Connected satellites · Estonian PhO 2018 #6

Physics · mechanics

Problem

Two satellites, both with a mass mm, are orbiting around a planet with a mass M≫mM\gg m on circular orbits of radiuses R1R_1 and R2=2R1R_2=2R_1. The satellites are connected to each other with a tensioned cable of negligible mass and of length R1R_1. Because of that the orbital period of both of the satellites is TT. How many times are the speeds v1v_1 and v2v_2 of the satellites bigger or smaller than the speeds v1′v'_1 and v2′v'_2 with what the satellites would revolve on their orbits if there was no cable?

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