P-Type Binary Star System

One of the systems in this little section of the universe will be a binary star system.  Why?  Because it’s cool.  Do I need really need more reason than that?  However, this does affect the calculations a bit, and there are now several other factors to consider.  The two suns combine to give off more light, and also interact with each other to create gravitational fluctuations.  There will also be the cultural considerations having twin suns will mean for the inhabitants of this system.

Again, I’m using Artifexian to provide inspiration.

The primary star should be larger than the secondary star.   My numbers aren’t entirely arbitrary.  I wanted a not insignificant size difference between the two, and I intend to have them give off different illumination.

Primary Star
Property Calculation Notes
Mass 1.25 Number Chosen by Me
Luminosity 1.95 Mass ^ 3
Diameter 0.93 Mass ^ 0 .74
Surface Temperature 1.12 Mass ^ 0.505
Lifetime 0.57 Mass ^ -2.5
Secondary Star
Property Calculation Notes
Mass 0.80 Number Chosen by Me
Luminosity 0.51 Mass ^ 3
Diameter 0.59 Mass ^ 0 .74
Surface Temperature 0.89 Mass ^ 0.505
Lifetime 1.75 Mass ^ -2.5

Now, the first thing we will have to do is figure out how the stars interact with each other.  Their average separation should be between .15 and 6 astronomical units, and making the system habitable will require that distance to be on the lower end.  We will also need to calculate the eccentricity of their orbit, with again, the lower end of the range being preferable.    Binary stars orbit each other around their common center of mass or barycenter.   Incidentally, the rest of the solar system also orbits around the barycenter.  I am at some point going to name a character Barry Center, and I will not apologize for it when that time comes.

Now we get into some tricky shit.  If you want to understand what is actually going on here, I recommend you watch the video.   Actually, just go check out Artifexian’s entire channel.  Behold, math:

Property Calculation Notes
Average Separation 0.30 Chosen by me
Distance of Primary Star to Barycenter 0.12 Average Separation (Secondary Mass / (Primary Mass + Secondary Mass))
Distance of Secondary Star to Barycenter 0.18 Difference between average separation and distance of primary star to the barycenter
Primary Eccentricity 0.40 Chosen by me, between 0.4 and 0.7, with lower being more circular and higher approaching parabolic
Secondary Eccentricity 0.50 Chosen by me, between 0.4 and 0.7, with lower being more circular and higher approaching parabolic
Maximum Primary Separation from Barycenter 0.16 (1 + eccentricity) x Distance to barycenter
Minimum Primary Separation from Barycenter 0.07 (1 – eccentricity) x Distance to barycenter
Maximum Secondary Separation from Barycenter 0.27 (1 + eccentricity) x Distance to barycenter
Minimum Secondary Separation from Barycenter 0.09 (1 – eccentricity) x Distance to barycenter
Maximum Separation 0.44
Minimum Separation 0.16
Inner Limit 0.21 Primary Mass + Secondary Mass X 0.1
Outer Limit 82.00 Primary Mass + Secondary Mass X 40
Frost Line 7.61 4.85 X square root of primary luminosity plus secondary luminosity
Habitable Zone 1.57 Square root of Primary Luminosity plus Secondary Luminosity
Minimum Habitable Zone 1.49 95% of Habitable Zone
Maximum Habitable Zone 2.15 137% of Habitable Zone
Inner Forbidden Zone 0.05 Minimum Separation / 3
Outer Forbidden Zone 1.31 Maximum Separation x 3
Uninhabitable Range 1.75 Maximum Separation x 4

This is the part where you ooh and ahh.  Done?

Alright, now we need to figure out where to place our planets.  It looks like there is space in the habitable zone that doesn’t fall into the forbidden zone.  The forbidden zone is the section of the system in which the gravitational interaction of the two suns makes it a bad place to be.  Furthermore, the uninhabitable range is the area in which other various interactions between the two suns makes general sorts of bad shit happen.  I did not major in astronomy, I’m not going to go into detail.  Doesn’t matter anyway, we have a nice sliver of range within which to place our habitable planet.

So, after running some random numbers in regards to the placement of our biggest gas giant, we come up with:

Planet Orbit In Kilometers Check <0.15 AU Apart
Habitable Planet 2.07 310,176,518 1.08
Next Orbit 3.15 471,468,308 1.36
Next Orbit 4.51 674,199,681 4.33
Biggest Gas Giant 8.83 1,321,431,374 8.30
Next Orbit 17.14 2,563,576,866 15.08
Next Orbit 32.22 4,819,524,507 21.59
Next Orbit 53.80 8,048,605,927

I had to generate the list three times to get a planet in the habitable range.  As you can see, it will be the very first planet in this system, the one closest to the suns.  That could also have cultural implications for the species that develop on such a world.


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