Question 13.3: The Weight of the Space Station The International Space Stat...
The Weight of the Space Station
The International Space Station operates at an altitude of 350 km. An online search for the station shows that a weight of 4.11 \times 10^6 N, measured at the Earth’s surface, has been lifted off the surface by various spacecraft during the construction process. What is the weight of the space station as it moves in its orbit?
Conceptualize The mass of the space station is fixed; it is independent of its location. Based on the discussions in this section and Section 13.2, we realize that the value of g is smaller at the height of the space station’s orbit than at the surface of the Earth. Therefore, the weight of the Space Station is 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=\frac{F_{\text {g,surface }}}{g_{\text {surface }}}=\frac{4.11 \times 10^6 N}{9.80 m/s^2}=4.19 \times 10^5 kgUse Equation 13.6 with h = 350 km to find the magnitude of the gravitational field at the orbital location:
g=\frac{G M_E}{r^2}=\frac{G M_E}{\left(R_E+h\right)^2} (13.6)
\begin{aligned}g_{\text {orbit }} & =\frac{G M_E}{\left(R_E+h\right)^2} \\& =\frac{\left(6.674 \times 10^{-11} N \cdot m^2 /kg^2\right)\left(5.97 \times 10^{24} kg\right)}{\left(6.37 \times 10^6 m+0.350 \times 10^6 m\right)^2}=8.82 m/s^2 \end{aligned}Use the particle in a field model again to find the space station’s weight in orbit:
F_{\text {g,orbit }} =m g_{\text {orbit }}=\left(4.19 \times 10^5 kg\right)\left(8.82 m / s^2\right)=3.70 \times 10^6 NFinalize 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.