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phys: clarify division by four and intensity

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eggy 2021-04-08 20:34:13 -04:00
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@ -466,15 +466,18 @@ The solar radiation reaching earth is equal to $\pu{S= 3.9\times10^{26} W}$ with
### Albedo
Derived from $I=\frac{P}{A}$, where $d$ is the distance from the Earth to the sun:
Derived from $I=\frac{P}{A}$, the intensity at a point in space can be related to the power of the radiation emitted by the source ($P$) and the distance between the two ($d$):
$$I=\frac{P}{4\pi d^2}$$
!!! example
The solar constant is derived in this way by substituting $d$ as the distance from the Earth to the sun.
As Earth and most other planetary bodies are not flat disks pointed at the sun, in reality the sun's intensity is reduced to a quarter due to the formula for a sphere. Therefore, the power absorbed/incident to the Earth is equal to, where $S$ is the solar constant:
$$P_\text{in}=(1-\alpha)\frac{S}{4}A$$
**Albedo** ($\alpha$) is the ratio of power from incident rays reflected or scattered to the power absorbed by a body, ranging from 0 to 1. A black body has albedo 0. On average, Earth's albedo is equal to $0.3$ due primarily to the atmosphere but also clouds and ice.
$$\alpha=\frac{\text{energy scattered/reflected}}{\text{energy absorbed}}$$
As Earth is not a flat disk pointed at the sun, in reality the sun's intensity is reduced to a quarter due to the formula for a sphere. Therefore, the power absorbed/incident to the Earth is equal to, where $S$ is the solar constant:
$$P_\text{in}=(1-\alpha)\frac{S}{4}A$$
Greenhouse gases are responsible for remaining increases in temperature. By absorbing and then re-emittng their natural frequencies of electromagnetic radiation (infrared for greenhouse gases), they delay the release of radiation back into space and heat up the atmosphere.
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