As background for this problem, review Conceptual Example 6. A 7370 kg satellite

Question

As background for this problem, review Conceptual Example 6. A 7370 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 side of the drawing. The point on the orbit that is closest to the earth is called the perigee and is at the far left side of the drawing. Suppose that the speed of the satellite is 2830 m/s at the apogee and 8150 m/s at the perigee. Figure 6.9b (a) Find the work done by the gravitational force when the satellite moves from the apogee to the perigee. . J (b) Find the work done by the gravitational force when the satellite moves from the perigee to the apogee.

Explanation / Answer

kinetic energy at apogee:

E1=mv^2/2 = 2.95e10 J

kineic energy at perigee

E2=mv^2/2=2.44e11 J

--> the work done by the gravitational force is the change in energy of the sat

--> W=E2-E1=2.15e11 J

(b) at movement from perigee to the apogee the work will be negative but wil have the same magnitide of 2.15e11 J

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