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Self-consistent internal structure of a rotating gaseous planet and its comparison with an approximation by oblate spheroidal equidensity surfaces
Kong, Dali1,2; Zhang, Keke2,3; Schubert, Gerald4
2015-12-01
Source PublicationPHYSICS OF THE EARTH AND PLANETARY INTERIORS
Volume249Pages:43-50
AbstractIn an important paper, Roberts (1963b) studied the hydrostatic equilibrium of an isolated, self-gravitating, rapidly rotating polytropic gaseous body based on a controversial assumption/approximation that all (outer and internal) equidensity surfaces are in the shape of oblate spheroids whose eccentricities are a function of the equatorial radius and whose axes of symmetry are parallel to the rotation axis. We compute the three-dimensional, finite-element, fully self-consistent, continuous solution for a rapidly rotating polytropic gaseous body with Jupiter-like parameters without making any prior assumptions about its outer shape and internal structure. Upon partially relaxing the Roberts' approximation by assuming that only the outer equidensity surface is in the shape of an oblate spheroid, we also compute a finite-element solution with the same parameters without making any prior assumptions about its internal structure. It is found that all equidensity surfaces of the fully self-consistent solution differ only slightly from the oblate spheroidal shape. It is also found that the characteristic difference between the fully self-consistent solution and the outer-spheroidal-shape solution is insignificantly small. Our results suggest that the Roberts' assumption of spheroidal equidensity surfaces represents a reasonably accurate approximation for rotating polytropic gaseous bodies with Jupiter-like parameters. The numerical accuracy of our finite-element solution is checked by an exact analytic solution based on the Green's function using the spheroidal wave function. The three different solutions in non-spherical geometries - the fully self-consistent numerical solution, the numerical solution with the outer spheroidal shape and the exact analytical solution - can also serve as a useful benchmark for other solutions based on different numerical methods. (C) 2015 Elsevier B.V. All rights reserved.
KeywordGaseous Planets Equilibrium Rotation Finite Element Method
WOS HeadingsScience & Technology ; Physical Sciences
DOI10.1016/j.pepi.2015.09.008
WOS KeywordGRAVITATIONAL SIGNATURE ; POLYTROPES ; JUPITER
Indexed BySCI
Language英语
WOS Research AreaGeochemistry & Geophysics
WOS SubjectGeochemistry & Geophysics
WOS IDWOS:000366235300005
Citation statistics
Cited Times:7[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://libir.pmo.ac.cn/handle/332002/16080
Collection南极天文中心
Affiliation1.Chinese Acad Sci, Key Lab Planetary Sci, Shanghai Astron Observ, Shanghai 200030, Peoples R China
2.Univ Exeter, Ctr Geophys & Astrophys Fluid Dynam, Exeter EX4 4QE, Devon, England
3.Macau Univ Sci & Technol, Lunar & Planetary Sci Lab, Macau, Peoples R China
4.Univ Calif Los Angeles, Dept Earth Planetary & Space Sci, Los Angeles, CA 90095 USA
Recommended Citation
GB/T 7714
Kong, Dali,Zhang, Keke,Schubert, Gerald. Self-consistent internal structure of a rotating gaseous planet and its comparison with an approximation by oblate spheroidal equidensity surfaces[J]. PHYSICS OF THE EARTH AND PLANETARY INTERIORS,2015,249:43-50.
APA Kong, Dali,Zhang, Keke,&Schubert, Gerald.(2015).Self-consistent internal structure of a rotating gaseous planet and its comparison with an approximation by oblate spheroidal equidensity surfaces.PHYSICS OF THE EARTH AND PLANETARY INTERIORS,249,43-50.
MLA Kong, Dali,et al."Self-consistent internal structure of a rotating gaseous planet and its comparison with an approximation by oblate spheroidal equidensity surfaces".PHYSICS OF THE EARTH AND PLANETARY INTERIORS 249(2015):43-50.
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