Convergence of Liapunov Series for Maclaurin Ellipsoids |
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| Authors: | Konstantin V Kholshevnikov Andrei V Elkin |
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| Institution: | (1) Astronomical Institute, St. Petersburg State University, 198504 St. Petersburg, Russia |
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| Abstract: | According to the classical theory of equilibrium figures surfaces of equal density, potential and pressure concur (let call them isobars). Isobars may be represented by means of Liapunov power series in small parameter q, up to the first approximation coincident with centrifugal to gravitational force ratio on the equator. A. M. Liapunov has proved the existence of the universal convergence radius q
 : above mentioned series converge for all bodies if  q < q
. Using Liapunov's algorithm and symbolic calculus tools we have calculated q
= 0.000370916. Evidently, convergence radius q
0 may be much greater in non-pathological situations. We plan to examine several simplest cases. In the present paper, we find q
0 for homogeneous liquid. The convergence radius turns out to be unexpectedly large coinciding with the upper boundary value q
0 = 0.337 for Maclaurin ellipsoids. |
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| Keywords: | figures of equilibrium Maclaurin ellipsoids Liapunov series convergence radius |
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