Q.5 a) The equations of motion in a central-force potential U(r) can be written as, dr...

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Q.5 a) The equations of motion in a central-force potential U(r) can be written as, dr == dt 2(E-U) 12 1127-2 de 8 = dr 14 where E,I are constants of motion (total energy and angular momentum, respectively) and is the reduced mass. By eliminating the time dependence in the above two equations, obtain the differential equation for the trajectory in terms of r and e. (10/20) b) Using the equation for the trajectory that you obtained in (a), determine the force law for a central-force field that allows a particle to move in a spiral orbit given by r = k82 where k is a constant. (10/20) Q.5 a) The equations of motion in a central-force potential U(r) can be written as, dr == dt 2(E-U) 12 1127-2 de 8 = dr 14 where E,I are constants of motion (total energy and angular momentum, respectively) and is the reduced mass. By eliminating the time dependence in the above two equations, obtain the differential equation for the trajectory in terms of r and e. (10/20) b) Using the equation for the trajectory that you obtained in (a), determine the force law for a central-force field that allows a particle to move in a spiral orbit given by r = k82 where k is a constant. (10/20)