The astronaut orbiting the Earth in Figure P4.32 is preparing to dock with a Wes
ID: 1429402 • Letter: T
Question
The astronaut orbiting the Earth in Figure P4.32 is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 640. km above the Earth's surface, where the free-fall acceleration (centripetal acceleration) is 8.25 m/s2. Take the radius of the Earth as 6370 km.
Determine the speed of the satellite in km/h. (Note: Specific units are given, so you do not have to enter them in this problem.)
km/h
Determine the time interval required to complete one orbit around the Earth in minutes.
min
Explanation / Answer
Speed of satellite is v = sqrt(G*Me/r)
G is the univesal gravitational constant
Me is the mass of the earth
r = 6370+640 = 7010 km
then v = sqrt(6.67*10^-11*5.98*10^24/(7010*1000)) = 7543.18 m/s = 7543.18 *18/5 = 27155.45 km/hr
Time interval is T = 2*pi*r/v = 2*3.142*7010*1000/(7543.18) = 5839.82 sec / 60 = 97.33 mins
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