Worldbuilding Guide Part 4: Intro to Planets

Links to previous parts: Part 1, Part 2, and Part 3
Planets are fun. They just are. Here, we will show you how to make all of them, to help make your system interesting.
== Method 1 ==
To start, choose the mass of your planet. Then, choose the composition by plugging in the respective percentages of Iron, Silicate, Water, Ice, Organics, Hydrogen, Osmium (y not tho?), Graphite, Diamond, Electron Degenerate Matter, and Neutron Degenerate Matter. Those last two will probably never be used, but it doesn't hurt! ;)
Then, plug in these values and the mass of the planet into our spreadsheet (the calculations are extraordinarily tedious without it).
The spreadsheet then finds the rest of the stats of the planet. That's kinda it.
== Method 2 (less accurate, less tedious) ==
Pick the mass and radius, and plug them into this equation:
g=M/R2=R⍴
You'll get the gravity and the density. If you want the escape velocity, use this equation.
Vesc=Squareroot(M/R)
Done!
== Orbits ==
An orbit is an elliptical path around a star or planet where a planet or moon travels around. Easy right? Pretty much! It’s a bit more complicated, though. They have a bunch of different statistics you need to figure out. However, they always look something like this, with the star at one focus. 
Here is a rough guide to how to make orbits for different types of planets.
=== Hot jupiters ===
==== Semi-major axis (a) ====
The semi-major axis is, in essence, a planet’s average distance from the sun. To ensure that a hot jupiter isn’t a cold jupiter, it’s semi-major axis should be anywhere between the inner edge of the habitable zone, and the inner limit of the system. 
==== Eccentricity (e) ====
Eccentricity shows how ‘stretched out’ or ‘squashed’ an orbit is and go from 0 to 1, with 0 being a perfect circle, and greater values getting progressively more stretched out, with 1 being a parabola. Hot jupiters have very circular orbits, because gas drag from the protoplanetary disc was gradually circularizing it and dragging it inwards. Therefore, it’s eccentricity should be very close to 0, without being 0. 0.00x-0.0x should be about right.
==== Semi-Minor axis (b) ====
The semi-minor axis is the short axis of an ellipse, divided by 2. It is given by:
b=a√1-e2 
Because of a hot jupiter’s low eccentricity, however, the semi-minor axis will be very close to the semi-major axis.
==== Periapsis & Apoapsis (q & Q) ====
Periapsis, the closest point in an orbit to the parent object, is given by:
q=a(1-e)
Apoapsis, the farthest point in an orbit from the parent object, is given by:
Q=a(1+e)
==== Orbital Period (p) ====
This bit is really important when it comes to worldbuilding. Orbital period, or year, is given by:  
p=√a3/M
However, if you for some reason wanted to find the semi-major axis from the year, 
a=∛p2/M
You can multiply this value by earth’s year, 365.2422 days, to find your planet’s year in earth days.
==== Orbital Velocity (vo) ====
Because hot Jupiters orbit very close to their stars, they have to orbit fast, right? Yup! This speed, or Orbital Velocity is given by:
vo=√M/a
Multiplying this value by earth’s orbital velocity, 29.78 km/s, will give you your planet’s orbital velocity in km/s
==== Inclination (i) ====
Inclination is a measure of how tilted a planet’s orbit is from some reference plane. Most orbits are prograde (they orbit in the same direction as their star rotates). Prograde orbits lie between 0-90º of inclination, and retrograde orbits lie between 90-180º. Most planets orbit prograde, but interestingly, half of hot jupiters orbit prograde and half orbit retrograde! This doesn’t mean you can just pick anywhere between 0 and 180º though. For extra added realism, keep your planetary orbits within 10º of your reference plane, unless you have a specific reason why it isn’t. 
If you’re doing pen-and-paper worldbuilding, you can stop, but if you are rendering your system in 3D, keep reading. 
==== Longitude of the ascending node (Ω) and Argument of periapsis (ω) ====
Both of these values range from 0-360º and we are free to choose whichever value we want for these. Essentially, what these do is defining how the orbit is oriented in 3d space. You can do the same for the other types of gas giant.
Note: This same principle works for hot neptunes and hot saturns, in case you want to build those too.
=== Classical Gas Giants and SuperJupiters ===
While gas giants can only form beyond the frost line, migration may happen and a gas giant formed there could migrate inwards. For them,
a=(Frost Line +1.2 AU)-Inner limit
For these and gas dwarfs the 0.0x-0.00x rule for eccentricity still holds. 
