A 7490-kg satellite has an elliptical orbit, as in the figure. The point on the
ID: 1280328 • Letter: A
Question
A 7490-kg satellite has an elliptical orbit, as in the figure. 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 2760 m/s at the apogee and 8050 m/s at the perigee. (a) Find the work done by the gravitational force when the satellite moves from the apogee to the perigee. (b) Find the work done by the gravitational force when the satellite moves from the perigee to the apogee.
A 7490-kg satellite has an elliptical orbit, as in the figure. 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 2760 m/s at the apogee and 8050 m/s at the perigee. (a) Find the work done by the gravitational force when the satellite moves from the apogee to the perigee. (b) Find the work done by the gravitational force when the satellite moves from the perigee to the apogee.Explanation / Answer
a >>> apogee
p >>> perigee
ra = distance of apogee from central planet (focus)
rp = distance of perigee from central planet
va = speed at apogee
vp = speed at perigee from central planet
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conservation of angular momentum (J = m v r), as is conserved in central inverse-square law, gives
ra * va = rp * vp
ra > rp >>> so va < vp
satellite starts to move faster when approaches perigee (closer) from apogee.
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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 [8050^2 - 2760^2]
W (a to p) = 2.859*10^11 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) = - 2.859*10^11 J
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