1. The problem statement, all variables and given/known data Two planets of masses [itex]m_1[/itex] and [itex]m_2[/itex] with radii [itex]r_1[/itex] and [itex]r_2[/itex] respectively are orbiting their common center of mass at some initial distance [itex]x_0[/itex] from each other with angular velocity [itex]\omega_0[/itex]. Find the amount of time it takes for these planets to collide. 2. Relevant equations N/A 3. The attempt at a solution So far, I've drawn my free-body diagram with the axes in the Center of Mass reference frame, figured that the position of the center of mass remains constant since no net external force acts, and that conservation of momentum applies since no net external torque acts either. However, I'm having difficulty setting the problem up (constructing a series of differential equations to solve) and would appreciate any advice. Thanks!