Three identical stars, each of mass M , are placed at the vertices of an equilateral triangle of side L . They revolve in a common circular orbit under the influence of their mutual gravitational attraction. The external work required to completely dismantle the system (i.e., to move all three stars to an infinite separation from each other) is:

Step-by-step solution

To find the work required to dismantle the system, we must first determine the total mechanical energy of the system. The gravitational force on any one star due to the other two is: F = ( GM^2 L^2 )^2 + ( GM^2 L^2 )^2 + 2 ( GM^2 L^2 ) ( GM^2 L^2 ) 60^ = 3 GM^2 L^2 The radius R of the circumcircle (the orbit) for an equilateral triangle of side L is R = L 3 . This gravitational force provides the necessary centripetal force for the circular motion: Mv^2 R = F Mv^2 L 3 = 3 GM^2 L^2 Mv^2 = GM^2 L The kinetic energy o