Youtube Edgar here and welcome to Artifexian
Here you will learn everything you ever wanted to know about world building
…and then some
Kuiper Belt objects come in 5 distinct dynamical classes
Resonant Objects, Classical Kuiper Belt objects, Scattered disk objects, detached objects and
finally Sednoids
In this video let's look at building an orbit for a resonant, Kuiper belt dwarf planet
First up let's define resonant
Two objects are said to be in mean motion resonance when their orbital periods can be
represented by the ratio of two small integers 1:2, 2:3 etc
Example planet A here has an orbital period of 30 years and is in a 2:3 mean motion resonance
with B as it has a 45 year orbital period
Similarly A and C are in a 1:2 mean motion resonance because C has a period of 60 years
If the relationship between the orbital period of any two planets can be boiled down to two
small whole numbers they are likely in resonance
Now we care about resonances because they enhance the mutual gravitational interaction
between the bodies and helping to stabilise their orbits
Think of it like this in a 1:2 resonance one planet will complete 1 orbit for every 2 orbits
of another planet.
This relationship is not approximate it’s exactly 1 orbit for every 2.
It is this precision that gives rise to intrinsic stability of mean motion resonances.
That said not all mean motion resonances are created equal
Broadly speaking the greater the difference between the numbers in the ratio the less
stable the resonance is
2:3 is whats known as a first order resonance and is very stable differing only by 1
3:5 differing by 2 is a second order resonance and less stable
Third order resonance will be less stable again.
Fourth less agin etc etc
The more stable the resonance the more objects we can place there
That said the weaker resonances could well be home to dwarf planets
Just their orbital eccentricities will need to be high to compensate for the lack of inherent
stability
But whats does this all mean for worldbuilding fictional systems?
Let's make a plan of a fictional Kuiper belt
Begin by noting the orbital period of the last gas giant in your system
Your resonant dwarf planets will be in resonance will this object
For convenience sake I'll say this guy here has a 100 year orbital period
Next up map out the resonances
Links in the doobly-doo for a big list of them
Choose at will and include a good mixture of stable and less stable resonances.
Here are my stable first order mean motion resonances and my less stable, second, third
and forth order resonances.
Incidentally our Kuiper belt, strictly speaking, is defined as being the region between Neptune’s
2:3 resonance and 1:2 resonance
Pluto along with 92 other objects is at 2:3 so we call everything there Plutinos and we
call the bodies at the 1:2 resonance Twotinos
Perhaps two different stable resonances could define your system Kuiper belt?
Anyways convert the ratios to orbital periods i.e year lengths using simple multiplication
Then convert the orbital periods into distances in AU using Kepler’s Third Law rearranged
like so
Where A is the semi-major axis of the orbit in AU, P the orbital period in earth years
and M the mass of your systems star in solar masses.
Next fill the figures in.
Here are my orbital periods in earth years and here my distances/semi-major axis in AU
Now I'll determine roughly how many objects will be at each resonance
This is important because dwarf planets by definition need to have cluttered orbital
neighborhoods
Keeping relative stability in mind and choosing numbers at will ill go with 50 objects at
2:3, 10 at 3:5, 5 at 4:7 and 15 at 1:2
With our mean motion resonances, semi-major axis, orbital period and general populations
well defined we need to consider the final two unique parameters
Eccentricity and Inclination
From studying our Kuiper belt I have set myself an orbital eccentricity range up to 0.25 and
an inclination range between 10 and 25 degrees
However given the sheer amount of objects in the Kuiper belt some will break these rules
For example 2005 TV189 has an inclination of 34.5 degrees and 1996 TP66 has an orbital
eccentricity of 0.33
And remember to stabilize a weaker resonance increase your orbits eccentricity
Finally I'm ready to build my orbit in accordance to the method outlined in a previous video
Links as always on screen or in the doobly-doo
For demo purposes I chose to construct a Plutino style orbit in a 2:3 mean motion resonance
with my outermost gas giant
Stats on this system also in the doobly-doo
Anyways, here's my star, heres my outermost gas giant and here, is my plutino
Notice how the orbits overlap
Usually this would be a problem but thanks to the all important mean motion resonance
the system is odd looking, yes, but geologically speaking, rather stable.
One resonant, Kuiper belt object: DONE!
That’s one down...many many more left to go
Happy building everyone
Good morning Interweb
I hope you enjoyed this video on resonant dwarf planet orbits
Now Kuiper belt dynamics are seriously trippy and I had to leave out a ton of info to keep
the video short
Links in the doobly-doo to a how pile of other reading
Go check it out
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Thank you all so much for watching
…Edgar out!