I disagree that the figure for the Earth's Solar constant at
Solar Constant are accurate,
I've read various different quotations of the value in texts and on the internet. A little accuracy wouldn't hurt:
R= 6.955e8 m (Sun's radius)
T= 5778 °K (Sun's
photosphere or
Effective temperature)
a= 5.67051e-8 (
Stefan-Boltzmann Constant)
d= 149597876600 meters (Earth's average distance,
Mariner 10 data), 1
AU
f=
flux or
Insolation.
L= 4pi·R2aT4
L = 4pi·d2f
Since both Luminosity formulas equal 3.84181e26 Watts for the Sun and Earth,
then 4pi·R2aT4 = 4pi·d2f
Therefore, f=(R2aT4) / d2
Then ((6.955e8 m)2 (5.67051e-8) (5778°K)4) / (149597876600)2 = 1366.0785 W/m2
(Which is only off by 0.1333% the so called satellite measured solar constant.)
This is the average. If you factor in the Earths's eccentricity (0.016710219),
then the range is 1321.5430 W/m2 to 1412.9039 W/m2
(((695500000)^2)*(0.0000000567051)*(5778^4))/ ((1-(1*0))*149597870691 )^2 = 1366.07868576308
=(((((0.0000000567051)*(3840^4))/(4*PI()*((0.0613*149597876600)^2))) * ((4*PI()*((0.29*695500000)^2))/(4*PI()*((11162)^2)))*((PI()*((11162)^2)*(1-0.64))))/0.0000000567051)^0.25
{R_\odot}
"FUNDAMENTALS OF ASTRONOMY" page 318 (QB43.3.B37 2006) by Dr.Cesare Barbieri, professor of Astronomy at the university of Pauda, Italy has a different planet Equilibium Temperature formula than the Selsis et al paper (very different) and is more accurate. It works out for Gliese 581 c to over 337°K/64°C (368.3°K /95°C at perihelion) with out the GHG effect (Earth is +33°C), with the Earth's increase added it would put it at 97°C! (130°C at perihelion). The full formula is T=(((((0.0000000567051)*(3840^4))/(4*π *((0.073*149597876600)^2))) * ((4*PI()*((0.29*695500000)^2))/(4*π *((11162)^2)))*((π *((11162)^2)*(1-0.3))))/0.0000000567051)^0.25 Using the same Albedos as they did for Earth, but nowhere near habitable. Tp=(((((5.67051E-8)*(Ts^4))/(4*π *((d*1au)^2))) * ((4*π *((Rs)^2))/(4*PI()*((Rp)^2)))*((PI()*((Rp)^2)*(1-A))))/5.67051E-8)^0.25
I disagree that the figure for the Earth's Solar constant at
Solar Constant are accurate,
I've read various different quotations of the value in texts and on the internet. A little accuracy wouldn't hurt:
R= 6.955e8 m (Sun's radius)
T= 5778 °K (Sun's
photosphere or
Effective temperature)
a= 5.67051e-8 (
Stefan-Boltzmann Constant)
d= 149597876600 meters (Earth's average distance,
Mariner 10 data), 1
AU
f=
flux or
Insolation.
L= 4pi·R2aT4
L = 4pi·d2f
Since both Luminosity formulas equal 3.84181e26 Watts for the Sun and Earth,
then 4pi·R2aT4 = 4pi·d2f
Therefore, f=(R2aT4) / d2
Then ((6.955e8 m)2 (5.67051e-8) (5778°K)4) / (149597876600)2 = 1366.0785 W/m2
(Which is only off by 0.1333% the so called satellite measured solar constant.)
This is the average. If you factor in the Earths's eccentricity (0.016710219),
then the range is 1321.5430 W/m2 to 1412.9039 W/m2
(((695500000)^2)*(0.0000000567051)*(5778^4))/ ((1-(1*0))*149597870691 )^2 = 1366.07868576308
=(((((0.0000000567051)*(3840^4))/(4*PI()*((0.0613*149597876600)^2))) * ((4*PI()*((0.29*695500000)^2))/(4*PI()*((11162)^2)))*((PI()*((11162)^2)*(1-0.64))))/0.0000000567051)^0.25
{R_\odot}
"FUNDAMENTALS OF ASTRONOMY" page 318 (QB43.3.B37 2006) by Dr.Cesare Barbieri, professor of Astronomy at the university of Pauda, Italy has a different planet Equilibium Temperature formula than the Selsis et al paper (very different) and is more accurate. It works out for Gliese 581 c to over 337°K/64°C (368.3°K /95°C at perihelion) with out the GHG effect (Earth is +33°C), with the Earth's increase added it would put it at 97°C! (130°C at perihelion). The full formula is T=(((((0.0000000567051)*(3840^4))/(4*π *((0.073*149597876600)^2))) * ((4*PI()*((0.29*695500000)^2))/(4*π *((11162)^2)))*((π *((11162)^2)*(1-0.3))))/0.0000000567051)^0.25 Using the same Albedos as they did for Earth, but nowhere near habitable. Tp=(((((5.67051E-8)*(Ts^4))/(4*π *((d*1au)^2))) * ((4*π *((Rs)^2))/(4*PI()*((Rp)^2)))*((PI()*((Rp)^2)*(1-A))))/5.67051E-8)^0.25