Question
the earth 's moon has a gravitational field strength of about 1.6 n/kg near its surface. the moon has a mass of 7.35x10^22 kg. what is the radius of the moon?
Answers
To answer this, you need to know
M, the mass of the earth
R, the radius of the earth
on moon, g = Gm/r^2 = 1.6
on earth, g = GM/R^2 = 9.81
(m/r^2) / (M/R^2) = 1.6/9.81
m/M * R^2/r^2 = 1.6/9.81
mr^2/MR^2 = 1.6/9.81
r^2 = M/m R^2 * 1.6/9.81
M, the mass of the earth
R, the radius of the earth
on moon, g = Gm/r^2 = 1.6
on earth, g = GM/R^2 = 9.81
(m/r^2) / (M/R^2) = 1.6/9.81
m/M * R^2/r^2 = 1.6/9.81
mr^2/MR^2 = 1.6/9.81
r^2 = M/m R^2 * 1.6/9.81