  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.

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/s2 and the radius of Earth is 6400 km. The gravitational constant is 6.67 x 10-11 m3/kg.s2 and the mass of Earth is 5.97 x 1024 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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