image credit: Mark S. Deprest, University Lowbrow Astronomer, Ann Arbor, MI; image source; larger image

The Laws of Planetary Motion

This photograph shows the planets Jupiter and Venus and also the four Galilean moons of Jupiter. In both the solar system and the Jupiter system, the mathematical relationship between the objects' orbital radius and period is the same: the square of the period is proportional to the cube of the radius.
-- Kepler's third law expressed this relationship for planets in the solar system (see The Laws of Planetary Motion).
-- Newton explained and generalized it (see Gravity, Newton's laws, and the orbits of planets from the University of New South Wales).

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Kepler Motion

For applets that illustrate Kepler's laws, visit this National Taiwan Normal University site Kepler Motion.

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Adapted and reprinted with permission from "Saturn's dynamical rings," by Carl D. Murray, Physics Today, August 2007, page 74. Cassini image courtesy of NASA/JPL/Space Science Institute; larger image

The Alphabet Soup of Saturn's Rings

The objects that make up Saturn's rings are in gravitational orbits about the planet, so the closer-in objects are moving faster than those further out (just as with the planets in the solar system or the moons of Jupiter). The image shows the gap swept out of the A ring by Saturn's moon Daphnis, and the disturbances it creates in the ring material in the nearby edges of this gap. The red arrows show the velocities of the material in the rings and also of Daphnis, and the black arrows show the relative velocities in Daphnis' frame of reference. You can watch an animation of Daphnis traveling through the gap here.
-- Since Daphnis moves faster than the particles in the ring just outside it, the disturbance on the outside looks like a wake, behind Daphnis.
-- Since Daphnis moves more slowly than the particles in the ring just on the inside, the disturbance on the inside is ahead of of Daphnis.

(This feature was updated on February 18, 2014.)

SolStation: Saturn

Visit SolStation: Saturn for a well-illustrated look at Saturn, starting with the latest research and including the planet itself, the rings, and the moons.