Resonant Dwarf Planet Orbits

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 As always if you’re interested in more Artifexian
content Click the links on screen or in the description And if you think I earned it Hit the subscribe button Thank you all so much for watching …Edgar out!


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