Question

answer Is b, please explain how to get to this

12. Consider a spacecraft in an elliptical orbit around the Earth. At the low point, or perigee, of its orbit, it is 250 km above the earth's surface; at the high point, or apogee, it is 3500 km above the Earth's surface. Find the speed of this spacecraft at perigee. A) 3960 m/s B) 5690 m/s C) 5960 m/s D) 6590 m/s E) 9650 m/s

Answer 1

the velocity of perigee can be found as

v = sqrt ( 2 * GM * R_a / R_p * (R_a + R_p)

where M is mass of earth, R_p is perigee distance, R_a is apogee distance

remember, we are given distance from surface of earth so we have to account for radius.

R_p = 250000 + 6375000 = 6625000 m

R_a = 3500 + 6375 = 9875000 m

so,

v = sqrt ( 2 * 3.986e14 * 6625000 / 9875000 * ( 9875000 + 6625000 )

v = 5693.3 m/s

so,

the closest option is option (b)

so,

option (b) is correct.