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 ....?

1 Answer
May 21, 2018

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.