The International Space Station operates at an altitude of 350 km. Plans for the

Question

The International Space Station operates at an altitude of 350 km. Plans for the final construction show that material of weight 4.22 times 10^6 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? 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 reduced at the height of the space station's orbit. Therefore, the weight of the space station will be smaller than that at the surface of the Earth. Categorize We model the space station as a particle in a gravitational field. Analyze From the particle in a field model, find the mass of the space station from its weight at the surface of the Earth: m = F_g/g = 4.22 times 10^6 N/9.80 m/s^2 = 4.31 times 10^5 kg Use the equation for the free-fall acceleration with h = 350 km to find the magnitude of the gravitational field at the orbital location: g = GM_E/(R_E + h)^2 = (6.674 times 10^-11 N middot m^2/kg^2)(5.97 times 10^24 kg)/(6.37 times 10^6 m + 0.350 times 10^6 m)^2 Use the particle in a field model again to find the space station's weight in orbit: F_g = mg = (4.31 times 10^5 kg) (8.82 m/s^2) = 3801420 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% decrease in the magnitude of the gravitational field. At what altitude is the space station's weight 27% of its value on Earth's surface? 1085.52

Explanation / Answer

mass =4.22*10^6/9.8 =4.31*10^5 kg
in orbit r =R+h =6400+350 =6750 km
hence g' =GM/r^2 =9.81*(6400/6750)^2 =8.82 m/s^2
hence weight = 4.31*10^5 *8.82 =3.8*10^6 N
................
new g ie g' should be 0.27g
g' =g*(R/(R+h))^2
0.27 =(6400/(6400+h))^2

Calculate h in unit km

h = 5916.8057km

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