Question
Two small, equal masses are attached by a light weight rod. This object orbits a planet ; the length of the rod is smaller than the radius of the orbit, but not negligible. The rod rotates about its axis in such a way that it remains vertical with respect to the planet. (Assume in each case perturbation maintains the rate of rotation, so that in the co-rotating frame the rod is  still stationary but at an angle to the vertical.)

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