Gravity Field and Interior Structure of Saturn from Cassini Observations

Details Gravity Field and Interior Structure of Saturn from Cassini Observations Gravity Field and Interior Structure of Saturn from Cassini Observations

May 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agusm.p23a..08a&link_type=abstract

American Geophysical Union, Spring Meeting 2007, abstract #P23A-08

Physics

1221 Lunar And Planetary Geodesy And Gravity (5417, 5450, 5714, 5744, 6019, 6250), 5714 Gravitational Fields (1221), 5724 Interiors (8147), 6275 Saturn, 8147 Planetary Interiors (5430, 5724, 6024)

Scientific paper

We discuss the sources for a determination of Saturn's external gravitational potential, beginning with a Pioneer 11 flyby in September 1979, two Voyager flybys in November 1980 for Voyager 1 and August 1981 for Voyager 2, four useful close approaches by the Cassini orbiter in May and June 2005, and culminating in an extraordinary close approach for Radio Science in September 2006. Results from the 2006 data are not yet available, but even without them, Cassini offers improvements in accuracy over Pioneer and Voyager by a factor of 37 in the zonal coefficient J2, a factor of 14 in J4, and a factor of 5 in J6. These improvements are important to our understanding of the internal structure of Saturn in particular, and to solar and extrasolar giant planets in general. Basically, Saturn can be modeled as a rapidly rotating planet in hydrostatic equilibrium. Consistent with the limited data available, we express the density distribution as a polynomial of fifth degree in the normalized mean radius β = r/R over the real interval zero to one, where R is the radius of a sphere with density equal to the mean density of Saturn. Then the six coefficients of the polynomial are adjusted by nonlinear least squares until they match the measured even zonal gravity coefficients J2,J4,J6 within a fraction of a standard deviation. The gravity coefficients are computed from the density distribution by the method of level surfaces to the third order in the rotational smallness parameter. Two degrees of freedom are removed by applying the constraints that (1)~the derivative of the density distribution is zero at the center, and (2)~the density is zero at the surface. Further, a unique density distribution is obtained by the method of singular value decomposition truncated at rank three. Given this unique density distribution, the internal pressure can be obtained by numerical integration of the equation of hydrostatic equilibrium, expressed in terms of the single independent parameter β. By means of this technique, a pressure of 3~Mbar is indicated at about half the distance to the surface, consistent with a phase transition from molecular to metallic hydrogen at 50% depth. However, a similar integration of the mass continuity equation does not use up all the mass. Mathematically this results in a point- mass core of about 10 Earth masses, although in reality the core must be sufficiently large to have a physically reasonable mean density. Our results are robust against the relatively large uncertainty in Saturn's rotation period.

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