Abstract
Hämeen-Anttila's (1984) analytical treatment of self-gravitating collisional particle disks is extended to include the particle spin. The equations derived for the coupled evolution of random velocities and spins indicate that friction and surface irregularity typically reduce the local velocity dispersion. Friction, and especially irregularity, also transfer significant amounts of random kinetic energy, E kin, to rotational energy, E rot. The equilibrium ratio E rot/Ekin = 2β/(14 − 5β) if the particles are spherical, and 2(1 + α)/7 if they are irregular but frictionless, α and β being the coefficients of restitution and friction. These results are not only exact for identical, non-gravitating mass points, but are rather accurate even if finite size, self-gravitational forces, or size distribution are included. Applications to the dynamics of Saturn's rings suggest that the inclusion of rotation is able to reduce the geometrical thickness of the layer of centimeter-sized particles to about one half, at most. Large particles are less affected.
Article PDF
Similar content being viewed by others
References
Borderies, N., Goldreich, P., and Tremaine, S.: 1983’, Icarus 55, 124.
Brahic, A.: 1977’, Astron. Astrophys. 54, 895.
Brahic, A. and Hénon, M.: 1977’, Astron. Astrophys. 59, 1.
Bridges, F. G., Hatzes, A., and Lin, D. N. C.: 1984’, Nature 309, 333.
Clairemidi, S.: 1983, in Proc. I.A.U. Colloquium 75, Planetary Rings (A. Brahic, Ed.), p. 397. Cepedues-Editions, Toulouse, France.
Cuzzi, J. N., Durisen, R. H., Burns, J. A., and Hamill, P.: 1979’, Icarus 38, 54.
Goldreich, P. and Tremaine, S.: 1978’, Icarus 34, 227.
Hämeen-Anttila, K. A.: 1978’, Astrophys. Space Sci. 58, 477.
Hämeen-Anttila, K. A.: 1981’, The Moon and the Planets 25, 477.
Hämeen-Anttila, K. A.: 1982’, The Moon and the Planets 26, 171.
Hämeen-Anttila, K. A.: 1983’, The Moon and the Planets 28, 267.
Hämeen-Anttila, K. A.: 1984’, Earth, Moon, and Planets 31, 271.
Hämeen-Anttila, K. A. and Lukkari, J.: 1980’, Astrophys. Space Sci. 71, 475.
Lukkari, J.: 1978’, Astrophys. Space Sci. 58, 113.
Lukkari, J. and Salo, H.: 1984’, Earth, Moon, and Planets 31, 1.
Marouf, E. A., Tyler, G. L., Zebker, H. A., Simpson, R. A., and Eshleman, V. R.: 1983, Icarus 54, 189.
Salo, H.: 1985’, Earth, Moon, and Planets 33, 189.
Salo, H.: 1986’, Icarus (in press).
Salo, H. and Lukkari, J.: 1982’, The Moon and the Planets 27, 5.
Salo, H. and Lukkari, J.: 1984’, Earth, Moon, and Planets 30, 229.
Shu, F. H., Dones, L., Lissauer, J. J., Yuan, C., and Cuzzi, J. N.: 1985’, Ap. J. 299, 542.
Shu, F. H. and Stewart, G. R.: 1985’, Icarus 62, 360.
Shukman, I. G.: 1984’, Sov. Astron. 28, 574.
Stewart, G. R., Lin, D. N. C., and Bodenheimer, P.: 1984, in Planetary Rings (R. Greenberg and A. Brahic, Eds.), p. 447. Univ. of Arizona Press, Tucson.
Trulsen, J.: 1972a’, Astrophys. Space Sci. 17, 241.
Trulsen, J.: 1972b’, Astrophys. Space Sci. 18, 3.
Author information
Authors and Affiliations
Additional information
On leave from Dept. of Astronomy, University of Oulu, 90570 Oulu, Finland.
Rights and permissions
About this article
Cite this article
Salo, H. Collisional evolution of rotating, non-identical particles. Earth Moon Planet 38, 149–181 (1987). https://doi.org/10.1007/BF00119681
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00119681