Answer:
X = 6910319.7 m
Step-by-step explanation:
let X be the distance where the acceleration of gravity is 85% of what it is on the surface and g1 be the acceleration of gravity at the surface and g2 be the acceleration of gravity at some distance X above the surface.
on the surface of the earth, the gravitational acceleration is given by:
g1 = GM/(r^2) = [(6.67408×10^-11)(5.972×10^24)]/[(6371×10^3)^2] = 9.82 m/s^2
at X meters above the earth's surface, g2 = 85/100(9.82) = 8.35m/s^2
then:
g2 = GM/(X^2)
X^2 = GM/g2
X = \sqrt{GM/g2}
= \sqrt{(6.67408×10^-11)(5.972×10^24)/ 8.35
= 6910319.7 m
Therefore, the acceleration of gravity becomes 85% of what it is on the surface at 6910319.7 m .