TY - JOUR
T1 - A new formulation of the viscosity in planetary rings
AU - Tanaka, Hidekazu
AU - Ohtsuki, Keiji
AU - Daisaka, Hiroshi
N1 - Funding Information:
The authors thank the anonymous reviewer and H. Salo for helpful comments. This work is supported by Grant-in-Aid for Specially Promoted Research of the Japanese Ministry of Education, Science, and Culture (11101002). K.O. is grateful for the support by the Cassini Project and NASA’s Planetary Geology and Geophysics Program.
PY - 2003/1/1
Y1 - 2003/1/1
N2 - We present a new formulation of the viscosity in planetary rings, where particles interact through their gravitational forces and direct collisions. In the previous studies on the viscosity in self-gravitating rings, the viscosity consists of three components, which are defined separately in different ways. The complex definitions make it difficult to evaluate the viscosity in N-body simulation of rings. In our new formulation, the viscosity is expressed in terms of changes in orbital elements of particles due to particle interactions. This makes the expression of the viscosity simple. The new formulation gives a simple way to evaluate the viscosity in N-body simulation. We find that for practical evaluation of the viscosity of planetary rings, only energy dissipation at direct inelastic collisions is needed. For tenuous particle disks (i.e., optically thin disks), we further derive a formula of the viscosity. The formula requires only a numerical coefficient that can be obtained from three-body calculation. Since planetesimal disks are also tenuous, the viscosity in planetesimal disks can be also obtained from this formula. In a subsequent paper, we will evaluate this coefficient through three-body calculation and obtain the viscosity for a wide range of parameters such as the restitution coefficient and the radial location in rings.
AB - We present a new formulation of the viscosity in planetary rings, where particles interact through their gravitational forces and direct collisions. In the previous studies on the viscosity in self-gravitating rings, the viscosity consists of three components, which are defined separately in different ways. The complex definitions make it difficult to evaluate the viscosity in N-body simulation of rings. In our new formulation, the viscosity is expressed in terms of changes in orbital elements of particles due to particle interactions. This makes the expression of the viscosity simple. The new formulation gives a simple way to evaluate the viscosity in N-body simulation. We find that for practical evaluation of the viscosity of planetary rings, only energy dissipation at direct inelastic collisions is needed. For tenuous particle disks (i.e., optically thin disks), we further derive a formula of the viscosity. The formula requires only a numerical coefficient that can be obtained from three-body calculation. Since planetesimal disks are also tenuous, the viscosity in planetesimal disks can be also obtained from this formula. In a subsequent paper, we will evaluate this coefficient through three-body calculation and obtain the viscosity for a wide range of parameters such as the restitution coefficient and the radial location in rings.
KW - Celestial mechanics
KW - Planetary rings
KW - Planetesimals
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U2 - 10.1016/S0019-1035(02)00015-5
DO - 10.1016/S0019-1035(02)00015-5
M3 - Article
AN - SCOPUS:0037218622
VL - 161
SP - 144
EP - 156
JO - Icarus
JF - Icarus
SN - 0019-1035
IS - 1
ER -