Question

The international space station has a mass of 3.03 x 10^5 kg. It takes 91.7 minutes to complete one orbit of the earth, and approximating its orbit as a circle, the Radius of the orbit measured from the center of the Earth is 6725 km.

a) Assuming the Space Station is in Uniform Circular Motion, calculate its tangent velocity.

b) Calculate the centripetal acceleration required to keep the Space Station in a circular orbit of the earth.

c) Calculate the centripetal force using the acceleration from part a.

d) Use Newtons Universal Gravitation to calculate the magnitude of gravitational force of Earth acting on the Space Station. The mass of Earth is 5.972 × 10²⁴ kg , and G = 6.674 x 10^-11 N m^2/kg^2.

e) Compare your answers for parts c) and d). Are they reasonably close?

Answer 1

Here ,

m = 3.03 *10^5 Kg

T = 91.7 minutes = 91.7 * 60 s

T = 5502 s

radius of orbit , r = 6725 km

r = 6725 *10^3 m

a) tanential velocity = 2pi * r/T

tanential velocity = 2pi * 6725 *10^3/5502

tanential velocity = 7678 m/s

the tanential velocity is 7678 m/s

b)

centripetal acceleration = v^2/r

centripetal acceleration = 7678^2/(6725 *10^3)

centripetal acceleration = 8.77 m/s^2

c)

centripetal force = m * centripetal acceleration

centripetal force = 8.77 * 3.03 *10^5

centripetal force = 2.66 *10^6 N

the centripetal force is 2.66 *10^6 N

d)

magnitude of gravitational force = G * m * M/d^2

magnitude of gravitational force = 6.673 *10^-11 * 5.98 *10^24 * 3.03 *10^5/(6725 *10^3)^2

magnitude of gravitational force = 2.67 *10^6 N

e)

c/d = 2.66/2.67

c/d = 0.996

the answers in c and d are approximately equal and they are close