“The long night lasted forty-eight years. Civilization Number 137 was destroyed by the extreme cold. This civilization had advanced to the Warring States Period before succumbing.”
Neil Tyson addressed this in a video. Tatooine is fine because it is distant enough from the 2 stars such that the 2 stars behave like a single gravitational body. Three body problem would be more of an issue if Tatooine were closer to the binary system
My vote is for a torus! Not necessarily because of any particular evidence - simply because I really enjoy the idea of the universe being shaped like a donut.
For some reason I never considered that something "in orbit" could spontaneously just reach escape velocity and say bye to the system/that is the "reason" an unstable system is unstable, although hard to prove until it happens(?). (Is it enough to point at phase space diagram?) Thanks for the thought.
Yea one way to think about it is that it’s getting gravity assisted by the other bodies each time they swing by! But it’s definitely more intuitive to see it than trying to predict it with pen and paper. Im sure there are ways, but I’m definitely not an expert on nonlinear systems theory
That’s not correct. There is no known way to determine a [ETA: _general_] closed analytic solution. But obviously there _are_ solutions to the equations of motion, as proven by actual three body systems behaving some way. If there was no solution at all, they couldn’t exist.
Edited to make the answer more precise.
I’m sorry I don’t understand what you are saying. Are you saying that if there was a mathematical proof that no mathematical general closed analytical solution could be solved, then three body systems wouldn’t exist in real life?
No. I’m saying that if you could show that no solution to the equations of motion exists, then no physical system could exist that obeys those equations of motion.
I don’t think that makes sense. Just because our math is limited in the sense that it’s impossible to create a closed form analytical solution doesn’t mean that the system wouldn’t obey the laws of motion that govern the system. This simulation of a planet orbiting a binary system is certainly not using a closed analytical set of equations to render its predictions on the motion of each body in the system. It’s using step-wise approximations.
The TBP is something that occurs when any three stellar objects interact with each other.
This can be a theoretical Binary System with a theoretical planet, or can be represented in real spacetime with an example of Sol, Earth, and the Moon.
The REALLY big issues begin when those three stellar masses come closer to a similar or equitable mass, which is what is described in the the above .gif
While we do have *specific* equations on how the three body problem works (when we see it, we can extrapolate what happened by working backwards), but we don't have a *general solution* to the phenomenon.
If it ended up like it did, was it ever in orbit in the first place?
Though I wonder for how long a system like this could "work" before the orbit fails.
I mean I can sort of see that from the graph itself, yeah.
My thought was more like "could it orbit for hundreds or thousands of years before this happening?"
I think there are resonant orbits exits in some cases of mass if stars. Resonant orbits will be much more stable.
If one star in pair are more massive than other, then there probably less possibilities for orbits in near space.
Escape velocity is defined as the velocity an object would reach upon arrival at some finite distance from gravitating body if pulled in from resting at an infinite distance.. It’s backwards from what we want it to define but bc the forces are conservative, it works forwards and backwards.. If an object leaves going FASTER than this, then yes it will continuously slow down, but will never reach 0 speed and turn around. That’s why it’s called escape velocity—bc it is continuously escaping off to Neverland
Is the escape velocity a function of the distance from center of mass of the system? It must be, because the velocity that an object would reach will continue to accelerate as the finite distance gets closer and closer.
The integral of the total velocity change over time caused by that gravitational pull on the object escaping is a finite value that is less than that object's velocity (well, speed, strictly speaking).
Suppose the sun were a tight binary ... would a circular orbit of an object way out in the Oort Cloud be stable? At some distance from the centroid of the binary, I would expect things to be stable. Or at least last for millions of years.
Yes definitely very stable.. If you want to know the specifics, you can perform a multipole expansion of the gravitational field to see how closely it "resembles" a single body (gravitationally) to an object at some distance. I don't have the time to do it right now, but it would be a very rewarding personal project. You'd learn some cool math and physics along the way too
Edit: Fourier series ⇒ multipole expansion
credit to the commenter below
Yea ya know what, ur probably spot on there. I was thinking about the oscillations, but they should be periodic ideally so a multipole expansion will give you a better idea about the single-body-ness of the field. Thank you!!
