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(b) For what angle e is the satellite closest to earth? Find the height of the satellite above the earth's surface for this value of 8. mi

(b) For what angle e is the satellite closest to earth? Find the height of the satellite above the earth's surface for this value of 8. mi

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Scientists and engineers often use polar equations to model the motion of satellites in earth orbit. Let's consider a satellite whose orbit is modeled by the equation 

r = 22600/(4 − cos(?)),

 where r is the distance in miles between the satellite and the center of the earth, and ? is the angle shown in the following figure

(a) On the same viewing screen, graph the circle r = 3960 (to represent the earth, which we will assume to be a sphere of radius 3960 mi) and the polar equation of the satellite's orbit. n/2 A/2 10 000 10 000 5000 5000 -10000 -5000 bo00 10 000 10 000 -5000 bo00 10000 - -3000 -5000 -10000- - 10 000 A/2 n/2 10000 10 000 5000 5000 -10000 -500 bo00 -10000 -50ok bo00 10 000 10000 5000 - 5000 - 10 000 -10000 Describe the motion of the satellite as 6 increases from 0 to 27. The motion of the satellite is elliptical. As 8 increases from 0 to T the satellite gets closer to the earth's center. As 6 increases from T to 2 the satellite moves away from the earth's center. The motion of the satellite is elliptical. As 8 increases from 0 to I the satellite moves away from the earth's center. As 8 increases from TI to 27 the satellite gets closer to the earth's center. . O The motion of the satellite is circular. The satellite is always the same distance from the earth's center. (b) For what angle 6 is the satellite closest to earth? Find the height of the satellite above the earth's surface for this value of 0. mi
Transcribed Image Text:(a) On the same viewing screen, graph the circle r = 3960 (to represent the earth, which we will assume to be a sphere of radius 3960 mi) and the polar equation of the satellite's orbit. n/2 A/2 10 000 10 000 5000 5000 -10000 -5000 bo00 10 000 10 000 -5000 bo00 10000 - -3000 -5000 -10000- - 10 000 A/2 n/2 10000 10 000 5000 5000 -10000 -500 bo00 -10000 -50ok bo00 10 000 10000 5000 - 5000 - 10 000 -10000 Describe the motion of the satellite as 6 increases from 0 to 27. The motion of the satellite is elliptical. As 8 increases from 0 to T the satellite gets closer to the earth's center. As 6 increases from T to 2 the satellite moves away from the earth's center. The motion of the satellite is elliptical. As 8 increases from 0 to I the satellite moves away from the earth's center. As 8 increases from TI to 27 the satellite gets closer to the earth's center. . O The motion of the satellite is circular. The satellite is always the same distance from the earth's center. (b) For what angle 6 is the satellite closest to earth? Find the height of the satellite above the earth's surface for this value of 0. mi
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