P^{2} = (\frac{4π^{2}}{GM} ) ^{3}

P_{years}^{2} = (\frac{1}{M_{solar}} ) a_{AU}^{3}

a_{AU}^{3} = (M_{solar}) P_{years}^{2}

M_{planet} = M_{star} (\frac{a_{star}}{a_{planet}} )

Incoming energy = (\frac{L_{∗}}{4πa^{2}} ) πR^{2}

Outgoing energy = ( σ T^{4} ) 4πR^{2}

(\frac{L_{∗}}{4πa^{2}} ) πR^{2} = ( σ T^{4} ) 4πR^{2}

T^{4} = \frac{L_{∗}}{16πa^{2}σ}

T = (\frac{L_{∗}}{16πσ} )^{1/4} (\frac{1}{a^{2}} )^{1/4}

\begin{aligned}\frac{T_{b}}{T_{Earth}} & = (\frac{0.00155/1.0}{(0.052/1.0)^{2}} )^{1/4} \\ & = 0.89 \end{aligned}