3. A satellite of mass m is in orbit around a planet with mass M and radius R. The satellite is initially in an elliptical orbit. At its closest approach (perigee), the distance from the satellite to the center of the planet is rp and its speed is vp. At its farthest point (apogee), the distance from the satellite to the center of the planet is ra and its speed is va. Assume that as the satellite reaches apogee, a force is applied to change its speed, allowing the satellite to enter a circular orbit at radius ra. Calculate the work required to change the satellite's orbit to a circular orbit at ra. GMm
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