Introduction
If our sun were to disappear, humans would die. The base of our food chain uses radiation emitted by the sun to make the magic happen (photosynthesize). Not only would we starve to death, but weather would cease. In this Sky Dive, we will explore this life-saving light.
You may be thinking, “okay I get why the food chain would collapse, but why would weather stop?” The answer is that the only reason Earth (and any planet for that matter) observes weather is because planets are unevenly heated by the sun. The atmosphere then transports the excess energy near the equator to the poles. This energy transport is not only performed by the atmosphere. Ocean currents also play a large part in distributing heat to the poles – but this is AtmoGuy, not OceanGuy. Global circulation will be explored in another Sky Dive.
This post will briefly cover:
- Electromagnetic Spectrum
- Planck’s Radiation Law
- The Sun’s color
- Wein’s Displacement Law
- Kirchhoff’s Law
- Blackbody/Graybody
Click here for a list of Sky Dives.
Updated: 2019-08-26
What is Solar Radiation?
The sun is an enormous ball of gasses mostly made up of hydrogen (~72%) and helium (~26%) and other trace gasses (source). Electromagnetic energy is generated through nuclear fusion (combine two nuclei to make a new nuclei) of hydrogen atoms to create helium. The exact process is more complicated than that, but it serves our purposes. This electromagnetic energy travels as photon’s which are particles traveling with an electric field and a magnetic field at a 90 degree offset. These fields constitute a wave with a specific wavelength and frequency.
Our sun doesn’t only produce visible light through fusion, it produces ultraviolet and infrared radiation as well. Visible light happens to be a relatively small portion of the electromagnetic spectrum as you can see in the figure below.
Encyclopædia Britannica; source link
“But does the sun emit more energy at a specific wavelength? Does it emit from all wavelengths evenly?”. I’m glad you asked! Planck’s Radiation Law (Plank 1901) provides a formula to calculate the distribution of electromagnetic power across different wavelengths (such as radio waves, visible light, x-rays, etc.). Max Plank was a smart fella. He figured out this formula in 1900 without the use of specialized equipment. One form of Plank’s Radiation Law (Equation 1) is flux density (irradiation) in units of power per area [\frac {W}{m^{-2}}] .
(1)\qquad\LARGE E_\lambda= \frac{2\pi hc^{2}}{\lambda^5} \times \frac {1}{exp(hc/kT\lambda)-1}\quad[W\>m^{-2}]
Where
- \lambda=\>wavelength\quad[m]
- h = Planck's\>Constant = 6.626 \times 10^{-34}\quad[j\cdot\>s]
- c = Speed\>of\>Light\>(in\>vaccum)= 299,792,458\quad[m\>s^{-1}]
- k = Boltzmann\>Constant=1.3806 \times 10^{-23}\quad[j\>K^{-1}]
- T = Temperature = Degrees\>Kelvin\quad[K]
Check out my Python Jupyter notebook for Planck's Law.
Using Planck’s Law, we can calculate the spectral density (distribution of energy by wavelength) of the flux density to see at which wavelengths the sun emits most of its electromagnetic energy (Wallace and Hobbs 2006). To calculate Equation 1, we need to know the temperature of the sun which happens to be 5772 K (NASA). Then we calculate the flux density for a range of wavelengths (lets say from 1\times10^{-7} \to 11\times10^{-6}\>[m]). The figure below was generated from a Jupyter notebook of Planck’s Law.
Humans are about 100 F (for arguments sake; ~310 K). When plotted along with the sun (flux density normalized by the respective maximum values so they are comparable) you can see how humans are shifted into the infrared spectrum (~9 micrometers). This is why humans are easy to see with an infrared (thermal) camera. At night, humans generally radiate more infrared radiation than the surrounding environment.
All infrared imagery is false color because humans cannot see infrared radiation (light). In the false-color infrared image below, you can easily see humans in a forested environment because they are darker (black is hotter, white is cooler). This means the humans below emit more infrared heat than anything else in the image. At night it would be nearly impossible to see these people walking through a forest without an infrared camera due to a large reduction of visible light compared to the daytime.
Your next question might be, “I get how the sun makes heat and light, but why does the sun look yellowish and not green?”
What color is the sun?
You probably don’t believe me right now, but the sun is not yellow, or orange, or red. Remember how I said the sun emits from ultraviolet to infrared radiation? What color do you get when you combine every visible color bracketed by ultraviolet and infrared waves? That’s right, white.
The temperature of an object determines the peak spectral color. We can calculate the peak spectral color of the sun using Wein’s Displacement Law.
(2)\qquad \LARGE \lambda_m=\frac{2897}{T}
Using a temperature of 5772 K in equation 2, the color temperature of the sun is ~500 nm. That’s pretty close to the peak of the flux density spectrum in Figure 3! But wait, that’s green. Shouldn’t the sun appear green!? No. Look again at the graph of spectral intensity (Figure 3). While the peak is green, the sun still emits all of the other visible light colors which makes it white. Stars that peak in the visible appear white, cooler stars appear a shade of orange/red, and hotter stars are a shade of blue.
The reason for this seemingly limited range of star colors is due to our eyes (source). We can only see the visible portion of the spectrum. Our eyes have receptors for the primary colors (red, blue, yellow) and they generate the other colors by a combination of those three.
Other Useful Radiation Laws
The following are introduced here, but will be explored further in the next subsequent Sky Dives.
All objects above absolute zero (kelvin) emit thermal radiation (Wallace and Hobbs 2006). This is referred to as blackbody radiation. The Stefan-Boltzmann Law says that the blackbody irradiance integrated over all wavelengths (i.e. sum of all irradiance under the curve in figure 3 for example) is equal to:
(3)\qquad\LARGE F\>=\>\sigma\>T^{4}
Where:
- \sigma \>=Stephan\>Botzman\>Constant\>=\>5.68 \times 10^{-8}\quad[W\>m^{-2}\>K^{-4}]
- T\>=\>Effective\>Emissivity\>Temperature \quad[K]
An equivalent blackbody temperature is the temperature an object must be in order to radiate at F (flux density). Take the sun for example. Using a temperature of 5772 K, the effective irradiance of the sun is 6.29 \times 10^{7}\>W\>m^{-2}. Not every object radiates as effectively as it could as a blackbody. In these cases, objects are referred to as graybody’s.
A graybody can reflect, transmit, and absorb radiation. Emissivity is the amount of radiation emitted versus it’s blackbody temperature. If an objects emissivity is less than 1, it’s a graybody. If emissivity is 1, it’s a blackbody. Other properties include an objects absorbtivity which relates how much radiation an object absorbs compared to the incident radiation. Reflectivity is the amount of radiation reflected per amount incident, and Transmissivity is the amount transmitted per amount incident. The amount of radiation (at a specific wavelength) equals the radiation absorbed (at a specific wavelength). This is known as Kirchhoff’s Law.
Our next Sky Dive will look at the interaction of sunlight and Earth’s atmosphere.
Sources
Plank, Max, 1901: On the Law of Distribution of Energy in the Normal Spectrum, Annalen der Physik, 4, 11 pp.
Wallace, J.M., and Hobbs, P.V., 2006: Atmospheric Science: An Introductory Survey, Elsevier, 92, 483 pp.
