The alignment of SaturnÕs magnetic pole with its rotation axis precludes the use of magnetic field measurements to determine its rotation period [ ] .
The period was previously determined from radio measurements by the Voyager spacecraft to be 10h 39m 22.4s [ ] .
When the Cassini spacecraft measured a period of 10h 47m 6s , which was additionally found to change between sequential measurements [ ] , it became clear that the radio period could not be used to determine the bulk planetary rotation period .
Estimates based upon Saturn ’ s measured wind fields have increased the uncertainty even more , giving numbers smaller than the Voyager rotation period , and at present Saturn ’ s rotation period is thought to be between 10h 32m and 10h 47m , which is unsatisfactory for such a fundamental property .
Here we report a period of 10h 32m 45s \pm  46s , based upon an optimization approach using SaturnÕs measured gravitational field and limits on the observed shape and possible internal density profiles .
Moreover , even when solely using the constraints from its gravitational field , the rotation period can be inferred with a precision of several minutes .
To validate our method , we applied the same procedure to Jupiter and correctly recovered its well-known rotation period .