The semi-minor axis, periapsis, apoapsis, orbital period, and orbital velocity you can just use the equations to find out. There are no special limitations for them. This also applies to gas dwarfs and eccentric jupiters.
For these, gas dwarfs, and eccentric jupiters, ensure that they orbit in a prograde fashion. For all four types of giant planet, pick an inclination between 0-90º. Again, you should still keep it within 10º of the reference plane unless you have a specific reason as to why it isn’t. For the gas giants in our solar system, their inclination ranges from 0.77-2.485º, so keep it low.
=== Gas Dwarfs ===
Gas Dwarfs’ semi-major axes should go between the frost line and the outer limit of the system (40•M). For extra realism, try and pick a distant orbit for your gas dwarf.
=== Eccentric Jupiters ===
For all intensive purposes, they can go wherever you want. But if you want to make your solar system habitable, please leave it farther away than 2•HZouter.
These will have orbital eccentricities of 0.1 or higher. Again, if you want your solar system to be habitable, keep the eccentricity below 0.3, unless you REALLY know what you’re doing, which I don’t.
=== Terrestrial planets ===
==== Semi-Major axis ====
If you’re building a habitable planet, the semi-major axis must fall within the habitable zone, otherwise, it won’t exactly be habitable, will it?
==== Eccentricity ====
Habitable planets should orbit on nearly circular paths. Therefore, a safe eccentricity range is:
0<e≥0.2
/interesting sidenote the more planets there are in a system, the less the average eccentricity will be. The equation to find the rough average eccentricity is:
eavg=0.584•N-1.2
Note: this is not a hard-and-fast rule, but more of a guideline, something to consider when building your planetary system. Also, don’t use this equation with more than one planet. Don’t. /sidenote end
==== Periapsis and apoapsis ====
This will be given, as always, by q=a(1-e) and Q=a(1+e). If either of these falls outside the habitable zone, you should lower the eccentricity or change your semi-major axis, otherwise it would get a bit hot/cold at times.
==== Orbital period ====
Like before, (Thanks, Kepler!) the orbital period will be given by: p=√a3/M
==== Orbital Velocity ====
Calculate this, as before with vo=√M/a
==== Inclination ====
Your main habitable world in the system will likely define that system’s reference plane, so set the inclination of the main habitable planet to 0º and measure other planets in the system relative to this plane. However, you should generally keep planets on low inclinations, and save the high inclinations for oddball asteroids and KBOs, unless you have an explicit reason for doing so.
==== Argument of Periapsis and Longitude of the Ascending Node ====
If an orbit is in any way inclined, both parameters can have values between 0-360º. However, with non-inclined orbits, the Longitude of the Ascending node will automatically be 0º and the Argument of periapsis will be ‘undefined’. Why? Short answer is that it’s because of the orbit being exactly in line with the reference plane. Nah, just set it to 0 and undefined and you’re done. 
OPTIONAL STEP: you can go to your favorite orbital simulator, plop down your planet, plug in the numbers and boom!
By the way, for uninhabitable terrestrial planets, follow the same principle, just ignore the habitable zone and set the longitude of the ascending node and argument of periapsis to anywhere between 0 and 360º.
=== Dwarf Planets ===
Kuiper belt objects come in 5 classes based on their orbit: Resonant, Classical, Scattered Disk, Detached, and Sednoids.
==== Resonant Objects ====
Two objects are defined to be in resonance when the ratio between their orbital periods can be simplified to 2 small integers, such as 1:2, 2:3, 1:3, etc. We care about resonances because they help stabilize each other’s orbits, so that definitely helps stabilize a chaotic kuiper belt. These relationships are not approximate, they’re exact! 
However, not all resonances are created equal. In general, the greater the difference between the numbers in the ratio, the less stable it is. For example, 1:2 is a first order resonance and is very stable. 3:5 is a second order resonance and is less stable etc. The more stable a resonance, the more things we can put there. 
First, take your farthest convenient gas giant and find its orbital period. Next map out the resonances. In other words, take your planet’s orbital period and divide it by the resonance and repeat for each resonance. Choose at will and pick a good mixture of stable and less stable resonances. 
Now, convert the ratios to orbital periods using simple multiplication. Then convert the orbital periods into distances using: a=∛p2/M. Once you fill the figures for each resonance in, determine roughly how many objects should be at each resonance. This is important because dwarf planets need to have cluttered orbital neighborhoods. Keep relative stability in mind and choose at will. 
