Back to Math And Terraforming
This page is made to help you see what kind of conditions settlers would encounter on a planet orbiting a specified type of star.
Light Spectra Edit
Before everything, keep in mind that stars are different and there is NO WAY a star will behave just as expected by your math. If at possible you can get some fresh data about your star, it is far better then trying yourself to calculate. The best example I can give you is our own Sun, which emits about 10% more light then it should be as a G2 main sequence star.
Amount of light for a specified wavelength Edit
The luminosity of a star is similar to a black-body radiation spectra. However, the formulas shown there are hard to apply, since you will need to work with a lot of difficult numbers, like Planck constant and Boltzmann constant. I made an overall formula, that should be a bit more simple:
Ls = 1.35E-44*(((L*1000000000000)^3)/(2.1828^(0.000000000048*(A93*1000000000000)/T)-1))
Here, Ls is the luminosity at specified wavelength, L is the wavelength in nanometers and T is the temperature in degrees Kelvin. To get a complete image of the luminosity spectra of a star, you can use Microsoft Excel and do as follows:
- Column A: type wavelengths in nanometers (see this article for more data).
- Column B: type temperature in degrees Kelvin (5772 for our Sun).
- Column C: type this formula (for row 3, then copy to other rows):
I like to run a simulation for wavelengths detailed for visible light and also including values for infrared and UV.
The values you get for our sun, Sol, should be considered as a reference. When you run a second simulation, for another star, you will get other values. See how strong they vary. What is important is the difference between each spectra. On a red dwarf you will get more infrared, while on a blue star, you will get more UV then visible light. Overall, a red star will give far less light then a blue one in all spectra, but not the amount is important. Here, we only look at differences.
Finding the main spectra Edit
If you know the temperature, you can easily get the wavelength in which the star emits most of its light. The formula is:
Lmax = (0.002897/T)*1000000000
Here, Lmax is the wavelength in nanometers and T is temperature in degrees Kelvin.
Temperature - Luminosity - Diameter Edit
There are 3 equations that can easily find basic properties of a star.
If you know temperature (T in degrees Kelvin) and diameter (dm in thousands km) of a star, then you can get the Solar Constant (Ks):
Ks = dm^2*(T^4)*1.03682E-17
Again, if you know diameter and solar constant, you can get the temperature:
T = ((Ks*103682000000000000)/(diam^2))^0.25
Finally, if you know temperature and solar constant, you can find the diameter:
dm = ((Ks*103682000000000000)/(T^4))^0.5
These formulas are very useful, for example if you want to study a planet orbiting Brown Dwarfs or a moon of a Rough planet, since almost all their light is in infrared. Also, you can get an image of the pale amount of visible light these bodies give to their planets.