Answer to Question #271680 in Classical Mechanics for mia

Question

A

surface of the earth. When the satellite orbits around the earth at a height equal to the diameter of the earth (above the surface of the earth), the magnitude of the gravitational force on the satellite will be:

satellite experiences a gravitational force with magnitude F when it is on the

A 3F

B 2F

C 1/3 F

D 1/9 F

Answer 1

The height equal to Earth's diameter (or $2R$) above the surface of the Earth is actually equivalent to the distance of $3R$ from the center of the planet. As we know, the gravitational force (at the surface) is

$$F=G\frac{Mm}{R^2}.$$

At distance of $3R$:

$$F_1=G\frac{Mm}{(3R)^2}=\frac F9.$$