The annual average temperature of a planet can be determined for a planet in thermal
equilibrium (amount of radiation entering equals amount of radiation leaving the system) thusly:!
The luminosity of the sun is!
!
And the separation between the earth and sun is:!
!
The solar luminosity at the earth is reduced by the inverse square law, so the solar constant is:!
!
This radiation is equal to the temperature to the fourth (temperature entering) by the Steffan-
Boltzmann constant sigma. The luminosity distributes itself over the entire disc of the earth
while 30% is reflected back into space because the earth albedo is a=0.3 so,…!
!
The atmosphere radiates energy back to the surface of the earth , which is added to the
radiation entering the earth to get the temperature at the surface of the earth but !
!
Which means!
!
!
!
So, the annual average temperature at the surface of the earth is…!
!
Which is 30 degrees centigrade or 86 degrees Fahrenheit. This is a little warmer than the actual
average temperature because we have not included convection, the energy absorbed by
evaporation of the ocean and returned by precipitation, the formation of rain. !
Click here to go to the homepage: https://eanbardsley.github.io/source/index.html
L
0
= 3.9 × 10
26
J/s
1.5 × 10
−11
m
S
0
=
3.9 × 10
26
4π (1.5 × 10
−11
)
2
= 1370
wat ts
m
2
π R
2
4π R
2
σ T
e
4
=
S
0
4
(1 − a)
σ T
a
4
σ T
e
4
σ T
s
4
σ T
a
4
= σ T
e
4
T
s
= 2
1
4
T
e
σ T
e
4
=
S
0
4
(1 − a)
σ = 5.67 × 10
−8
T
s
= 255Kelvi n
