a satellite of mass m is orbiting in an orbit of radius R. Work done by gravity per revolution is given by?
Answers
Answer:
Explanation:
Gravity acts towards the center of the earth. So if the satellite moves in a circular orbit with center of earth as the orbit center the work done at any point is zero, since the force and the displacement are perpendicular.
s=v.dt
F perpendicular to v so W=0.
Whereas if the the orbit is some other conic section(usually elliptical) the work done by gravity changes at almost every point( there are few points where W=0). Though the total energy is constant as potential energy is changed at the expense of kinetic energy.
To expand on that a little, if the speed of the satellite was just a little bit faster then it would still fly off into space, while if it was going a bit slower then gravity would cause it to fall to Earth.
However, the net work done over one complete orbit is 0: in some cases, work is done by gravity, in others, work is done against gravity, the total is 0. A simple way to see this is to consider the satellite at some point on its orbit and again after it completes one orbit. Since the orbit is closed, it is at the same point, so no change in potential energy; since the orbit is periodic, same velocity, so no change in kinetic energy. Hence, total work done = 0.