From 6b6154699ec1c50a0aa0adc9db6e7d35ffae3d16 Mon Sep 17 00:00:00 2001 From: eggy Date: Thu, 8 Apr 2021 20:34:13 -0400 Subject: [PATCH] phys: clarify division by four and intensity --- docs/sph4u7.md | 11 +++++++---- 1 file changed, 7 insertions(+), 4 deletions(-) diff --git a/docs/sph4u7.md b/docs/sph4u7.md index 382ed63..ca9f0ea 100644 --- a/docs/sph4u7.md +++ b/docs/sph4u7.md @@ -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. ## Resources