Worldbuilding Guide Part 1: Stars

Worldbuilding is fun, and making guides about it is also fun. We will start with planets because they can be pretty important to the story, so it's important to understand how to create detailed and cool planets.

## Stars

When building a star, you need to take into consideration whether you want planets to go around it, and if so, what kind and whether they are habitable. Stars have several classes, some of which are habitable and some are not. On average, 1000 stars will contain 900 main sequence stars, 96 white dwarfs and 4 giant stars. Among the 900 main sequence stars, there are 1 O star, 1 B star, 5 A stars, 30 F stars, 70 G stars, 98 K stars and 695 M stars. Let’s just add in a neutron star and a black hole, for good measure.

There are many different types of stars, which have different methods to make them.

### Main Sequence Stars

The first step in building a star is to set the mass. The mass controls LITERALLY EVERYTHING ELSE about your main-sequence star. Main sequence stars go from 0.08 Solar Masses to 50 Solar Masses. Within this range, there are smaller ranges based on the different stellar types.

* P/O: >55 MSol
* O: 17-500 MSol
* B: 2.1-17 MSol
* A: 1.4-2.1 MSol
* F: 1.04-1.4 MSol
* G: 0.8-1.04 MSol
* K: 0.45-0.8 MSol
* M: 0.0748-0.45 MSol

By the way, only G, K, M and maaaybe F stars are truly habitable for long enough for intelligent life to evolve. Luckily, they’re more common than dirt! O, B and A stars can theoretically have habitable planets around them, but they wouldn’t be habitable long enough for intelligent life to evolve. However, they can still be colonies and stuff like that.

[Sidenote] also, smaller stars live longer. [end sidenote]

Now that THAT’S over with, Equation time!

#### **Radius, Circumference, Surface Area, Volume, Gravity and Density**

If you’ve chosen a mass less than our sun, the radius is given by:

M0.8

If you’ve chosen a mass more than our sun, the radius is given by:

M0.55

Now that you have your radius, circumference, surface area, volume, gravity, density can be found like so, in relative values.

C=R

SA=R2

V=R3

⍴=M/V

g=M/R2

If you wish, here are some absolute values.

C=2πR

SA=4πR2

V=4/3πR3

⍴=M/V

#### **Luminosity**

The intrinsic luminosity of your star is given by the mass-luminosity relationship:

L=M3.5

This is a good fit for the main sequence (assuming this is in the present era of the universe), but it isn’t perfect. Here are some better ones if you want to be REALLY accurate:

L=0.23•M2.3 (M<0.43)

L=M4 (0.43<M<2)

L=1.4•M4 (2<M<55)

L=32000•M (M>55)

#### **Lifetime (time on the main sequence)**

Your star’s time on the main sequence is given by:

Tms= (M/L)

Multiplying by a solar lifetime, 10-11 billion years, will give your star’s lifetime in earth years.

[interesting side note] the least massive main sequence stars will remain on the main sequence for approximately 5.5 trillion years, which is a long time. In fact it’s about 400 times longer… than time itself. [interesting side note end]

#### **Effective (surface) Temperature**

The effective temperature of your star will be given by:

Teff= (L/R2)0.25

Multiplying by the temperature of the sun, 5778K, gives you your star’s temperature in Kelvin.

Then, use these charts to determine your star's approximate color.

 P
 WC and WN
 O
 B
 A
 F
 G
 K
 M

#### **Habitable Zone**

If you want your star to have planets that support life similar to earth life, you must ensure your planets are in the habitable zone, unless you want to do something really weird.

The habitable zone extremities in AU are given by:
HZinner=√(L/1.1)

HZ=√L

HZouter=√(L/0.53)

If you want to make life that uses methane as a solvent, and know how to find the habitable zone for methane, PLEASE TELL ME!

#### **Frost Line**

The frost line is the distance beyond which gas giants can form. It is given by:

FL=4.85•HZ

This is important, because gas giants always form outside this line, though they can and often do migrate inwards, like Jovoterra.

## Post Main Sequence Stars

Post Main Sequence Stars are really weird, and are therefore very hard to calculate using simple mAtHs. However, we'll try.

### Giants, Supergiants and Hypergiants, Method 1 (easier, but less accurate)

Giants, supegiants, and hypergiants are really weird, and are therefore very hard to calculate using simple mAtHs. However, we'll try. As an approximation, plug in the mass, the radius, and the luminosity, as these are the hardest to calculate. With these, you can calculate the other stats.

#### Circumference, Surface Area, Volume, Gravity, and Density

The circumference, surface area, volume, gravity, and density can all be calculated in the same way as with main sequence stars.

#### Surface Temperature

That can also be calculated the same way as main sequence stars.

### Giants, Supergiants and Hypergiants, Method 2 (harder, but more accurate and gives more information)

To begin with this method, choose the mass in solar masses (M), the temperature in Kelvin (T), the radius in Solar Radii (R), and the percentage of fuel left (not hydrogen, helium) in the core (F).

