The moon revolves round the earth `13` times in one year. If the ratio of sun-earth distance to earth-moon distance is `392`, then the ratio of masses of sun and earth will be

Explanation

The time period `T_(e)` of earth around sun of mass `M_(s)` is given by
`T_(e)^(2) = (4pi^(2))/(GM_(s)) xx r_(e)^(3)` …(1)
Where `r_(e)` is the radius of the earth.
Similarly, time period `T_(m)` of moon around earth is given by
`T_(m)^(2) = (4pi^(2))/(GM_(e)) xx r_(m)^(3)` ...(2)
Dividing equation(1) by equation (2), we get
`((T_(e))/(T_(m)))^(2) = ((M_(e))/(M_(s)))((r_(e))/(r_(m)))^(3)`
or `((M_(s))/(M_(e))) = ((T_(m))/(T_(e)))^(2) xx ((r_(e))/(r_(m)))^(3)` ..(3)
Substituting the given values, we get
`((M_(e))/(M_(s))) = {((13))/(1)}^(2) xx (392)^(2) = 3.56 xx 10^(5)`