Question

On the ground the gravitational force,of the satellite is w. What is the gravitational force on the satellite,when at a height R/50. A) 0.96w B) 0.98w C) 1.02w D) 1.04w ....?

Answer 1

If the distance to the center of the earth increases by 2% the inverse square law dictates the force of gravity decreases by 4% (approximately) so choice A, `.96w.`

Explanation:

OK, sure Sana. The way I understand the question I guess the original amount of gravitational force on the satellite on the surface of the earth, its weight, is

`w = {GM m }/r^2`

where `M` is the mass of the earth, `m` the mass of the satellite, `r` the radius of the earth and `G` is Newton's constant.

Once it's launched, the distance from the satellite to the center of the earth we're told is `r + r/50 = 1.02 r` so the force is

`F ={GM m }/(1.02 r)^2 = 1/(1.02)^2 w`

That's about `.96 w`, choice A.