Physics of planetary rings: celestial mechanics of continuous medium.

Worked out was the closed theory of collisional, collective and resonance phenomena in the planetary rings. The mechanism of formation of hierarchical structure of Saturn's rings (observed by "Voyager-1") was explained. Gravitational dissipative instability accounted for the formation of the most narrow ringlets $\sim 100 m$ was discovered. This is a first example of the negative energy waves generation in the gravitating medium. The another new instability named by authors as accretion instability results in the formation of the widest ring $\sim 1000 km$. It is connected with observed accretion dusty flux to the planet. This mechanism looks like the formation of sandy dunes in a desert.

The mechanism leading to the observed coexistence of gaps and narrow ringlets in the planetary rings is found.It is based upon the quasi--stationary radial drift caused by nonlinear density wave. To describe the nonlinear accretion drift of this type correctly, real three--dimensional structure of the wave should be taken into account. A good fit of the theory results with observations in the Saturn system was shown.

An original transport theory in the planetary rings with account for differential rotation, inhomogeneous density and inelastic collisions was developed. It was shown that around the planet there are two neighbouring zones: rings zone and satellites zone. In both zones two competitive processes coexist: destruction and growth of particles as result of their mutual collisions. The former processes dominates in the rings zone, the latter - in the satellites zone.

This theory allowed to predict the existence of a set of new Uranian satellites one half year before their discovery by "Voyager-2". The main predictions were following:

1. the existence of a series of small satellites outside the external boundary of the Uranian rings (9 of 10 new Uranian satellites were discovered in this region);
2. the impossibility of the satellites formation inside the Uranian ring zone (only one smallest satellite was discovered in the intermediate zone - near the external boundary of the rings);
3. the location of not yet discovered satellites in region between 50, 000 km and 82, 500 km, is determined by the lowest Lindblad resonances 2:1, 3:2 and 4:3 with rings (8 of 10 new satellites were discovered in this zone; they have resonances of predicted types, the correlation coefficient $Q$ between positions of rings and lowest resonances from satellites is high: $Q \approx 0,84$);
4. 5 the most probable orbits of satellites, each in resonance with two rings simultaneously (orbits of 4 discovered satellites are in resonance with two rings simultaneously and coincide with predicted orbits with an accuracy of $\stackrel{<}{\sim} 0.5 \%$);
5. the availability of shepherd-satellites in the neighbourhood of the external $\varepsilon-$ring only (shepherd-satellites were detected in the neighbourhood of the $\varepsilon-$ring only);
6. the average diameter of satellites $\sim 100 km$ (the average diameter of discovered satellites is $\approx 70 km$);
7. the region of the satellites albedo $\alpha:$ $0,03 \stackrel{<}{\sim} \alpha \stackrel{<}{\sim} 0.3$ (one turned out $\alpha \approx 0.05$).