Sleeping Satellite

Consider a small geostationary satellite consisting of four point masses mm connected by light rigid rods of length aa and bb to a central mass MM (MmM\gg m) as shown in the figure. In addition, four light rods of length a2+b2\sqrt{a^{2}+b^{2}} ensure that the satellite behaves as rigid body. It turns out that if ab>1\frac{a}{b}>1, the satellite can oscillate about its center of mass in the plane of the orbit. In other words, the configuration showed in the figure is stable. For what ratio η=ab \eta=\frac{a}{b} the period of small oscillations of the satellite equals its orbital period? Assume that the dimensions of the satellite are much smaller than the radius its orbit.

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