Question

Use the exact values you enter to make later calculations.

Satellites feel the gravitational pull of the Earth. They remain in orbit because of their velocity, which acts to counteract gravity. (The satellite wants to fly out in a straight line, but gravity forces it to curve towards the Earth.) Consider a communications satellite that needs to be 41,000 km above the Earth's surface.

(a) Assuming the satellite travels in a perfect circle, what is the radius of the satellite's travel? (The radius of the Earth is 6375 km.)


(b) At the satellite's altitude, the acceleration of gravity is 0.177 m/s². What is the magnitude of the tangential velocity that the satellite must have to remain in orbit?


(c) How much time will the satellite take to orbit the Earth?

Answer 1

(a) radius of orbit = altitude of satellite above earth surface + radius of earth

r = 41000 + 6375

r = 47375 km

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(b) the question has given value of g because they want us to find the mass of earth

g = GM / r²

0.177 = 6.673e-11 * M / 47375000²

M = 5.95e24 Kg

so,

v = sqrt ( GM / r)

v = sqrt ( 6.673e-11 * 5.95e24 / 47375000)

v = 2894.97 m/s

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(c) time = distance / speed

time = 2 * pi * r / v

time = 2 * pi * 47375000 / 2894.97

time = 1.0282e5 seconds

or

time = 28.56 hours