport N. (2003b). Origin of chaos in the Prometheus–Pandora system. Icarus 166: 320–327
Goździewski K. and Maciejewski A.J. (1995). On the gravitational fields of Pandora and Prometheus. Earth Moon Planets 69: 25–50
Hairer E., Nørsett S.P. and Wanner G. (1987). Solving Ordinary Differential Equations I. Nonstiff Problems. Springer-Verlag, Berlin
Klavetter J.J. (1989a). Rotation of Hyperion. I—Observations. Astron. J. 97: 570–579
Klavetter J.J. (1989b). Rotation of Hyperion. II—Dynamics. Astron. J. 98: 1855–1874
Kouprianov V.V. and Shevchenko I.I. (2003). On the chaotic rotation of planetary satellites: the Lyapunov exponents and the energy. Astron. Astrophys. 410: 749–757
Kouprianov V.V. and Shevchenko I.I. (2005). Rotational dynamics of planetary satellites: a survey of regular and chaotic behavior. Icarus 176: 224–234
Kouprianov V.V. and Shevchenko I.I. (2006). The shapes and rotational dynamics of minor planetary satellites. Sol. Sys. Res. 40: 393–399 [Astron. Vestnik 40, 428–435]
Markeev A.P. (1990). Theoretical Mechanics. Nauka Publishers, Moscow
Melnikov A.V. (2001). Bifurcation regime of synchronous resonance in the transitional-rotational motion of nonspherical natural satellites of planets. Cosmic Res. 39: 68–77 [Kosmich. Issled. 39, 74–84]
Melnikov A.V. and Shevchenko I.I. (1998). The stability of the rotational motion of nonspherical natural satellites, with respect to tilting the axis of rotation. Sol. Sys. Res. 32: 480–490 [Astron. Vestnik 32, 548–559]
Melnikov A.V. and Shevchenko I.I. (2000). On the stability of the rotational motion of nonspherical natural satellites in synchronous resonance. Sol. Sys. Res. 34: 434–442 [Astron. Vestnik 34, 478–486]
Melnikov A.V. and Shevchenko I.I. (2007). Unusual rotation modes of minor planetary satellites. Sol. Sys. Res. 41: 483–491 [Astron. Vestnik 41, 521–530]
Porco, C.C., Weiss, J.W., Thomas, P.C., Richardson, D.C., Jacobson, R.A., Spitale, J.: Physical characteristics and possible accretionary origins for Saturn’s small satellites. 37th Annual Lunar and Planetary Science Conference. Abstract No. 2289 (2006)
Seidelmann P.K., Abalakin V.K., Bursa M., Davies M.E., de Bergh C., Lieske J.H., Oberst J., Simon J.L., Standish E.M., Stooke P. and Thomas P.C. (2002). Report of the IAU/IAG working group on cartographic coordinates and rotational elements of the planets and satellites: 2000. Celest. Mech. Dyn. Astron. 82: 83–110
Seidelmann P.K., Archinal B.A., A’Hearn M.F., Cruikshank D.P., Hilton J.L., Keller H.U., Oberst J., Simon J.L., Stooke P., Tholen D.J. and Thomas P.C. (2005). Report of the IAU/IAG working group on cartographic coordinates and rotational elements: 2003. Celest. Mech. Dyn. Astron. 91: 203–215
Seidelmann P.K., Archinal B.A., A’Hearn M.F., Conrad A., Consolmagno G.J., Hestroffer D., Hilton J.L., Krasinsky G.A., Neumann G., Oberst J., Stooke P., Tedesco E.F., Tholen D.J., Thomas P.C., Williams I.P., Cruikshank D.P., Hilton J.L., Keller H.U., Oberst J., Simon J.L., Stooke P., Tholen D.J. and Thomas P.C. (2007). Report of the IAU/IAG working group on cartographic coordinates and rotational elements: 2006. Celest. Mech. Dyn. Astron. 98: 155–180
Shevchenko I.I. (1999). The separatrix algorithmic map: application to the spin-orbit motion. Celest. Mech. Dyn. Astron. 73: 259–268
Shevchenko I.I. and Kouprianov V.V. (2002). On the chaotic rotation of planetary satellites: the Lyapunov spectra and the maximum Lyapunov exponents. Astron. Astrophys. 394: 663–674
Stooke P.J. (1993). The shapes and surface features of Prometheus and Pandora. Earth Moon Planets 62: 199–221
Thomas P.C. (1989). The shapes of small satellites. Icarus 77: 248–274
Thomas P.C., Black G.J. and Nicholson P.D. (1995). Hyperion: rotational dynamics. Icarus 117: 128–148
von Bremen H.F., Udwadia F.E. and Proskurowski W. (1997). An efficient QR based method for the computation of Lyapunov exponents. Physica D 101: 1–16
Wisdom J. (1987). Rotational dynamics of irregularly shaped natural satellites. Asron. J. 94: 1350–1360
Wisdom J., Peale S.J. and Mignard F. (1984). The chaotic rotation of Hyperion. Icarus 58: 137–152
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Melnikov, A.V., Shevchenko, I.I. On the rotational dynamics of Prometheus and Pandora. Celest Mech Dyn Astr 101, 31–47 (2008). https://doi.org/10.1007/s10569-008-9131-z
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DOI: https://doi.org/10.1007/s10569-008-9131-z