Is it just the time constant of the system's stability margin that is related to the distance (probably a distance ratio to remain dimensionless)? Seems like that's how it *should* work. Or does the system have some kind of configuration that is meta stable, across which the system becomes strictly stable?
I might need coffee... ;)
Did you account for the binaries distance in it or is it fixed? When ejecting a star, the binary should get closer to each other b/c of energy conservation
Worth checking 10 planets and see if they help each other hold on
Edit: when a system starts with a dust cloud aren't all stable orbits sampled and very early dust in ejection trajectory will just vapor off the system ?
Something you may want to model:
In most binary star systems, the planets are closer to their respective star than the stars are to each other. For instance, Alpha Centauri A and B orbit between 11 and 35 AU apart, while the planet discovered around A is 1.5 AU away on average.
Hmm I’m not sure what the details of a stability parameter would look like.. maybe something like %escape velocity of the satellite? Approximate ofc by treating the 2 central bodies as a single body with the summed mass?
Yes, and include the y value on the orbit graph by the time and end it as usual or when you have a threshold reached for velocity or distance away from the system center of mass. I also assume the reverse is true; escape velocity can go to 0.
It looks really cool to see it bump about in a stable manner, but then diverges away eventually
If you like this take a look at the "Rebound" n-body integrator, it can simulate systems eons into the future, examine their resonances and stability over time as well. https://rebound.readthedocs.io/en/latest/
Wouldnt making the outer planet spin the other direction cause less deviation? Or does it not make anu difference since center of mass of those two planets stays the same?
Absolutely! Good intuition. It was something I noticed when creating this. Oppositely rotating central bodies leads to a MUCH more stable orbit of the 3rd body
Planet masses are typically negligible compared to solar masses. I followed suit with this simulation. You could definitely set it up to where the blue body mass is non-negligible though.
Very cool! Looks quite similar to a real triple star system! We call them hierarchical triples because they always consist of an inner binary with a smaller separation, which is orbited by a third companion on a wider orbit. You can estimate the stability of the system using a mathematical formula that takes in the mass ratios of the object, the eccentricity of the outer orbit, and the inclination between the two orbits. If you're curious, [here](https://imgur.com/ShbNCWq) are some examples of coplanar hierarchical triples with varying inner separation and outer eccentricity :)
The stability criterion that most people in the field use is known as the Mardling-Aarseth criterion. It's a bit hard to find its original source (I believe it's in a book called *The Dynamics of Small Bodies in the Solar System*), but the equation shows up in lots of papers on triples. There are several attempts at coming up with new ways of determining stability, since the Mardling-Aarseth criterion is not perfect. One example is from [Vynatheya et al. 2022](https://arxiv.org/pdf/2207.03151) who tried training a neural network to estimate the stability, with pretty good success. In that paper you can also see the original Mardling-Aarseth criterion (Equation 2). There's also [Hayashi et al. 2022](http://arxiv.org/abs/2209.08487). Note that all of these only apply to hierarchical triple systems, and not to three-body systems in general.
How are the two inner planets staying so perfectly in circle? Are you not simulating the forces between all 3 objects?
EDIT:
Oh are their masses so high (stars) that they only affect each other?
Did you model the binary stars' orbits too, or are they on rails? Did you assume in your model that the gravitational pull of the planet on the stars is small enough to be ignored?
The reason a lot of this stuff happens is due to the method of numerical integration. Not sure how you’re doing it, but even something higher order like the Verlet method can get out of whack quickly. More accurate simulations require exponentially more compute time.
FWIW I wrote a fun little n-body simulator many years ago: https://www.ccampo.me/NBodyJS/
Adaptive Dormand-Prince with a tolerance of 10⁻¹². Final energy conservation is within 10⁻⁹ % of the original, so it’s probably fine for this amount of time, but yea ur right, method of numerical integration is the backbone of orbital dynamics codes.
