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Annette [7]
2 years ago
10

From the gravitational law calculate the weight W (gravitational force with respect to the earth) of a 89-kg man in a spacecraft

traveling in a circular orbit 261 km above the earth's surface. Express W in both (a) newtons and (b) pounds.
Physics
1 answer:
zhannawk [14.2K]2 years ago
4 0

Answer:

W=\frac{773}{4.45}=173.76 l b f

Explanation:

W=\frac{G \cdot m_{e} \cdot m}{(R+h)^{2}}

The law of gravitation

G=6.673\left(10^{-11}\right) m^{3} /\left(k g \cdot s^{2}\right)

Universal gravitational constant [S.I. units]

m_{e}=5.976\left(10^{24}\right) k g

Mass of Earth [S.I. units]

m=89 kg

Mass of a man in a spacecraft [S.I. units]

R=6371 \mathrm{~km}

Earth radius [km]

Distance between man and the earth's surface

h=261 \mathrm{~km} \quad[\mathrm{~km}]

ESULT 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}

W=\frac{773}{4.45}=173.76 l b f

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