1. The problem statement, all variables and given/known data Two satellites connected by a string revolve in concentric circular orbits of radius r and 2r Two satellites of equal masses m revolve around the planet of mass M. The satellites have extremely small mass compared to the planet, m≪M. The radii of the orbits of the satellites are r and 2r. The satellites are connected by a light string, directed along the radius of the orbit, that keeps their periods of revolution equal. Find the force of tension Fτ in the string. 2. Relevant equations I first drew an FBD and wrote the Newton's Second Law equations for both satellites, keeping in mind circular motion: (equation 1 corresponds to the inner satellite, and 2 to the outer) (1) ∑ F = m(a_c1) = F_g1 - Fτ (2) ∑ F = m(a_c2) = F_g2 + Fτ Also, since I am given that the periods of revolution are constant, I used the following formula's defining the period: (Kepler's 3rd law) T^2 = 4*pi^2*α^3/(G*M) [α is the semi-major axis of an elliptical orbit... in this case either of the two given radii] [ G is the universal gravitational constant, but can be expressed simply as G for the sake of the problem.] and T = 2*pi*r/v_orbital, which can also be written as 2*pi/√(a_c/r) 3. The attempt at a solution I used the two equations for the period to determine a value for a_c1 (i chose to work with the inner sattellite, so α = r..) Thus: T^2 = 4*pi^2*α^3/(G*M) = 4*pi^2*r/a_c1, given that α = r we should get 4*pi^2*r^3/(G*M) = 4*pi^2*r/a_c1 --> G*M/r^2 = a_c The issue with this is that if this is indeed the centripetal acceleration, then Fτ = zero when I plug the centripetal acceleration into equation (1).. I'm stumped. Any help would be appreciated. Thank you in advance!