39. (a) The momentum of the two-star system is conserved, and since the stars have the same mass, their speeds and kinetic energies are the same. We use the principle of conservation of energy. The initial potential energy is Ui= −GM2/ri, where Mis the mass of either star and riis their initial center-to-center separation. The initial kinetic energy is zero since the stars are at rest. The final potential energy is Uf= −2GM2/risince the final separation is ri/2. We write Mv2for the final kinetic energy of the system. This is the sum of two terms, each of which is ½Mv2. Conservation of energy yields
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.