Question

The Weight of the Space Station The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 ✕ 106 N, measured at the Earth's surface, will have been lifted off the surface by various spacecraft during the construction process. What is the weight of the space station when in orbit? SOLUTION Conceptualize The mass of the space station is fixed; it is independent of its location. Based on the discussion in this section, we realize that the value of g will be at the height of the space station's orbit. Therefore, the weight of the space station will be than that at the surface of the Earth. Categorize We model the space station as a particle in a gravitational . Analyze From the particle in a field model, find the mass of the space station (in kg) from its weight at the surface of the Earth: m = Fg g = kg Use the equation for the free-fall acceleration with h = 350 km to find the magnitude of the gravitational field (in m/s2) at the orbital location: g = GME (RE + h)2 = m/s2 Use the particle in a field model again to find the space station's weight in orbit (in N): Fg = mg = N Finalize Notice that the weight of the Space Station is less when it is in orbit, as we expected. It has about 10% less weight than it has when on the Earth's surface, representing a 10% in the magnitude of the gravitational field.

Answer 1

Mass of space station when in orbit = 6.119×10^27kg

Step-by-step explanation:

Mass of the space station can be calculated by:

Fg ×g = M

Using the equation

g = GMe(Re + h)^2

Where g = gravitational acceleration in m/s^2

M = mass of earth = 5.972×10^24kg

R = radius of the earth = 6371000m

Substituting into the equation

g = (6.67×10^-11)(5.972×10^24)(6371000-350000)^2

g = 1.45×10^22m/s^2

Calculate mass of space station, m = Fg × g

But Fg = 4.22×10^6N

m =( 4.22×10^6 )× (1.45 ×10^22)

m = 6.099×10^28kg

This is mass when on the surface of the earth.

mass when in orbit is 10% of gravitational feild × Fg

g = 10/100 × (1.45×10^22)

g = 1.45 ×10^21 m/s^2

Therefore mass of space station when in orbit = Fg × g = (4.22×10^6)×(1.45×10^21)

m = 6.119× 10^27kg