Astronomy and Astrophysics – Astrophysics – Earth and Planetary Astrophysics
Scientific paper
2009-12-11
Astronomy and Astrophysics
Astrophysics
Earth and Planetary Astrophysics
The manuscript with 10 pages, 5 figures; accepted to the Monthly Notices of the Royal Astronomical Society
Scientific paper
We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary solutions) in this model, which was already studied by Kinoshita (1970). We extend and generalize his results, showing that the equilibria solutions may be found by solving at most two non-linear, algebraic equations, assuming that the potential function of the symmetric rigid body is known explicitly. We demonstrate that there are three classes of the relative equilibria, which we call "cylindrical", "inclined co-planar", and "conic" precessions, respectively. Moreover, we also show that in the case of conic precession, although the relative orbit is circular, the point-mass and the mass center of the body move in different parallel planes. This solution has been yet not known in the literature.
Gozdziewski Krzysztof
Vereshchagin Mikhail
~Maciejewski Andrzej J.
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