On the moon surface the acceleration due to gravity is 1.67 m S if the radius of the moon is 1.74* 10 m calculate the mass of the moon

Question

On the moon surface the acceleration due to gravity is 1.67 m S^-2 if the radius of the moon is 1.74* 10 m calculate the mass of the moon

Answer 1

g = 1.67 ms²

R = 1.74 x 10⁶m

M = ?

we know, g = \(\frac{GM}{R^2}\) 

1.67 = \(\frac{6.67\times10^{-11}\times M}{(1.74\times10^6)^2}\) 

M = \(\frac{1.67\times(1.74\times10^6)^2}{6.67\times10^{-11}}\) 

= \(\frac{1.67\times1.7\times1.74}{6.67}\)x 10¹²⁺¹¹

= 0.758 x 10²³

= 7.58 x 10²²