Given that `d_(e), d_(m)` are densities of the Earth and moon, respectively, `D_(e), D_(m)` are the diameters of the Earth and the moon, respectively. `g_(e) "and" g_(m)` are the acceleration due to gravity on the surface of the Earth and moon, respectively. Find the ratio of `g_(m) "and" g_(e)`

Explanation

Acceleration due to gravity on the surface of the Earth and the moon be `g_(E) "and" g_(M)` and its mass and radius be `M_(e), R_(e) "and" M_(m), R_(m)`, respectively.
`(g_(E))/(gm)=(GM_(E))/(R_(e)^(2)) xx (R_(m)^(2))/(GM_(m))`
Here, diameters of the Earth and the moon are `D_(E) "and" D_(m)`, respectively.
Then, `R_(e) =(D_(e))/(2) "and" R_(m) = (D_(m))/(2)`
Find the relation between acceleration due to gravity on the Earth and on the moon with their diameters.