QUESTION 12 What is the orbital speed of a satelite in a circular orbit at 15,25

Question

QUESTION 12 What is the orbital speed of a satelite in a circular orbit at 15,250 kilometers above the Earth surface? Express your answer in km/s and round it to two decimals. Earth's mean radius is RE 6.37 x106 m: Earth's mass is ME 5.97x1024kg. QUESTION 13 What is the orbital period of a satelite in a circular orbit at 8,469 kilometers above the Earth surface? Express your answer in minutes (enter "min" for minutes) and round it to the nearest integer. Earth's mean radius is RE 6.37 x106 m; Earth's mass is ME 5.97x1024kg

Explanation / Answer

12. G M m / r^2 = m v^2 / r

G M / r = v^2

r = Re + h = (6.37 x 10^6) + (15.25 x 10^6) = 21.62 x 10^6 m

v = sqrt[ (6.67 x 10^-11)(5.97 x 10^24) / (21.62 x 10^6)]

v= 4292 m/s = 4.29 km/s

13. G M m / r^2 = m w^2 r

w^2 = (6.67 x 10^-11) (5.97 x 10^24) / (6.37 x 10^6 + 8.469 x 10^6)^3

w = 3.49 x 10^-4 rad/s

T = 2 pi / w = 18000 sec

T = 300 min

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