1. The International Space Station (ISS) has a mass of 419,600kg. Assume for thi

Question

1. The International Space Station (ISS) has a mass of 419,600kg. Assume for this problem that it orbits the Earth in uniform circular motion, 400km above the surface (its orbit actually varies). a. What’s the gravitational force on the ISS due to the Earth (take the radius of the earth to be , and take the Earth’s mass to be )?

b. With what translational speed does the ISS circle the Earth?

c. How much time does the ISS take to make one complete revolution around the Earth (give your answer in minutes)?

Explanation / Answer

Here ,

a)

gravitational force on ISS = G * m * Me/r^2

gravitational force on ISS = 6.673 *10^-11 * 419600 * 5.98 *10^24/(400 *10^3 + 6371 *10^3)^2

gravitational force on ISS = 3621095 N

b)

translational speed of ISS = sqrt(G * M/R)

translational speed of ISS = sqrt(6.673 *10^-11 * 5.98 *10^24/(400 *10^3 + 6371 *10^3))

translational speed of ISS = 7677 m/s

c)

time taken to complete one revolution = total distance/v

time taken to complete one revolution = 2pi * (400 *10^3 + 6371 *10^3)/7677

time taken to complete one revolution = 5542 s

time taken to complete one revolution = 92.4 hour

the time taken to complete one revolution is 92.4 hour

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