A comet orbits the Sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed (b) angular speed (c) angular momentum (d) kinetic energy (e) potential energy (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.
A comet while going on elliptical orbit around the Sun has constant angular momentum due to no external torque and total energy due to Law of conservation of energy at all locations but other quantities vary with locations. (a) Since angular momentum is constant, L=rmv2 is constant. As r changes in elliptical orbit, speed is not constant. (b) Since angular momentum is constant, L=mω2r is constant. As r changes in elliptical orbit, angular speed is not constant. (c) Angular momentum is constant because there is no external torque. (d) Since speed is not constant, Kinetic Energy is not constant. (e) Total energy is constant by law of conservation of energy. T.E.=P.E.+K.E.=constant Since K.E. is not constant, P.E. is not constant. (f) Total energy is constant by law of conservation of energy.
