A THOUGHT EXPERIMENT: let's compare Te.moon =270K with Tsat.io =110K
A THOUGHT EXPERIMENT
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Let's perform a thought experiment, let's suggest Moon is a heavy cratered planet, and therefore, Moon has Φ = 1;
It can be shown, Moon's (thought experiment) mean surface temperature would be then very much close to the Moon's effective temperature
Te.moon = 270K
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The comparison coefficient is:
[ (1-a) (1/R²) (N*cp)¹∕ ⁴ ]¹∕ ⁴
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Moon:
R = 1
a = 0,11
N = 0,0339 rotations/day
cp = 0,19 cal /gr.oC
Moon's comparison coefficient calculation:
[ (1-a) (1/R²) (N*cp)¹∕ ⁴ ]¹∕ ⁴
[ (1-0,11) (1²) (0,0339*0,19)¹∕ ⁴ ]¹∕ ⁴ =
[ (0,89) (1) (0,00641)¹∕ ⁴ ]¹∕ ⁴ =
[ (0,89) (1) (0,2833) ]¹∕ ⁴ =
(0,25213)¹∕ ⁴ = 0,70861
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Io:
R = 5,20
1/R² = 1/5,2044² = 0,0369
a = 0,63
N = 0,5559 rotations/day
cp = 0,145 cal /gr.oC
Io's satellite measured mean surface temperature is
Tsat.io = 110K
Comparison coefficient calculation:
[ (1-a) (1/R²) (N*cp)¹∕ ⁴ ]¹∕ ⁴
[ (1-0,63) (1/5,2044²) (0,5559*0,145)¹∕ ⁴ ]¹∕ ⁴ =
[ (0,37) (0,0369) (0,08060)¹∕ ⁴ ]¹∕ ⁴ =
[ (0,37) (0,0369) (0,53283) ]¹∕ ⁴ =
(0,0072747)¹∕ ⁴ = 0,29205
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Let's proceed,
let's compare Te.moon =270K with Tsat.io =110K:
Te.moon /Tsat.io = 270K /110K = 2,4545
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Let's compare the Moon's and Io's comparison coefficients:
Coeff.moon /Coeff.io = 0,70861 /0,29205 = 2,4263
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2,4545 /2,4263 = 1,0116
or only 1,16% difference !!!
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Conclusion:
Everything is all right.
It is a demonstration of the Planet Surface Rotational Warming Phenomenon!
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