Question

An astronaut orbiting the Earth is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 700 km above the Earth's surface, where the free-fall acceleration is 8.11 m/s^2. Take the radius of the Earth as 6400 km.

(a) Determine the speed of the satellite in meters/second.

(b) Determine the time interval required to complete one orbit around the Earth, which is the period of the satellite, in minutes.

Step 1

Given that the circular orbit of satellite is 700 km above the Earth’s surface, the free fall acceleration at the position is 8.11 m/s^{2} and the radius of Earth is 6400 km. The gravitational constant is 6.67 x 10^{-11 }m^{3}/kg.s^{2} and the mass of Earth is 5.97 x 10^{24} kg.

Step 2

(a)

The expression for speed of satellite is,

Step 3

Here, *v* is the orbital velocity of the satellite, *G* is the gravitational constant, *M* is the mass of Earth, *R* is the distance between the satellite and center of Earth, *RE* is the radius of Earth and *r* is the...

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