Gravitational Interactions Of Rings With Satellites

Orbital resonances between rings and satellites are responsible for features in all four ring systems, with the possible exception of the Jupiter ring system. These resonances occur when the orbital period of a given satellite and the orbital period of the ring particles it affects have a simple, generally low-number fractional relationship to one another.

The outer edge of Saturn's A ring occurs at a point where the ring particles complete seven orbits of Saturn for every six orbits of the satellite Janus; that outer ring edge is consequently seven-lobed in shape. Similarly, ring particles at the outer edge of Saturn's B ring complete two orbits of Saturn for each orbit of Mimas, and that ring edge is two-lobed. These strong resonances are known as 7:6 and 2: 1 inner Lindblad resonances, respectively. Ring particles at the inner and outer edges of Uranus's Epsilon ring are prevented from escaping that ring by a 24: 25 outer Lindblad resonance of Cordelia and a 14: 13 inner Lindblad resonance of Ophelia, respectively. A 42: 43 outer Lindblad resonance of Galatea may not only radially confine particles in Neptune's Adams ring, but the 42 lobes caused by that orbital resonance may additionally impede longitudinal spreading of material in the ring arcs from one 8.57° cell to the next.

Three other types of gravitational interactions between ring particles and satellites are noted. Density waves are initiated by orbital resonances that are somewhat weaker than the ring-confinement mechanisms of the previous paragraph. More than 50 such density waves have been identified in Saturn's A and B rings. A tentative identification was also made of a density wave in Uranus's Delta ring. Vertical tugs by Mimas, whose orbit is inclined to Saturn's equator by 1.51°, cause so-called bending waves or local corrugations in rings. Thus far, the only identified bending waves in any of the planetary ring systems are located in Saturn's A ring and are caused by Mimas. The third type of interaction occurs when a satellite is imbedded within an otherwise continuous ring. If the satellite is massive enough, it can actually clear a gap, such as the Encke gap in Saturn's A ring, which is caused by the satellite Pan. In addition, Pan also gives rise to satellite wakes at the inner and outer edges of the Encke gap. Because of differential rotation, the wakes on the inner edge of the Encke gap precede Pan in its orbit; those at the outer edge trail Pan. As discussed in Chapter 10, a new moonlet (Daphnis) found in the Keeler gap in the outer A ring also creates wakes along the edge of that gap. Furthermore, there are a number of other structures at the limits of visibility in the A ring that may be wakes of even tinier moons. It now seems likely that all of the empty gaps seen in Saturn's rings are due to clearing by moonlets not yet discovered.

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