Resonant Orbits and Saturn's Rings
Physics of How Moons Cause Complex Planetary Ring Structures
Feb 17, 2008
Saturn's Ring Structure
Prior to the space program we thought Saturn had only a few rings. The Voyager mission to Saturn sent back pictures of the rings that revealed tens of thousands of individual rings. Scientists scrambled to solve the puzzle of this structure.
Two of the most likely causes of Saturn's ring structure are resonances with Saturn's larger moons and small shepherd moons.
Familiar Example of Resonance
Think about pushing a child on a swing. If one gives even small pushes at the same position of the swing, the result of many pushes will add up. Pretty soon the child will be swinging rather high. These pushes are an example of resonance.
If on the other hand, the pushes are at random positions of the swing, they will tend to cancel rather than add up. The child will not swing very high. These random pushes are an example of nonresonant pushes.
Resonances
The period of time it takes a moon or ring particle to orbit Saturn depends on its orbital distance. At distances where the ratios of orbital periods of a moon and ring particles is a simple integer fraction or multiple (2/1, 3/2, etc.), there is a resonance.
For example if a moon has exactly twice the orbital period of a ring particle, the ring particle is between the moon and Saturn every two orbits at precisely the same point in the orbit. When the ring particle is between Saturn and the moon, it is at its closest distance to the moon. The moon therefore exerts a stronger gravitational pull on the ring particle.
The extra gravitational tug is not much, but because it occurs at the same point in the ring particle's orbit every time (like the resonant pushes of the swing) the tugs add up. They pull the ring particle into an elliptical, rather than circular, orbit. The new elliptical orbit has its most distant point from Saturn at the point where the gravitational tugs from the moon occurred. Collisions with other ring particles in orbits farther from Saturn then cause the elliptical orbit to become circular at a greater distance from Saturn than the original resonant orbit. The moon therefore tends to pull ring particles away from a resonant orbit and leave a gap in the ring structure.
Ring particles that are not located in resonant orbits get the extra gravitational tugs from the moon at random points in their orbits. Hence the tugs do not add up to pull ring particles from that orbit.
The Cassini Division between Saturn's A and B rings is at an orbital distance that has a 2/1 resonance with Saturn's moon, Mimas. Mimas therefore pulls ring particles out of this orbit, leaving a gap in the ring structure large enough to be visible from Earth. The 60 known moons of Saturn have lots of resonant orbits and can therefore produce a very complex ring structure
Taken together resonances and shepherd moons cause the fantastically detailed ring structures we observe around Saturn, the crown jewel of our solar system.
Further Reading
Chaisson, E, and McMillan, S. Astronomy Today 5th ed., Pearson, 2005.
Beatty, J.K., O'Leary, B., and Chaikin, A. The New Solar System 2nd ed., Cambridge, 1982.
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