The astronaut orbiting the Earth in Figure P4.32 is preparing to dock with a Wes

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 650. km above the Earth's surface, where the free-fall acceleration (centripetal acceleration) is 8.16 m/s2. Take the radius of the Earth as 6370 km.

1. 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.)

2.Determine the time interval required to complete one orbit around the Earth in minutes.

Explanation / Answer

A. acceleration:

a = v^2/r = w^2r

v = sqrt(a*r) = sqrt(8.16*7020*10^3)

v = 7568.56 m/sec = 27246.816 km/hr

B.

T = 1/f = 2*pi/w

T = 2*pi/sqrt(a/r)

T = 2*3.14/sqrt(8.16/(7020*10^3)) = 5824.82 sec

T = 97.08 min.

Let me know if you have any doubt.

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