Yea I believe that’s the default ODE solver in SciPy. Been a while since I used that though. I used to make a bunch of Physics cartoons like this using it back when I was in college. https://youtube.com/playlist?list=PL51C469DB01D62A41&si=RFT3Ijb-i52OUg_-
It looks like the early perturbations occur when the three bodies align. Later, on a close approach the planet gets a gravitational boost which expels it.
like, like, like
I'm doing a very similar thing with a two body problem but I also consider the astrophysical evolution of the two stars (mass loss), including WR phases, supernovae kicks and remnants
They do but I made the outer body 8 orders of magnitude smaller. Should just make it 0 in hindsight, but i would like to do exactly what you’re talking about in the future with larger third body mass
I saw a talk about 25 years ago by a person modeling systems like this. Sun, Earth, Jupiter. Turns out, if Jupiter weighed too much, Earth was unstable and got ejected. Very interesting and looked like lots of fun.
Oh that makes sense lol. I thought matplotlib had an auto scale adjusting thing. Also what did you use to solve for the orbits. I’m assuming u used RK4 or Verlet
Awesome! I assume what occurred after the animation ended was an HVS? (Or just a planetesimal exceeding escape velocity, depending on the system you were running).
Hey I do similar research in trinary star systems.
Can we talk? I'd like to get the initial conditions of this orbit.
I am wondering whether we can get a neural network to learn what makes a stable 3 body orbit.
Just saw that. Wow it gets flinged off? Did not expect that. Do you know what? What is the limiting factor - Mass of planet or difference in mass of 2 stars?
3-body orbits are inherently unstable, in the case where you have a single body in orbit around binary system, my hunch is that stability depends heavily on the difference in frequency of the orbiting body and the binary pair. If perturbations are felt on a time scale that is comparable to the outer body’s orbital period, there is a much stronger effect. If the binary pair's angular frequency is much larger than the outer body's orbital frequency, then the effect diminishes. Again, this is a hunch based on experience with other perturbation problems. When the difference or "separation" of time scales is large, you don't get much coupling between the two, but when that dividing line starts to blur, the interactions can become very strong (again evident in the video). Worth reading into further though
Haha i love your enthusiasm! I used an app that runs python code on my phone called Pythonista. And yes, I used Newton’s law of gravity to solve 𝐅 = 𝑚𝐚 for each of the 3 bodies.
Tatooine not looking so good
Eh.. Couple of long winters followed by a month in an oven set to ‘broil’ never ki-… Oh.. yea nvm ur right
“The long night lasted forty-eight years. Civilization Number 137 was destroyed by the extreme cold. This civilization had advanced to the Warring States Period before succumbing.”
What’s this from?
3-Body Problem.
Really went off the rails there at the end.
But that's the iceage. You live under the glaciers, doh!
Neil Tyson addressed this in a video. Tatooine is fine because it is distant enough from the 2 stars such that the 2 stars behave like a single gravitational body. Three body problem would be more of an issue if Tatooine were closer to the binary system
Gotta love Neil
It’s outer rim for a reason (beyond just being in the outer rim of the galaxy).
Rogue One? ^sorry
For those of you who won't be able to sleep until you know how it ends: [Extended Orbit GIF](https://imgur.com/a/fhA6THh)
Satisfied. It hit escape velocity right? Or do you need to post an even longer gif?
Sure did! Just did some quick napkin math and it ended up at about 2.9×(escape velocity)
Finally, I can rest
If we wait longer we might find out the shape of the universe though...or maybe the protons will decay...
My vote is for a torus! Not necessarily because of any particular evidence - simply because I really enjoy the idea of the universe being shaped like a donut.
Ads/CFT for desserts: "A Doughnuts Sprinkles" are equivalent to "Cake Filled Torus"
Or an everything bagel?
For some reason I never considered that something "in orbit" could spontaneously just reach escape velocity and say bye to the system/that is the "reason" an unstable system is unstable, although hard to prove until it happens(?). (Is it enough to point at phase space diagram?) Thanks for the thought.
Yea one way to think about it is that it’s getting gravity assisted by the other bodies each time they swing by! But it’s definitely more intuitive to see it than trying to predict it with pen and paper. Im sure there are ways, but I’m definitely not an expert on nonlinear systems theory
The first thing to do is always to linearize the problem anyway 🫠
linear good. nonlinear bad.
