Question

The International Space Station operates at an altitude of 350 km. Plans for the final
construction show that material of weight 4.22 x 10^6N 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?​

Answer 1

⭐ Question : The International Space Station operates at an altitude of 350 km. Plans for the final  construction show that material of weight 4.22 x 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?​

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$\sf{\displaystyle m=\frac{F_{g}}{g}=\frac{4.22 \times 10^{6} \mathrm{N}}{9.80 \mathrm{~m} / \mathrm{s}^{2}}=4.31 \times 10^{5} \mathrm{kg}}$

$\sf{g=\dfrac{GM_{E}}{\left(R_{E}+h\right)^{2}}}$ $\sf{\displaystyle=\frac{\left(6.674 \times 10^{-11} \mathrm{N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\right)\left(5.97 \times 10^{24} \mathrm{kg}\right)}{\left(6.37 \times 10^{6} \mathrm{m}+0.350 \times 10^{6} \mathrm{m}\right)^{2}}=8.82 \mathrm{m} / \mathrm{s}^{2}}$

$\sf{F_{g}=m g=\left(4.31 \times 10^{5} \mathrm{kg}\right)\left(8.82 \mathrm{m} / \mathrm{s}^{2}\right)=3.80 \times 10^{6} \mathrm{N}}$

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