A satellite of mass 5.0x10 kg is initially in a circular orbit about the earth with a radius 4.1x10m and velocity 3.1x10' m/s around the earth. Assume the earth has mass 6.0x10" Ag and radius r 6.4x10m. Since m >> m, you may find it convenient to ignore certain terms. Justify any terms you choose to ignore

a) What is the magnitude of the gravitational force acting on the satellite? What is the centripetal acceleration of the satellite? b) What are the kinetic and potential energies of the satellite earth system? State any assumptions that you makSpecify your reference point for zero potential energyWhat is the total energy?

As a result of a satellite maneuver, the satellite trajectory is changed to an elliptical orbit. This is accomplished by firing a rocket for a short time interval and increasing the tangential speed of the satellite to (5/4), You may assume that during the firing, the satellite does not noticeably change the distance from the center of the earth

c) What are the kinetic and potential energies of the earth-satellite at the point of closest approach? Specify your reference point for zero potential energyWhat is the total energy?

d) How much energy was necessary to change the orbit of the satellite?

e) What speed would the satellite need to acquire so that it can escape to infinity?