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On the rotation and the figure of celestial bodies
Author(s) -
Kalitzin Nikola St.
Publication year - 1961
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.19612860404
Subject(s) - angular velocity , physics , rotation (mathematics) , gravitational field , classical mechanics , celestial mechanics , jupiter (rocket family) , gravitation , constant angular velocity , perfect fluid , angular momentum , basis (linear algebra) , mechanics , geometry , mathematics , astronomy , space shuttle
Determining the form of celestial bodies one usually assumes according to celestial mechanics, that they rotate as solid bodies, i. e. with a constant angular velocity over the whole body. The equations of rotation of a free fluid subjected to the influence of the forces of its own gravitation and of pressure considered as a solid body are not the general solution of E ULER 's hydrodynamical equations for the case of rotation. As P OINCARÉ and J EANS have shown there exists an infinite number of other solutions describing the movement of a rotating fluid with angular velocity depending on the distance from the axis of rotation. We examine in the present paper these more general solutions generalizing the well known P OINCARÉ theorem of the maximum possible angular velocity. Within the framework of these generalizations we examine R OCHE 's model which treats the whole mass of the fluid concentrated in the center of gravity. Some of our results are shown to be applicable for the determination of the form and the gravitational field of non‐uniformly rotating celestial bodies, for instance the Sun, Jupiter and Saturn. On the basis of L IAPOUNOFF 's classical works (1903 and 1904) we prove the existence of unique solutions of the generalized problem of a non‐uniformly rotating fluid at small angular velocities. We arrive at a system of integrodifferential equations which generalize the C LAIRAUT ‐L IAPOUNOFF equations for the case of a non‐uniformly rotating fluid. By means of these exact solutions we examine a model which enables us, assuming some restrictive conditions, to refute the objection put forward against K ANT ‐L APLACE 's theory concerning the distribution of moment of momentum in the Solar system.