Question $12(1$ point$)$ Retake question

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Hemispherical von Neumann Bolometric Space Antenna of radius $r=1\mathrm{.}7m$ receives total of $0\mathrm{.}8{10}^{-6}W$ of radiative power across the whole EM spectrum when directed at the distant $B-$type star $($at distance $D=8$ lightyears$).$ Given that the radius of the star is known $($from independent measurement$)$ to be $R_{\text{s}\text{t}\text{a}\text{r}}=700,000km,$ find the star surface temperature.

NOTE:

Light year $--$ astronomical distance corresponding to the distance that light travels in on year.

Take: a year to be $365\mathrm{.}25$ days, the speed of light to be $c=3{10}^8\frac{m}{s}$;

Stefan Boltzmann Constant to be $={5\mathrm{.}670}^{**}{10}^{-8}\frac{W}{m^2}{K}^4$

State your answer to the nearest Kelvin.

NOTE: hemisphere is half of the sphere.