here is the problem: a satellite is orbiting the earth just above the surface. t

Question

here is the problem: a satellite is orbiting the earth just above the surface. the centripetal force making te satellite follow a circular trafectory is just its weight, so its centripetal acceleration is about 9.8 m/s2. if the earth's radus is about 6375 km, how fast must the satellite be moving, and how long will it take for the satellite to complete one trip around the earth?

This is my attempt:
Centripetal force= satellite’s weight
Centripetal acceleration = 9.8 m/s^2
Earth’s radius = 6,375,000 m
Speed of satellite: I think this is v^2 = 9.8 m/s^2 *6,375,000m
Time it will take satellite to complete one trip around the earth: do not know how to get this. is it velocity = distance/time? It doesn't seem right.

thanks.


6375 km · 1000 m/1km = 6,375,000 m

Explanation / Answer

how fast must the satellite be moving

v2 = gr = (9.8 m/s2)(6375000 m) = 6.25 ´ 107 (m/s)2. Therefore v = 7904 m/s.

how long will it take for the satellite to complete one trip around the earth?

t= d/v. The distance for a round trip is d= 2r = 6.28*6375000 m = 40055 km.

t = (6.28*6375000 m)/(7904 m/s) = 5068 s = 84 min.

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