Question

The radius of the Earth is approximately 4000 miles. If Sputnik I (the first satellite) roughly weighs 184 lbs on the surface of the Earth, find the amount of work W (in mile-pounds) required to launch it into orbit at an altitude of 141 miles.

The universal law of gravity states that the force of gravity acting on the satellite is F(r)= k/r^2. where r is the distance from the astronaut to the center of the Earth.

Answer 1

Still need help on this? Work is the integral of force over distance

\[\Large W = \int\limits\limits_{h _{1}}^{h _{2}} F dr\]

Plugging in F and the limits \[\Large W = \int\limits\limits\limits_{4000}^{4141} \frac{ k }{ r^2 } dr\]


I think to find the constant k you need to use 184 lbs as the force in F(r)= k/r^2, while r is the radius of Earth:
\[\Large 184 = \frac{ k }{ 4000^2 }\]