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Formulation and analytic calculation for the spin angular momentum of a moonlet due to inelastic collisions of ring particles
Earth, Planets and Space volume 56, pages 909–919 (2004)
Small moonlets embedded in planetary rings acquire spin angular momentum by inelastic collisions of a number of ring particles. We obtain analytic expressions for the mean and mean square spin angular momenta delivered to a moonlet in the high-velocity case where mutual gravity between the moonlet and particles can be neglected. We find that the mean angular momentum brought by a large number of small impacts would result in an equilibrium rotation of a moonlet in the prograde direction that is slower than the synchronous rotation, while large impacts would significantly affect the rotation when the mass of largest impactors is comparable to the moonlet’s mass and/or the velocity dispersion of particles is larger than the Kepler shear across the moonlet’s radius. We present a new formulation that allows a unified analysis of these two components of moonlet rotation, and confirmed the validity of this formulation and the above analytic calculations using N-body simulation.
Araki, S., The dynamics of particle disks. II. Effects of spin degrees of freedom, Icarus, 76, 182–198, 1988.
Araki, S., The dynamics of particle disks. III. Dense and spinning particle disks, Icarus, 90, 139–171, 1991.
Araki, S. and S. Tremaine, The dynamics of dense particle disks, Icarus, 65, 83–109, 1986.
Daisaka, H. and S. Ida, Spatial structure and coherent motion in dense planetary rings induced by self-gravitational instability, Earth Planets Space, 51, 1195–1213, 1999.
Dones, L. and S. Tremaine, Why does the Earth spin forward?, Science, 259, 350–354, 1993a.
Dones, L. and S. Tremaine, On the origin of planetary spins, Icarus, 103, 67–92, 1993b.
Giuli, R. T., On the rotation of the Earth produced by gravitational accretion of particles, Icarus, 8, 301–323, 1968.
Greenzweig, Y. and J. J. Lissauer, Accretion rates of protoplanets, Icarus, 87, 40–77, 1990.
Greenzweig, Y. and J. J. Lissauer, Accretion rates of protoplanets. II. Gaussian distribution of planetesimal velocities, Icarus, 100, 440–463, 1992.
Hanel, R., B. Conrath, F. M. Flasar, V. Kunde, W. Maguire, J. Pearl, J. Pirraglia, R. Samuelson, L. Herath, M. Allison, D. Cruikshank, D. Gautier, P. Gierasch, L. Horn, R. Koppany, and fPonnamperuma, Infrared observations of the Saturnian System from Voyager 1, Science, 212, 192–200, 1981.
Ida, S. and K. Nakazawa, Did rotation of the protoplanets originate from the successive collisions of planetesimals?, Icarus, 86, 561–573, 1990.
Lissauer, J. J. and D. M. Kary, The origin of the systematic component of planetary rotation. I. Planet on a circular orbit, Icarus, 94, 126–159, 1991.
Lissauer, J. J. and V. S. Safronov, The random component of planetary rotation, Icarus, 93, 288–297, 1991.
Lissauer, J. J., A. F. Berman, Y. Greenzweig, and D. M. Kary, Accretion of mass and spin angular momentum by a planet on an eccentric orbit, Icarus, 127, 65–92, 1997.
Lissauer, J. J., L. Dones, and K. Ohtsuki, Origin and evolution of terrestrial planet rotation, in Origin of the Earth and Moon, edited by R. M. Canup and K. Righter, pp. 101–112, University of Arizona Press, Tucson, 2000.
Morishima, R. and H. Salo, Spin rates of small moonlets embedded in planetary rings: I. Three-body calculations, Icarus, 167, 330–346, 2004.
Nakazawa, K., S. Ida, and Y. Nakagawa, Collisional probability of planetesimals revolving in the solar gravitational field. I. Basic formulation, Astron. Astrophys., 220, 293–300, 1989.
Ohtsuki, K., Equilibrium velocities in planetary rings with low optical depth, Icarus, 95, 265–282, 1992.
Ohtsuki, K., Capture probability of colliding planetesimals: Dynamical constraints on accretion of planets, satellites, and ring particles, Icarus, 106, 228–246, 1993.
Ohtsuki, K., Evolution of particle velocity dispersion in a circumplanetary disk due to inelastic collisions and gravitational interactions, Icarus, 137, 152–177, 1999.
Ohtsuki, K., On the rotation of a moonlet embedded in planetary rings, Icarus, 2004 (in press).
Ohtsuki, K. and H. Emori, Local N-body simulations for the distribution and evolution of particle velocities in planetary rings, Astron. J., 119, 403–416, 2000.
Ohtsuki, K. and S. Ida, Planetary rotation by accretion of planetesimals with nonuniform spatial distribution formed by the planet’s gravitational perturbation, Icarus, 131, 393–420, 1998.
Salo, H., Collisional evolution of rotating, non-identical particles, Moon Planets, 38, 149–181, 1987a.
Salo, H., Numerical simulations of collisions between rotating particles, Icarus, 70, 37–51, 1987b.
Salo, H., Simulations of dense planetary rings. III. Self-gravitating identical particles, Icarus, 117, 287–312, 1995.
Spilker, L., C. Ferrari, M. R. Showalter, J. N. Cuzzi, R. Achterberg, J. Pearl, M. Flasar, V. Kunde, S. Edberg, B. Wallis, J. Aiello, S. Edgington, and Cassini CIRS Investigation Team, Cassini CIRS observations of Saturn’s rings, Bull. Amer. Astron. Soc., 34, 900, 2
Tanikawa, K., S. Manabe, and R. Broucke, On the origin of the spin angular momentum by accretion of planetesimals: Property of collision orbits, Icarus, 79, 208–222, 1989.
Weidenschilling, S. J., C. R. Chapman, D. R. Davis, and R. Greenberg, Ring particles: Collisional interactions and physical nature, in Planetary Rings, edited by R. Greenberg and A. Brahic, pp. 367–415, University of Arizona Press, Tucson, 1984.
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Ohtsuki, K. Formulation and analytic calculation for the spin angular momentum of a moonlet due to inelastic collisions of ring particles. Earth Planet Sp 56, 909–919 (2004). https://doi.org/10.1186/BF03352538
- Celestial mechanics
- rotational dynamics
- planetary rings
- origin of solar system