Worldbuilding Guide Part 3: Planetary Systems

Links to previous parts: Part 1 and Part 2
Welcome to part 3 of the Worldbuilding Guide! Today, we will build some planetary systems.
== Classical Planetary System ==
First, build a star. Go to part 1 for that.
=== Boundaries ===
Next up, we have to determine the inner and outer boundaries of your system. Too close to the star and planets will get ripped apart. Too far away from the star, they won’t be held in orbit. With that in mind, here are two useful equations to help determine these boundaries:
==== Inner limit (AU) ====
I=0.1M
==== Outer Limit (AU) ====
O=40M
However, a better way of determining the inner limit of the system is the roche limit, but we’ll get into that another page.
==== Frost Line ====
The frost line is the distance beyond which gas giants can form. It’s location in AU will be given by:
FL=4.85•√L
==== Habitable Zone ====
I believe this was referred to in Part 1.
=== Orbits ===
Orbits tend to be logarithmically spaced and are arranged so the ratio between adjacent stable orbits is between 1.4 to 2. First, place an orbit anywhere (but I usually place it at the location noted by √L AU) and then go inwards, dividing the distance each time by a number between 1.4 and 2 (calculators are encouraged) until you reach the inner limit. Then, go back to that first orbit, and multiply it’s distance by a number between 1.4 and 2 until you reach the outer limit. Note: It does not have to be the SAME number. In fact, it SHOULDN’T be the same number. More realistic that way. Now that we have our orbits, we can start making our planets! After all, what is a solar system without planets?
== P-Type Binary System ==
P-type binaries are binary star systems in which any planets present will orbit around both stars at once, similar to tatooine.
The first thing you need to do is build not one, but two stars. The only consideration is that your Primary star is the most massive of the pair, otherwise it would be the secondary star. Also, if you want your solar system to be habitable, the primary should be less than 1.4 solar masses. Again, less is better.
=== Average Separation ===
The average separation of the stars is a crucial factor! Set the average separation of your stars between 0.12 and 6 AU, though if you want your system habitable, stick to the EXTREME LOW end of this range.
=== Barycenter ===
The barycenter is the center of mass of the two stars as they orbit around each other. We need to know where this is because any planets present will orbit around this point, rather than the actual stars. The average distance from the primary star to the barycenter is given by:
b1=a(Mb/Ma+Mb)
a = average separation
Mb= Mass of secondary
Ma= Mass of primary
The average distance from the secondary star to the barycenter is given by:
b2=a-b1
Binary stars usually orbit on elliptical orbits. Eccentricity is a measure of how elliptical an orbit is. Values here go from 0-1, with 0 being a perfect circle and 1 being a parabola. Select a value between 0-0.7 for each of your stars. However, habitable P-type binaries tend to have lower eccentricities, so i would advise sticking to the low end.
The maximum and minimum separation to the barycenter for each of your stars is given by:
maxsep=(1+e)•(b1 (or b2)) 
minsep=(1-e)•(b1 (or b2))
Note: each of these equations only works for one of the stars. You need to swap b1 with b2 for it to work for the other star.
However, what’s really important here, and will come into play later on, is the overall maximum and minimum separation of your system. Find this by adding the maximum separations for both stars and minimum separations for both your stars.
Last thing to note is that the stars should never come closer than 0.1 AU. If they do, they start to merge, and that really isn’t a good thing.
=== Moar Boundaries ===
The inner and outer limits for the system are given in a P-type configuration by:
I=0.1(Ma+Mb)
O=40(Ma+Mb)
Frost line
The frost line is given, in a P-Type configuration, by:
FL=4.85(√La+Lb)
Habitable zone
The habitable zone boundaries in a P-type system are given by:
HZinner=√(La+Lb)/1.1
HZavg=√(La+Lb)
HZouter=√(La+Lb)/0.53
Forbidden Zone! *ominous music*
The forbidden zone is a region of space where orbits are unstable because of the gravitational interactions between the two stars. The edges of the forbidden zone are given by:
Forbinner=Minsep/3 (this boundary surrounds each individual star, not the barycenter)
Forbouter=Maxsep•3 
Never ever EVER place planets within this zone! Period! If your habitable zone is partially covered by the forbidden zone, be careful in placing planets. 