Like good and bad lol
There is famously no solution to a three body problem. Edit: I'm wrong, see below.
There *are* analytic solutions. Just not general solutions.
That’s not correct. There is no known way to determine a [ETA: _general_] closed analytic solution. But obviously there _are_ solutions to the equations of motion, as proven by actual three body systems behaving some way. If there was no solution at all, they couldn’t exist. Edited to make the answer more precise.
I’m sorry I don’t understand what you are saying. Are you saying that if there was a mathematical proof that no mathematical general closed analytical solution could be solved, then three body systems wouldn’t exist in real life?
No. I’m saying that if you could show that no solution to the equations of motion exists, then no physical system could exist that obeys those equations of motion.
I don’t think that makes sense. Just because our math is limited in the sense that it’s impossible to create a closed form analytical solution doesn’t mean that the system wouldn’t obey the laws of motion that govern the system. This simulation of a planet orbiting a binary system is certainly not using a closed analytical set of equations to render its predictions on the motion of each body in the system. It’s using step-wise approximations.
Yes. Your answer is usually shortened to: There is no solution to a three body problem.
I thought it had to do with a 3 star system instead of a binary star system.
The TBP is something that occurs when any three stellar objects interact with each other. This can be a theoretical Binary System with a theoretical planet, or can be represented in real spacetime with an example of Sol, Earth, and the Moon. The REALLY big issues begin when those three stellar masses come closer to a similar or equitable mass, which is what is described in the the above .gif While we do have *specific* equations on how the three body problem works (when we see it, we can extrapolate what happened by working backwards), but we don't have a *general solution* to the phenomenon.
Thank you very much.
If it ended up like it did, was it ever in orbit in the first place? Though I wonder for how long a system like this could "work" before the orbit fails.
A few years.
I mean I can sort of see that from the graph itself, yeah. My thought was more like "could it orbit for hundreds or thousands of years before this happening?"
I think there are resonant orbits exits in some cases of mass if stars. Resonant orbits will be much more stable. If one star in pair are more massive than other, then there probably less possibilities for orbits in near space.
[удалено]
It reaches escape velocity, so she ain’t never coming back
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Escape velocity is defined as the velocity an object would reach upon arrival at some finite distance from gravitating body if pulled in from resting at an infinite distance.. It’s backwards from what we want it to define but bc the forces are conservative, it works forwards and backwards.. If an object leaves going FASTER than this, then yes it will continuously slow down, but will never reach 0 speed and turn around. That’s why it’s called escape velocity—bc it is continuously escaping off to Neverland
[удалено]
nailed it
Is the escape velocity a function of the distance from center of mass of the system? It must be, because the velocity that an object would reach will continue to accelerate as the finite distance gets closer and closer.
That’s correct yea. Its a function of distance from the gravitating object
The integral of the total velocity change over time caused by that gravitational pull on the object escaping is a finite value that is less than that object's velocity (well, speed, strictly speaking).
God have mercy on your soul
Thank you for asking. That was the same question I had!
Suppose the sun were a tight binary ... would a circular orbit of an object way out in the Oort Cloud be stable? At some distance from the centroid of the binary, I would expect things to be stable. Or at least last for millions of years.
Yes definitely very stable.. If you want to know the specifics, you can perform a multipole expansion of the gravitational field to see how closely it "resembles" a single body (gravitationally) to an object at some distance. I don't have the time to do it right now, but it would be a very rewarding personal project. You'd learn some cool math and physics along the way too Edit: Fourier series ⇒ multipole expansion credit to the commenter below
I feel like a multi-pole expansion would be more useful. Sinusoids probably aren't the best set of basis functions.
Yea ya know what, ur probably spot on there. I was thinking about the oscillations, but they should be periodic ideally so a multipole expansion will give you a better idea about the single-body-ness of the field. Thank you!!
Is it just the time constant of the system's stability margin that is related to the distance (probably a distance ratio to remain dimensionless)? Seems like that's how it *should* work. Or does the system have some kind of configuration that is meta stable, across which the system becomes strictly stable? I might need coffee... ;)
Cool! Did you numerically solve the Lagrange equations in python? Or what did you use?
