Okay, I kept googling and found this awesome page.
The Real 'Inconvenient Truth'
http://www.junkscience.com/Greenhouse/
This article hits on all of the main points and offers some help on Venus as well.
Near the start of the page is this section talking about temperature of the Earth that should let you compute the temperature that Venus
should be.
How much does the so-called 'greenhouse effect' warm the Earth?
It's estimated that the Earth's surface would be about -18 °C (0 °F, 255 K) with atmosphere and clouds but without the greenhouse effect and that the (we'll call it "natural") greenhouse effect raises the Earth's temperature by ~33 °C (59 °F).
We should note that devoid of atmosphere Earth would actually be a less-cold -1 °C (272 K) because the first calculation strangely includes 31% reflection of solar radiation by clouds (which obviously could not occur without an atmosphere) while ignoring that clouds add significantly to the greenhouse effect. Granted it's kind of a bizarre to include clouds in one half the calculation and not the other but that is the way it's commonly done, so, for simplicity, just stick with ~33 °C.
The workings: thermal equilibrium for an Earth without an atmosphere:
The sun behaves approximately like a black body of radius rs=6.599 x 105 Km, at a temperature of Ts=5,783 K. The radiative flux at the sun's surface is given by the expression σTs4, where σ is the Stefan-Boltzmann Constant (5.6704 x 10-8 Wm2K4). Flux refers to radiation per unit area. Thus, at the Earth's distance from the sun, res=1.496 x 108 Km, this flux is reduced by the factor (rs/res)2. The Earth's disk has a cross section, acs=πre2, where re is the Earth's radius (6.378 x 103 Km), and thus intercepts acsσTs4(rs/res)2 radiation from the sun. In order to balance this intercepted radiation, the Earth would warm to a temperature Te, where σTe44πre2 = acsσTs4(rs/res)2. This leads to a solution Te=272 K.
Clouds, which obviously require an atmosphere, and other features of the Earth reflect 31% of the incident radiation. Taking this into account reduces Te to 255 K.
Theoretically, if the planet's surface cooled by radiation alone, then the greenhouse-induced surface temperature would be much warmer, about 350 K (77 °C). Atmospheric motion (convective towers carrying latent and sensible heat upwards and large scale circulation carrying it both upwards and polewards) circumvent much of the greenhouse effect and significantly increase the "escape" of energy to space, leaving Earth's surface more than 60 °C cooler than a static atmosphere would do.
Additionally, greenhouse gases are only able to absorb radiation in very specific electromagnetic frequencies and Earth does not radiate limitless amounts of energy in the appropriate bandwidths. This means there is 'competition' for available energy and significant greenhouse potential is unrealized (carbon dioxide could absorb more than 3 times the energy it currently does in the atmosphere were it not for competition from clouds and water vapor, clouds alone could absorb 50% of available energy but manage to capture just 14% and so on...).
So, despite there being far more greenhouse gas in the atmosphere than required to achieve the current greenhouse effect, something which has been true since before humans discovered fire, evapo-transpiration and thermals transport heat higher in the atmosphere where radiation to space is increased. This is why Earth remains about 15 °C (288 K) rather than about 77 °C (350 K).
This is the main equation:
σT
e44πr
e2 = a
csσT
s4(r
s/r
es)
2
This equation simplifies down to:
T
e = 1/4 root of ( 0.25 (T
s4(r
s/r
es)
2))
Go to the webpage to see the formula clearly and then plug in the numbers for Earth and Venus from Wiki:
Earth
http://en.wikipedia.org/wiki/Earth
Earth Numbers
Semi-major axis 149,598,261 km
~ r
es = 1.496 x 10
8 Km
Albedo - 0.367 (geometric)
0.306 (Bond)<---------I think that they are using this number.
Venus
http://en.wikipedia.org/wiki/Venus
Venus numbers
Semi-major axis 108,208,930 km
~ r
vs = 1.082 x 10
8 Km
Albedo - 0.67 (geometric)
0.90 (Bond)<---------Venus has an albedo of 0.90! That means that most of the light hitting Venus is reflected away! Looking at the Wiki page, a value of 0.90 is the same albedo as "Fresh snow".
Albedo
http://en.wikipedia.org/wiki/Albedo
So whatever the T
v for Venus is it will be that much cooler.
Earth (To check the example given above.)
T
e = 1/4 root of ( 0.25 (5,783 K)
4(6.599 x 10
5 Km / 1.496 x 10
8 Km)
2)) = 272 K
I don't see how the albedo of 0.306 fits into the equation to get their value of T
e = 255 K, but at least my number without atmosphere matches theirs.
Now here's Venus
T
v = 1/4 root of ( 0.25 (5,783 K)
4(6.599 x 10
5 Km / 1.082 x 10
8 Km)
2)) = 318 K
Notice that the distance of Venus from the Sun is not much less than the Earth. As I mentioned up thread, Pre Space Age Venus was well within the "life zone", and with the albedo making the planet as reflective as "fresh snow" the actual temperature of Venus should have been only a bit more than Earth.
Like I've mentioned, I've lost my ability to do simple Math, so please check my numbers. If you see how to work the albedo into the equation, let me know. Thanks...