Answer:
3.46 x 10^8 m
Explanation:
Let the distance from the earth be r, total distance from earth to moon be d,
then distance from the moon to the point of equal gravity= d -r.
Mass of the earth, M_E = 598 x 10^22 kg
Mass of the moon, M_m= 7.36 x 10^22 kg
Distance of the mood from the earth, d = 3.85 x 10^8 m
Force of gravity exerted on a mass, m by the earth,
F_E = G. M_E×m/r^2
Force of gravity exerted on a mass, m by the moon,
F_m = G×M_m×m/(d-r)^2
These are equal, So
G×M_E.m/r^2 =G×M_m.m/(d-r)^2
[r/(d - r)]^2= M_E/M_m
= 598/7.36 = 81.25
r/(d - r) = √81.25 = 9.014
9.014×(d - r) = r
10.014.r = 9.014 x 3.85 x 108
Hence, r= 9.014 x 3.85 x 108 /10.014
= 3.46 x 10^8 m
