The astronaut orbiting the Earth in Figure P4.32 is preparing to dock with a Wes
ID: 1581001 • 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 680. km above the Earth's surface, where the free-fall acceleration (centripetal acceleration) is 8.18 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
Given :-
h = 680 km
a = 8.18 m/s^2
R = 6370 km
orbital radius of satellite,
r = R + h
r = 6370 km + 680 km
r = 7050 km = 7050000
a = v^2/r
v = sqrt(a x r)
v = sqrt(7050000 x 8.18)
v = 7594 m/s or 27338.4 km/h
T = 2pi*r / v
T = (2pi x 7050 x 10^3) / 7594 m/s
T = 5833.1 s
T = 97.22 min
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