Mars and Earth act as black bodies. The \(\frac{{{\text{power radiated by Mars}}}}{{{\text{power radiated by the Earth}}}} = p\) and \(\frac{{{\text{absolute mean temperature of the surface of Mars}}}}{{{\text{absolute mean temperature of the surface of the Earth}}}} = t\).

What is the value of \(\frac{{{\text{radius of Mars}}}}{{{\text{radius of the Earth}}}}\)?

A.     \(\frac{p}{{{t^4}}}\)

B.     \(\frac{{\sqrt p }}{{{t^2}}}\)

C.     \(\frac{{{t^4}}}{p}\)

D.     \(\frac{{{t^2}}}{{\sqrt p }}\)

B