Core-Envelope Interior Models of the Outer Planets

Details Core-Envelope Interior Models of the Outer Planets Core-Envelope Interior Models of the Outer Planets

Dec 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009agufm.p42b..01s&link_type=abstract

American Geophysical Union, Fall Meeting 2009, abstract #P42B-01

Computer Science

Sound

[5714] Planetary Sciences: Fluid Planets / Gravitational Fields, [5724] Planetary Sciences: Fluid Planets / Interiors

Scientific paper

The constraints on giant planet interior models with density discontinuities, for example, a core-envelope boundary, are more difficult to treat than a continuous density distribution that decreases monotonically and continuously from the center to the surface of the planet. We revise our previous interior calculations (Anderson, J. D., and G. Schubert, Saturn’s gravitational field, internal rotation, and interior structure, 2007, Science, 317, 1384-1387, doi: 101126/science.1144835, 2007), which solved a system of integro-differential equations to third order in the smallness parameter ω2a3/GM (ω is the angular velocity of the planet, a is the planet’s equatorial radius, G is the gravitational constant, and M is the planet’s mass), and introduce Clairaut’s differential equation for the flattening f, with appropriate boundary conditions at the planet’s surface and at its center. The calculations can be carried to second order in the smallness parameter by solving Darwin’s differential equation for k, a parameter that describes a second-order deviation from sphericity. In principle, the calculations can be extended to differential equations of arbitrary order in smallness. As with our earlier method, we apply this revised method to the outer planets with interiors comprising a compressible core, obeying a linear density distribution, and an envelope in which density vs. radius is described by a sixth degree polynomial. This method of gravity sounding, with cores and envelope polynomial density distributions, can yield insights into a class of possible cores that fit the boundary conditions, consisting of the measured even zonal gravitational harmonics, plus the measured size and total mass of the planet. We apply the method to the four outer planets.

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