Answer
a) $P_{net}=3.9\times 10^{26}W$
b) $solar \space constant=1.4KW/m^2$
Work Step by Step
(a) We can find the required power as follows:
$P_{net}=\sigma(4\pi r^2)(T^4-T_S^4)$
We plug in the known values to obtain:
$P_{net}=5.67\times 10^{-8}W/(m^2.K^4)4\pi(7.0\times 10^8m)^2[(5773K)^-(3K)^4]$
$P_{net}=3.9\times 10^{26}W$
(b) We can find the solar constant as
$solar\space constant=\frac{P}{A}$
We plug in the known values to obtain:
$solar\space constant=\frac{3.9\times 10^{26}}{4\pi (1.5\times 10^{11}m)^2}$
$solar \space constant=1.4KW/m^2$