Nested spheroidal figures of equilibrium – III. Connection with the gravitational moments <i>J</i>2<i>n</i>

نویسندگان

چکیده

ABSTRACT We establish, in the framework of theory nested figures, expressions for gravitational moments J2n a systems made ${\cal L}$ homogeneous layers separated by spheroidal surfaces and relative rotational motion. then discuss how to solve inverse problem, which consists finding equilibrium configurations (i.e. internal structures) that reproduce ‘exactly’ set observables, namely equatorial radius, total mass, shape, first moments. Two coefficients being constrained per surface, L}=1+\frac{n}{2}$ (n even) are required fix J2 J2n. As shown, this problem already suffers from severe degeneracy, inherent fact two system confocal with each other leave unchanged all The complexity, increases number involved, can be reduced considering rotation rate layer. Jupiter is used as test-bed illustrate method, concretely L}=2,3$, 4. For planet, possible structures infinite L} &amp;gt; 2$. Intermediate have smaller or larger oblateness, rotate slower faster than surroundings. Configurations large massive cores always present. Low-mass (of order few Earth masses) predicted \ge 4$. results good agreement numerical solutions obtained self-consistent field method.

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ژورنال

عنوان ژورنال: Monthly Notices of the Royal Astronomical Society

سال: 2023

ISSN: ['0035-8711', '1365-8711', '1365-2966']

DOI: https://doi.org/10.1093/mnras/stad151