I have searched for at least 45 minutes and I can't seem to find it. If you don't know what I'm talking about, in Biblaridion's first Alien Biospheres Video, he mentioned the you could calculate a star based off its luminosity.
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3$\begingroup$ I've added an appropriate tag for you. By "calculate a star" do you mean it's mass, composition, age - that sort of thing? Perhaps you might edit to say. Any worldbuilding context (what you want the star to be like) might help in finding the right answer. $\endgroup$– Escaped dental patient.Commented Nov 11, 2021 at 9:48
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1$\begingroup$ If I recall correctly, the planetary formation was a collaboration with Artifexian for his alien biosphere serie, is in his channel that you will find lots of worldbuilding tutorials on celestial mechanics and geology. $\endgroup$– LuizPSRCommented Apr 10, 2022 at 23:56
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2 Answers
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A Suggestion
I watched that video a few years ago and, as I recall, the star/world building was done by Artifexian. I would recommend reviewing some of his (much shorter) videos if you're still getting the hand of this. That said, below are the basic star equations.
Star Equations
For reasons that will be obvious shortly, it's generally easier to start with a stellar mass and derive the luminosity and other properties.
NOTES:
- In the equations below, any value with a subscript of "☉" (e.g., $M_☉$) is the relevant value for our sun while a subscript of "*" (e.g., $L_*$) will be the value for the created star.
- The equations below all assume you're dealing with a main sequence star. Results will almost certainly be wrong if you're doing some other type.
- In general, all of these equations give approximations as the relationships are not exact.
Luminosity
In terms of solar luminosity ($L_☉$): $$ L_* = \begin{cases} 0.23M_*^{2.3}, & \text{if }M_* < 0.43M_☉ \\ M_*^4, & \text{if }0.43M_☉ < M_* < 2M_☉ \\ 1.5M_*^{3.5}, & \text{if }M_* > 2M_☉ \end{cases}$$ If desired, we can convert this common units with simple multiplication: $$ L_☉ = 3.828\times10^{26} w $$
Radius
In terms of solar radii ($R_☉$): $$ R_* = M_*^{0.8} $$ Again, convert to common units with multiplication: $$ R_☉ = 6.955\times10^{5} km $$
Surface Temperature
In terms of solar temperature ($T_☉$): $$ T_* = \left({{L_*}\over{R_*}}\right)^{.25} $$ or, if you prefer: $$ T_* = \sqrt[4]{{{L_*}\over{R_*}}} $$ Again, convert to common units with multiplication: $$ R_☉ = 5778K $$ $$ R_☉ = 5504.84°C $$
With temperature you can look up spectral class and determine approximate color.
MASS
As shown in the luminosity equations, the relationship between mass and luminosity is complex. A little playing with those equations will show you the break points are around $0.033L_☉$ and $16L_☉$. If you need to start from luminosity for some reason, you can either solve each equation for $M_*$ or you can start plugging in mass numbers until you get your luminosity.
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Simply use a calculator to get the stars mass from luminosity like this one here, then use the mass to calculate everything else. Artifexian has a pretty good videos on making a planetary system, and he has all the calculations in the description.
