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Question:

A satellite is in circular orbit 600 km above the Earth's surface, where the free-fall acceleration is 8.21 m/s^2. Take the radius of the earth as 6400 km. Determine the speed of the satellite and the time required to complete one orbit around the earth.

Work:

Radius from to center of the earth to the satellite is 600000 m + 6400000 m = 7000000 m.

For uniform circular motion a = v^2/r, so v = sqrt(ar).

v = sqrt(ar) = sqrt(8.21 m/s^2 * 7000000 m) = 7580.897 m/s

d = rt, so t = d/r.

t = d/r = (2pi * 7000000 m)/(7580.897 m/s) = 5801.727 s

So with the correct number of sig figs velocity would be 7.58e3 m/s and the time required to complete one orbit would be 5.80e3 s.

Thanks,

hk