Two spherical objects, \(X\) and \(Y\), behave as ideal blackbodies. Object \(Y\) has a radius twice that of Object \(X\), and the wavelength corresponding to peak radiation intensity for Object \(Y\) is half that for Object \(X\). What is the ratio \(\dfrac{P_Y}{P_X}\) of the total power radiated by Object \(Y\) to the total power radiated by Object \(X\)?