The power density leaving the sun is given by the Stefan-Boltzmann Law.pic.twitter.com/Rt8xL1w0LL
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The power density leaving the sun is given by the Stefan-Boltzmann Law.pic.twitter.com/Rt8xL1w0LL
The Sun’s temperature is 5778 K, and the Stefan-Boltzmann constant is 5.670e-8 in SI units. Thus, the radiated intensity at the "surface" is 6.320e7 Wm-2. [e7 means "times ten to the seven", so times 10 illion]pic.twitter.com/KOwYK1XQle
By the time it gets to Earth, the density of radiation has fallen off as the square of the ratio of the radius of the Sun to that of Earth’s orbit. The Sun’s radius is 6.955e8 m, and the Earth’s orbit is 1.496e11 m. This gives Fs = 1366 Wm-2 at the top of the atmosphere.
We first consider an Earth that absorbs all incoming sunlight without reflections. The Earth intercepts an area given by πR² (area of the disc presented to the Sun), but can radiate over its total area, which is the surface area of a sphere, 4πR².pic.twitter.com/huTkmbPcjJ
To maintain energy balance, Fs πR² = Fg 4πR², where Fg is the average power density radiated by the Earth's surface. Thus Fg = Fs/4, is 341 Wm-2. Rearranging the Stefan-Boltzmann Law (above), we can calculate the surface temperature needed to radiate this much energy.
The surface temperature is given by the fourth-root of the ratio of Fg to sigma. This gives 279 K, or 6 C. Well, that’s not too bad, but we ignored that Earth actually reflects 30% of incoming radiation (The Albedo is A = 0.3).pic.twitter.com/TJfgEv4nQl
Reducing the incoming radiation at the surface by a factor of (1 - 0.3) = 0.7 adjusts the predicted average temperature to 255 K (-18 C), which we know is much below the observed average surface temperature of +15 C (288 K).pic.twitter.com/tEeBS58Lxb
Why did we get it so wrong? The answer is hinted at by looking at the predicted surface temperatures for the planets (and Pluto!) compared to observations (for the gas giants, there is no surface, but the temperature is at the top of the observed gas clouds).
The planets lie on a neat line of x = y, except for two notable exceptions. Venus and Earth. Both have considerable atmospheres. In PART 2, we will see how consideration of a simple atmosphere can increase the predicted surface temperature.pic.twitter.com/Y01VpljDEn
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