Posted by Bobbie on .
determine the distance from earths centre where the force of gravity acting on a space probe is only 11% of the force acting on the same probe at earths surface. Express your answer in terms of earths radius, rE
Force is inversely prop to distance squared, so...
F = G Me m/R^2
Fe= G Me m/Re^2
F/Fe = 11/100 = 1/R^2 / 1/Re^2 = Re^2/R^2
11/100 = Re^2/R^2
R/Re = sqrt(100/11) = 10/sqrt 11
R = 3.01 Re
The force of gravity is proportional to 1/r^2, where r is measured from the center of the earth. Therefore
(r/rE)^-2 = 0.11
r/rE = sqrt (1/0.11) = sqrt 9.09 = 3.015