On the conditional extremum for the gravitational energy inherent to the oblate spheroid.

Details On the conditional extremum for the gravitational energy inherent to the oblate spheroid. On the conditional extremum for the gravitational energy inherent to the oblate spheroid.

Apr 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26at....7..173a&link_type=abstract

Astronomy and Astrophysics Trans., Vol. 7, No. 2 - 3, p. 173 - 176

Astronomy and Astrophysics

Astrophysics

Gravitation Theory: Energies

Scientific paper

The authors prove that the oblate spheroid has a maximum (by modulus) of gravitational energy among of all homogeneous bodies with various external shapes, when both the volume and the moment of inertia about the plane are fixed. To solve this problem, a new method of covering the body by infinitely thin layers of matter has been developed. In application to an arbitrary figure, this method generalizes the known principle of covering an ellipsoid by confocal elementary ellipsoidal layers. In addition to the main result, the authors have proved also three auxiliary theorems about some extremal properties of other functionals for a sphere and an oblate spheroid.

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