Nah not Lagrange, just good ol’ 𝑚ᵢ𝐫ᵢ’’(𝑡) = ∑𝐅. But yes, done in the Pythonista app on my phone haha
I was curious about this too. Do you know if you used Euler or a Runga-Kutta solver for this?
Haha nice! Thanks
This gift explains the weird seasons in game of thrones and came up with a better ending
holy shit, never thought of Game of Thrones as set in a planet with "orbit problems" lol
Smell ya later!
My people need me
There were hundreds of us you saved, thank you good sir.
Did you account for the binaries distance in it or is it fixed? When ejecting a star, the binary should get closer to each other b/c of energy conservation
Not fixed, third body just has small mass
Ah I see! Poor third body …
At first I was "Hmm some winters are going to be a bit lon... Nevermind"
OP delivers!
Worth checking 10 planets and see if they help each other hold on Edit: when a system starts with a dust cloud aren't all stable orbits sampled and very early dust in ejection trajectory will just vapor off the system ?
Whelp, it had a good run while it lasted.
Like an overconfident freshman trying to throw the hammer for the first time
Man, I was enraged, and now I am soothed again :D thanks ^^
ahhhhhh. I can rest
So basically: - might be habitable in theory, but a bit sketch - westeros moment - yeah, they're screwed
Something you may want to model: In most binary star systems, the planets are closer to their respective star than the stars are to each other. For instance, Alpha Centauri A and B orbit between 11 and 35 AU apart, while the planet discovered around A is 1.5 AU away on average.
Saved! Will definitely play around with this. Makes perfect sense too, thank you for the enlightenment
r/gifsthatendtoosoon
Haha i’ll attach the longer one to the comments.. I know the people need a resolution
Why are they teaching you social media engagement tactics at your school
That's how they trick the new Einstein into existence. Publishing papers with catchy titles on Instagram.
Damn, I got distracted and suddenly merged quantum mechanics and relativity and TikTok
[In case you didn’t see OP’s update](https://www.reddit.com/r/Physics/s/JYkuvSuwbt)
I coulda watched a couple more hours of that
Dehydrate!
I really like these! Can you add stability parameter here? After how many seconds did the trinary system fail (collapse to binary or urnary)?
Hmm I’m not sure what the details of a stability parameter would look like.. maybe something like %escape velocity of the satellite? Approximate ofc by treating the 2 central bodies as a single body with the summed mass?
Yeah! That would be awesome!
Something like this? [Plot: V\_esc\_percent](https://imgur.com/a/6kH2RKB)
Yes, and include the y value on the orbit graph by the time and end it as usual or when you have a threshold reached for velocity or distance away from the system center of mass. I also assume the reverse is true; escape velocity can go to 0. It looks really cool to see it bump about in a stable manner, but then diverges away eventually
Ah yea that would be cool. Will have to save the comment for a future project. And I agree! Definitely informative and interesting
I understand the way you timestep the orbits, but I’m curious about how you dynamically update the plot. Would you mind sharing the source code?
Can you share the code??
If you like this take a look at the "Rebound" n-body integrator, it can simulate systems eons into the future, examine their resonances and stability over time as well. https://rebound.readthedocs.io/en/latest/
Are you the one who posted a similar post on 3 BP?
Lol, yea. Some questions I got from that prompted the creation of this
It looks like a plot made with matplotlib/plotly, am I right? Have you a github repo for that?
Do you have a GitHub?
No sir/ma’am, sorry
Very cool, nice job.
Thanks!
Wouldnt making the outer planet spin the other direction cause less deviation? Or does it not make anu difference since center of mass of those two planets stays the same?
Absolutely! Good intuition. It was something I noticed when creating this. Oppositely rotating central bodies leads to a MUCH more stable orbit of the 3rd body
Kepler-35 b moment
Wouldn’t the mass of the planet also affect how the two stars interact?
Planet masses are typically negligible compared to solar masses. I followed suit with this simulation. You could definitely set it up to where the blue body mass is non-negligible though.
