PX158 - H2 - temperature of solar system bodies

\begin{aligned} P_{i n} & = P_{o u t} \\ \frac{L_{⊙}}{4 π d^{2}} π R^{2} & = 4 π σ R^{2} T^{4} \\ \frac{L_{⊙}}{16 π d^{2}} & = σ T^{4} \\ ∴ T_{e q} & = {(\frac{L_{⊙}}{16 π σ d^{2}})}^{\frac{1}{4}} \end{aligned}

where,
$R =$ radius of the object,
$d =$ distant from the sun,
$T_{e q} =$ equilibrium temperature

eg: what is the equilibrium temperature for the earth?
$L_{⊙} = 3.8 \times 10^{26} W$
$d = 1 A U = 1.5 \times 10^{11} m$
$$\therefore T_{eq,,\oplus} = 280,K$$
eg: what is the equilibrium temperature for venus?
- $d = 0.7 A U$
$∴ T_{e q, v e n u s} \approx 330 K$
- but, $T_{v e n u s} \approx 730 K$ , due to the greenhouse effect, venus is not a blackbody