Saturn's fast spin determined from its gravitational field and oblateness

TL;DR

This paper determines Saturn's rotation period by analyzing its gravitational field and shape, providing a more accurate estimate than previous radio-based measurements, and validates the method on Jupiter.

Contribution

It introduces a novel method to estimate Saturn's rotation period using gravitational and shape data, overcoming limitations of magnetic and radio measurements.

Findings

Saturn's rotation period is 10h 32m 45s ± 46s.

The method accurately recovers Jupiter's known rotation period.

Gravitational and shape constraints can determine planetary rotation with minutes-level precision.

Abstract

The alignment of Saturn's 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 +- 46s, based upon an optimization approach using Saturn's 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.