Now that we have considered Semi-major axis, MMR, Orbital period, and general population, we need to consider the final two unique parameters. Dwarf planets should have inclination ranges between 10º and 25º and eccentricity ≤0.25. However, given the rather large amount of stuff in the kuiper belt, some will break these rules. For example, 2005 TV189 has an inclination of 34º and 1996 TP66 has an eccentricity of 0.33. And remember, to stabilize a weaker resonance, increase your eccentricity. Now you can build your orbit with the same process and equations as on page 14, 15 and 16. Once you have plotted your orbit relative to the reference gas giant, don’t worry if they overlap. Thanks to the resonance, they are guaranteed never to collide.
==== Classical KBOs ====
To start, choose a semi-major axis within one of your asteroid or kuiper belts. Then choose an inclination up to 30º and an eccentricity up to 0.4. Now you can simply build your orbit with the same process and equations as on page 14, 15 and 16. That was much shorter than last time!
==== Scattered Disk Objects ====
Use the same process as above, simply choose a semi-major axis from 1.1-2x the distance to the outer edge of one of your asteroid/kuiper belts. 
==== Detached Objects ====
Detached objects are defined as objects with periapses at least 1.5x the distance of Neptune, or your outermost gas giant. When you calculate your orbit, make sure it has a relatively high eccentricity, but it’s periapsis doesn’t dip below 1.5x the distance of your outermost gas giant.
Disclaimer: Outermost gas giant does not count planet-nine like objects.
==== Sednoids ====
Sednoids are a subclass of detached objects with very high eccentricity and periapses at least 2.2x the distance of your outermost gas giant. Therefore, same process as detached objects, just with even higher orbits. YARG
=== Comets ===
Comets are small asteroids that generally have very elliptical orbits. There are many different types of comets, defined by their orbital periods.
==== Short-Period and Long-Period Comets ====
Short period comets, like Halley, are comets with orbital periods less than 1.5x that of the outermost gas giant. All you need to do is calculate an orbit with an orbital period less than 1.5x that of the outermost gas giant. Done! Long period comets have the same process, just their orbital periods are MORE than 1.5x that of the outermost gas giant. Short period comets are more likely to have inclinations less than 15º, but long period comets can have any inclination you want. 
==== Jupiter-Family Comets ====
Jupiter-family comets are comets that have semi-major axes equal to or less than the Frost Line. Calculate their orbits by choosing a semi-major axis smaller than the frost line, an eccentricity from 0.3-0.7, and calculating from there. Jupiter-family comets usually have inclinations under 5º.
==== Hyperbolic Comets ====
Hyperbolic comets are comets with an eccentricity greater than 1 and as such will never return to the solar system. They can either come from interstellar space or be ejected from the solar system by encounters with major planets. 
==== Asteroids ====
Asteroids can often be in very wonky orbits, and you need to take this into consideration when designing them for your solar system. There are different types of asteroids, but they aren’t really defined by orbit. First, choose basically any semi-major axis, within reason, and then choose an eccentricity less than 0.4. Any inclination will work, but stay under 30º. Again, pick any Longitude of the Ascending Node and any Argument of Periapsis. Then calculate the rest of the statistics with the method outlined earlier. 
Note: The physical characteristics can be calculated with the same method as minor moons.
== Rotation ==
A planet's rotation can allow for some very interesting surface conditions. You should design your planet's rotation with these in mind.
=== Day And Night™ ===
To begin, choose a sidereal (relative to the stars) rotation rate. CHOOSE WISELY, FOR YOU CAN NEVER TURN BACK! just kidding.
Once you have that, find the solar rotation rate with the following equation:
rsolar = |p/(p/rsiderial-1|
those bars mean Absolute Value.
Warning: The faster the planet spins, the stronger the storms are, and the slower the planet spins, the more drastic the temperature variations across the planet are.
=== Axial Tilt ===
A planet's axial tilt can determine a lot of things. Here's a chart.
As Axial Tilt goes up...	As Axial Tilt goes up...
/\ 	\/
Average Temperature 	Snow
Seasonal Extremes 	Ice
 	Humidity
 	Clouds
 	Albedo
Because axial tilt is determined by the vagaries of the last few large impacts in the early history of your planet, you can basically set it to whatever you want. However, keep in mind the conditions you wish your planet to have, and set your tilt accordingly.
We have finished the majority of the number crunching on your planet, but we should add cool looking stuff around it. Join us next time in Worldbuilding Guide Part 5: Moons and Rings!
Category:Worldbuilding Guide
Category:Helpful