Answer:
[tex]W=\frac{773}{4.45}=173.76 l b f[/tex]
Explanation:
[tex]W=\frac{G \cdot m_{e} \cdot m}{(R+h)^{2}}[/tex]
The law of gravitation
[tex]G=6.673\left(10^{-11}\right) m^{3} /\left(k g \cdot s^{2}\right)[/tex]
Universal gravitational constant [S.I. units]
[tex]m_{e}=5.976\left(10^{24}\right) k g[/tex]
Mass of Earth [S.I. units]
[tex]m=89 kg[/tex]
Mass of a man in a spacecraft [S.I. units]
[tex]R=6371 \mathrm{~km}[/tex]
Earth radius [km]
Distance between man and the earth's surface
[tex]h=261 \mathrm{~km} \quad[\mathrm{~km}][/tex]
ESULT [tex]W=\frac{6.673\left(10^{-11}\right) \cdot 5.976\left(10^{24}\right) \cdot 89}{\left(6371 \cdot 10^{3}+261 \cdot 10^{3}\right)^{2}}=773.22 \mathrm{~N}[/tex]
[tex]W=\frac{773}{4.45}=173.76 l b f[/tex]
