A 8570-kg satellite has an elliptical orbit, as in Figure 6.9b. The point on the

Question

A 8570-kg satellite has an elliptical orbit, as in Figure 6.9b. The point on the orbit that is farthest from the earth is called the apogee and is at the far right of the drawing. The point on the orbit that is closest to the earth is called the perigee and is at the left side of the drawing. Suppose that the speed of the satellite is 2970 m/s at the apogee and 7650 m/s at the perigee. Find the work done by the gravitational force when the satellite moves from (a) the apogee to the perigee and (b) the perigee to the apogee.

Explanation / Answer

work done by gravity = change in KE = final - initial
W (gravity) = from apogee to perigee to = KE(p) - KE(a)
W (a to p) = 0.5 m [7650^2 - 2970^2]
W (a to p) = 2.49*10^7 Joules
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since gravity is a conservative force field >> work done along closed path (p to a + a to p) =0
W (total ellipse) = 0 = W(a to p) + W(p to a)
W(p to a) = - W(a to p) = - 2.49*10^7 J

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