#### Luminosity

This can be found with the following equation:

L = (T/5778)4 • R2

#### Lifetime Left

This, which can be useful for plot elements, can be found with this equation in million years:

Tleft=((M•F)/L)•11200

#### Habitable Zone, Circumference, Surface Area, Volume, Gravity and Density

These can be derived from the same equations as main sequence stars. Ain't that convenient?

### White Dwarfs

These are significantly easier to calculate than giant branch stars, and all statistics can be found by choosing the mass (M) and age (A).

#### Radius, Circumference, Surface Area, Volume, Gravity and Density

A white dwarf's radius actually gets smaller as it gains mass, and this ballpark equation is designed to reflect that.

R=(M-1/3) • (0.95+(0.05/(1+(A0.25)))

The Circumference, Surface Area, Volume, Gravity and Density can be found in the same way as main sequence stars, as they are both spheres.

#### Surface Temperature

A white dwarf's surface temperature is mainly dependant on the mass and the age. However, its equation is a little convoluted.

Teff = ((M•10)0.5) • (8/(1+A0.25)

#### Luminosity

A white dwarf's luminosity is very small, and can be found with this equation.

L = (Teff4) • (R/109.5•2)2

#### Habitable Zone and Frost Line

This can, again be found in the same way as with main sequence stars.

### Neutron Stars and their Variants

Neutrons stars are insanely tiny, and this kind of messes with their statistics, which increases the convolutedness of the equations. However, all you need are the mass (M), and the age (A).

#### Radius, Circumference, etc.

The radius can be found by the below equation. Again, the Circumference, Surface Area, and so on (except density and gravity) can be found the same way as with main sequence stars.

R = (7/(M0.2) • (1 + 1/((A+1)0.07))

#### Density & Gravity

The density will be in Tons/cm3 and is given by this equation:

⍴ = (M/1000)/((4/3) • 3.141 • (1000R))

The gravity will be in m/s2 and is given by the equation below:

g = ((((6.674•10-11) • (M•1.9884•1030))/((1000R)2)) • 27.959

#### Surface Temperature

This is given in Kelvin. Here's the equation.

Teff=(7000000/(1+(A0.5))) • M0.5

#### Luminosity

Neutron Stars, given their tiny size, can have very large luminosities, even up to 1 solar luminosities! Equation:

L = (T/5778)4 • (R/696342)2

### Black Holes

Black holes are even easier to calculate, especially if they are nonspinning. You only need the mass (M) and the Rotation (S), which is from 0 to 1, and defines the ratio between the black hole's spin rate and its maximum spin rate.

#### Schwarzschild Radius, Photon Sphere, and ISCO

The Schwarzschild Radius defines the event horizon. It is given by the following equation:

R = M•2.96 • (1-S)0.585

The Photon sphere is the innermost possible orbit and is given by the following very simple equation:

Ps = 1.5R

The Innermost Stable Circular Orbit is the innermost possible S T A B L E orbit, for objects that have mass, and is given by the following simple equation:

Iorbit = 3R

#### Lifetime

The lifetime of a black hole is the length of time after which it decays from hawking radiation, assuming no infall of matter. Here's the equation:

L = M2 • 2•1069

### Brown Dwarfs

Brown dwarfs are very common and very interesting, so it is useful to know how to build them.

#### Mass

Brown dwarfs have a mass between 13 - 75-80 M♃. That was easy!

#### Radius

Sadly, the easiness ends here. Radius has a very complicated equation based on the Mass (M) and the Age (A).

R = ((2+((M0.18)•(1/(1+(M•0.018)5)) • (1+((M•0.013)7)))/3) • (0.95+(0.05/((1+0.1A)0.5)))

Doesn't that look insane? Luckily, we have it in our spreadsheet.

#### Temperature

Teff = ((M0.92)•30 + 250) / (0.8 + (A•0.0001)0.5)

At least its shorter...

#### Luminosity

L = 0.1027198667R • (Teff/5778)2)2

They're getting easier! WOOOOHOOOO!

### Supernovae

Supernovae are insane and can be used for plot points. it is helpful to know what they can do.

#### Explosion Energy

If a star is greater than 200 solar masses, the explosion energy, in BILLION YEARS OF SOLAR OUTPUT, is given by the following equation:

E = 204.029 / (1 + (M - 200)2)

If the star is less than 200 solar masses, the explosion energy is given by the following equation:

E = M0.7 • 5

#### Luminosity

The maximum luminosity of a supernova in solar luminosities is given by the following equation:

L = E • 3.1536•1016

#### Initial Temperature

The initial temperature of a supernova, in Kelvin, is given by this equation:

Tinitial = (((M0.5)•5) • 5)/30)0.7)•1000000000

## Planetary Systems

Stars just floating in space with nothing around them is kinda boring, right? We'll build the surroundings of this star in Worldbuilding Guide Part 2: Galaxies and Nebulae