# Sleeping Satellite

Consider a small geostationary satellite consisting of four point masses $$m$$ connected by light rigid rods of length $$a$$ and $$b$$ to a central mass $$M$$ ($$M\gg m$$) as shown in the figure. In addition, four light rods of length $$\sqrt{a^{2}+b^{2}}$$ ensure that the satellite behaves as rigid body. It turns out that if $$\frac{a}{b}>1$$, 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 $$\eta=\frac{a}{b}$$ 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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