Acceleration due to gravity?

How far from the center of the earth must a person be to experience acceleration due to gravity that is one half the acceleration at the surface?





The vital statistics of the earth are: Radius = 6.38e6 m; Mass = 5.97e24 kg; G = 6.67e-11 Nm2/kg2; g = 9.8 m/s2 at earth surface.

Acceleration due to gravity?
Acceleration due to gravity varies inversely with the square of the distance to the center of the earth. Let R be distance at the surface and R1 be the distance that gives g/2. Let M be the mass. So the value 9.8 m/s^2 comes from Newton's Universal Law of Gravitation.





g = G*M / R^2


If you want g/2 the expression is


g/2 = G*M / R1^2





So some algebra will give you


g*R^2 = G*M


and


(g/2)*R1^2 = G*M





I'll let you do the remaining steps.