Consider a satellite in a circular orbit around a planet. Suppose that the satellite is to be moved to a new circular orbit that is at a greater di...

Consider a satellite in a circular orbit around a planet. Suppose that the satellite is to be moved to a new circular orbit that is at a greater distance from the planet. The required change in the satellite's speed can be accomplished by firing the satellite's rockets in the direction of motion or in the direction opposite to the motion. Suppose that the satellite is in the initial circular orbit of radius r1 and speed v1, and that it is to be moved to a new circular orbit of radius r3 and speed v3. The required change in speed can be accomplished in three steps, as shown in the figure. During step A, the satellite is moved into an elliptical orbit that intersects the new circular orbit. During step B, the satellite's rockets are fired along the direction of motion to change the point of intersection of the elliptical orbit and the new circular orbit. During step C, the satellite's rockets are fired again to change the elliptical orbit into the new circular orbit. Which of the following quantities are the same for steps A and C?

a) The kinetic energy of the satellite.
b) The potential energy of the satellite.
c) The work done by the motors to accomplish step B.
d) The period of the satellite's motion.
a) a and b
b) b and c
c) c and d
d) a and d
e) b and d