IMPORTANT! 
In order to produce a p-type configuration, the outer edge of the forbidden zone MUST fall within the outer edge of the system.
=== Orbits (again) ===
Last step is to place your habitable planet and fill the other stable orbits in the system. The process here is literally the same as in the classical planetary systems, on page 5.
== S-type Binaries ==
S-type binaries are binary systems where any planets present will orbit around only one of the two stars.
=== More stars ===
First, build 2 stars that, if you want them to be habitable, should be less than 1.4 solar masses.
=== Average separation ===
When you set the average separation of the stars, it should be somewhere between 100 and 600 AU. However, if you want your system to be habitable you should stick to the middle-high end. Also, eccentricity should be between 0.2-0.7. 
Next, use your average separation and eccentricity to calculate the barycenter and max-min separation the same way as on page 6 and 7.
=== Still more freaking boundaries ===
Now, calculate the inner and outer limits for both of your stars with the same equations as on page 5.
=== Forbidden zone ===
All we need to know for an S-type binary is the inner edge of the forbidden zone, given by:
Forbinner=minsep/3
The goal here is to have the inner edge of the forbidden zone to be outside the outer limit of the system so the gravitational effect on each system by the other star is minimized.
=== Orbits ===
Now, calculate the habitable zone, frost line, throw in a habitable planet, and calculate the remainder of the orbits for each system. 
== Multiple Star Systems ==
Multiple star systems are systems with 3 or more stars. They can take a long time to build, so fair warning.You can have any number of stars in a multiple star system, but don’t go above 6, or it starts to just be a star cluster and not an actual system.
=== How many stars do we need to build in this book anyway? ===
First, choose any number of stars between 3 and 6. Systems with 3 stars are the most common, 4 stars less common, etc. so I would advise sticking with 3, 4 and maybe 5, because 6 star systems are, like, really rare. Take your stars and group them into subsystems with two or 1 stars in them such as: AB C, AB CD, AB CD  E, etc. Next, decide if each of your binary pairs are P-type or S-type. Now we can actually build our stars! However, your primary must be the most massive star, and B, C, etc. must be progressively less massive. Secondly, The first subsystem must be more massive than the second subsystem, etc. Thirdly, for a star to host habitable worlds, remember that it must be between 0.09 and 1.4 solar masses. Interestingly, if you want to build an uninhabitable star, it doesn’t have to actually be a star! You can build a brown dwarf, in which case the mass range is 0.013-0.08 Msol. Having considered all of these things, proceed and build your stars.
=== Configuration ===
Essentially, the multiple star system build is a mashup of the classical system, P-type binary, and S-type binary methods. 
Build your systems with the steps above and go to any section applicable to you. 
=== Quote-unquote “glue” ===
Now we need to ‘glue’ our subsystems together to make a fully fledged multiple star system. Firstly, find the total mass of each of your subsystems. You can pretend there’s a massive star at the barycenter of each subsystem with the combined mass of the subsystem. Then you can treat the two largest subsystems as 1 distant binary.
=== Average separation (again) ===
Now, set the separation of the subsystems to be anywhere between 1200-60000 AU. Then choose the eccentricity to be anywhere between 0.2-0.7. Then calculate the barycenter and max-min separation of the two subsystems. 
Note: If you have 3 or more subsystems, repeat this step, and treat the 4 stars you just did as 1 subsystem and repeat as many times as you need to. Just make sure that the total distance between the first two subsystems and the next one or two is at least 3.5 times the distance between the the first two subsystems.
Done!
== Done™ ==
Now that we have stars, a planetary system, and some stable planetary orbits, now its time to fill those orbits in Worldbuilding Guide Part 4: Intro to Planets.Category:Helpful
Category:Worldbuilding Guide