Question

Calculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface if its mass is 1650 kg .

Answer 1

Answer:

F = 1.8 KN

Explanation:

Given that the spacecraft is 2.00 Earth radii above the Earth's surface, the force of Earth's gravity on it can be determined by;

F = $\frac{GMm}{(R + h)^{2} }$

Where: F is the force, G is the universal gravitation constant, M is the mass of the earth, m is the mass of the spacecraft, and R is the radius of the earth and h is the distance of the spacecraft to the surface of the earth.

G = 6.67 x $10^{-11}$ N$m^{2}$$kg^{-2}$, M = 5.972 x $10^{24}$ kg, m = 1650 kg, R = 6371 km, h = (2.0 x 6371 km) = 12742 km.

Thus,

F = $\frac{6.67*10^{-11}*5.972*10^{24} *1650 }{(6371*10^{3}+12742*10^{3}) ^{2} }$

  = $\frac{6.5725*10^{17} }{(19113000)^{2} }$

  = 1799.17

F = 1.8 KN

The force of the Earth's gravity on the spacecraft is 1.8 KN.