  Anderson & Schubert (2007, Science,317,1384) proposed that Saturn's rotation
period can be ascertained by minimizing the dynamic heights of the 100 mbar
isosurface with respect to the geoid; they derived a rotation period of 10h 32m
35s. We investigate the same approach for Jupiter to see if the Jovian rotation
period is predicted by minimizing the dynamical heights of its isobaric (1 bar
pressure level) surface using zonal wind data. A rotation period of 9h 54m 29s
is found. Further, we investigate the minimization method by fitting Pioneer
and Voyager occultation radii for both Jupiter and Saturn. Rotation periods of
9h 55m 30s and 10h 32m 35s are found to minimize the dynamical heights for
Jupiter and Saturn, respectively. Though there is no dynamical principle
requiring the minimization of the dynamical heights of an isobaric surface, the
successful application of the method to Jupiter lends support to its relevance
for Saturn. We derive Jupiter and Saturn rotation periods using equilibrium
theory in which the solid-body rotation period (no winds) that gives the
observed equatorial and polar radii at the 100 mbar level is found. Rotation
periods of 9h 55m 20s and 10h 31m 49s are found for Jupiter and Saturn,
respectively. We show that both Jupiter's and Saturn's shapes can be derived
using solid-body rotation, suggesting that zonal winds have a minor effect on
the planetary shape for both planets. The agreement in the values of Saturn's
rotation period predicted by the different approaches supports the conclusion
that the planet's period of rotation is about 10h 32m.
