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T
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16
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{\displaystyle T_{\mathrm {p} }=\left({\frac {L(1-A)}{16\pi \sigma D^{2}}}\right)^{\tfrac {1}{4}}}
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{\displaystyle T_{\mathrm {p} }=T_{\ast }\left^{\frac {1}{4}}}
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T
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4
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{\displaystyle \sigma \cdot T_{\mathrm {p} }^{4}={\frac {\sigma \cdot T_{\ast }^{4}}{4\pi \cdot d^{2}}}\cdot {\frac {4\pi \cdot R_{\ast }^{2}}{4\pi \cdot R_{\mathrm {p} }^{2}}}\cdot \pi \cdot R_{\mathrm {p} }^{2}(1-A_{\mathrm {p} })}
code for Earth at Perihelion:
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6.955
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10
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2
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5.67051
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10
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8
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×
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5778
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1
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0.016710219
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149597876600
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2
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1
,
412.903
W
/
m
2
{\displaystyle f_{p}={\frac {((6.955\times 10^{8})^{2})\times (5.67051\times 10^{-8})\times (5778^{4})}{((1-(1\times 0.016710219))\times 149597876600)^{2}}}=1,412.903\ W/m^{2}}
code for Gliese 581 c at Periastron:
f
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0.38
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6.955
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10
8
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2
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5.67051
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8
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×
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3480
4
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0.073
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0.073
×
0.16
)
)
×
149597876600
)
2
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6.9
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10
3
W
/
m
2
{\displaystyle f_{p}={\frac {((0.38\times 6.955\times 10^{8})^{2})\times (5.67051\times 10^{-8})\times (3480^{4})}{((0.073-(0.073\times 0.16))\times 149597876600)^{2}}}=6.9\times 10^{3}\ W/m^{2}}
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{\displaystyle {\frac {Gl\ 581\ c\ Periastron\ Insolation}{Earth's\ Solar\ Constant}}=}
6.9
×
10
3
W
/
m
2
1
,
366.079
W
/
m
2
=
505
%
{\displaystyle {\frac {6.9\times 10^{3}\ W/m^{2}}{1,366.079\ W/m^{2}}}=505\%}
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