If the ratio of the orbital distance of the two planets `(d_(1))/(d_(2)) = 2`, what is the ratio of gravitational field experienced by these two planets?

Explanation

Ratio of orbital distance of two planets `(d_1)/(d_2) = 2`
Raio of gravitational field distance of two planets `(E_1)/(E_2) = ?`
`E = (Gm)/(x^2) :. E_(1) = (GM)/(d_1^2) , E_(2) = (GM)/(d_2^2)`
`:. (E_1)/(E_2) = (GM)/(d_1^2) xx (d_2^2)/(GM)`
`(E_1)/(E_2) = ((d_2)/(d_1))^(2)`
`:' (d_1)/(d_2) = 2 ("given"), :' (d_2)/(d_1) = 1/2`
`:. (E_1)/(E_2) = ((d_2)/(d_1))^(2) = (1/2)^(2)`
`:. (E_1)/(E_2) = 1/4, E_(4) = 4 E_(1)`.