(A) A satellite of mass m is in circular orbit about theearth.
The radius of the orbit is r0 and the mass of the earth isME.
Find the total mechanical energy of the satellite.
(B) Now suppose that the satellite moves in the extreme upper
atmosphere of the earth where it is retarded by a constant
weak frictional force f. The satellite will slowly spiral intoward
the earth. Since the friction force is weak, the change
in radius will be very slow. We can therefore assume that
at any instant the satellite is effectively in a circular orbitof
average radius r. Find the approximate change in radius r
per revolution of the satellite.
(C) Calculate r for these parameters: r = 1.045 RE; f =
\ensuremath{1.300\times 10Ë{-4}} N; m = 91 kg.
(D) Find the approximate change of kinetic energy of the
satellite K per revolution, for the same parameters as (C).
Express the result as the fraction of the current kineticenergy.
Is K positive or negative? Explain briefly.
(A) A satellite of mass m is in circular orbit about theearth.
The radius of the orbit is r0 and the mass of the earth isME.
Find the total mechanical energy of the satellite.
(B) Now suppose that the satellite moves in the extreme upper
atmosphere of the earth where it is retarded by a constant
weak frictional force f. The satellite will slowly spiral intoward
the earth. Since the friction force is weak, the change
in radius will be very slow. We can therefore assume that
at any instant the satellite is effectively in a circular orbitof
average radius r. Find the approximate change in radius r
per revolution of the satellite.
(C) Calculate r for these parameters: r = 1.045 RE; f =
\ensuremath{1.300\times 10Ë{-4}} N; m = 91 kg.
(D) Find the approximate change of kinetic energy of the
satellite K per revolution, for the same parameters as (C).
Express the result as the fraction of the current kineticenergy.
Is K positive or negative? Explain briefly.