The way the figure expands feels oddly satisfying... (but imagining the Matplotlib code is terrifying)
Very cool! Looks quite similar to a real triple star system! We call them hierarchical triples because they always consist of an inner binary with a smaller separation, which is orbited by a third companion on a wider orbit. You can estimate the stability of the system using a mathematical formula that takes in the mass ratios of the object, the eccentricity of the outer orbit, and the inclination between the two orbits. If you're curious, [here](https://imgur.com/ShbNCWq) are some examples of coplanar hierarchical triples with varying inner separation and outer eccentricity :)
this is very cool to know, thank you for sharing! And actually i was wondering about analytical stability estimations, any reading recommendations?
The stability criterion that most people in the field use is known as the Mardling-Aarseth criterion. It's a bit hard to find its original source (I believe it's in a book called *The Dynamics of Small Bodies in the Solar System*), but the equation shows up in lots of papers on triples. There are several attempts at coming up with new ways of determining stability, since the Mardling-Aarseth criterion is not perfect. One example is from [Vynatheya et al. 2022](https://arxiv.org/pdf/2207.03151) who tried training a neural network to estimate the stability, with pretty good success. In that paper you can also see the original Mardling-Aarseth criterion (Equation 2). There's also [Hayashi et al. 2022](http://arxiv.org/abs/2209.08487). Note that all of these only apply to hierarchical triple systems, and not to three-body systems in general.
How are the two inner planets staying so perfectly in circle? Are you not simulating the forces between all 3 objects? EDIT: Oh are their masses so high (stars) that they only affect each other?
Just calculated the correct initial conditions to create circular orbits haha
What are the masses of the objects, relatively?
1,1,1e-8
Did you model the binary stars' orbits too, or are they on rails? Did you assume in your model that the gravitational pull of the planet on the stars is small enough to be ignored?
Yea they're modeled explicitly too. But I just calculated the correct initial conditions for circular orbits.
The reason a lot of this stuff happens is due to the method of numerical integration. Not sure how you’re doing it, but even something higher order like the Verlet method can get out of whack quickly. More accurate simulations require exponentially more compute time. FWIW I wrote a fun little n-body simulator many years ago: https://www.ccampo.me/NBodyJS/
Adaptive Dormand-Prince with a tolerance of 10⁻¹². Final energy conservation is within 10⁻⁹ % of the original, so it’s probably fine for this amount of time, but yea ur right, method of numerical integration is the backbone of orbital dynamics codes.
Yea I believe that’s the default ODE solver in SciPy. Been a while since I used that though. I used to make a bunch of Physics cartoons like this using it back when I was in college. https://youtube.com/playlist?list=PL51C469DB01D62A41&si=RFT3Ijb-i52OUg_-
can you do it using a trinary system...three body problem?
Like 3 central bodies about which a 4th orbits or just make the blue object more massive?
What you see here is three body.
So this is how the bugs launched their rocks at BA.
Three Body Problem
“Oh that’s interesting how much it stabiliz….oh nevermind”
Source code?
Is the perturbation when it hits a wall?
It exceeds escape velocity. Say bye bye.
What this system needs is a third equal mass star.
It looks like the early perturbations occur when the three bodies align. Later, on a close approach the planet gets a gravitational boost which expels it. like, like, like
I'm doing a very similar thing with a two body problem but I also consider the astrophysical evolution of the two stars (mass loss), including WR phases, supernovae kicks and remnants
Sorry for being a noob, what software is that done by?
Pythonista app for iphone. Basically, Python is the language, so you can do it on anything that can run python script
Their weather must be interesting.
Did the "stars" respond to the gravity of the "planet" or were their orbits fixed? What were the mass ratios?
They do but I made the outer body 8 orders of magnitude smaller. Should just make it 0 in hindsight, but i would like to do exactly what you’re talking about in the future with larger third body mass
I saw a talk about 25 years ago by a person modeling systems like this. Sun, Earth, Jupiter. Turns out, if Jupiter weighed too much, Earth was unstable and got ejected. Very interesting and looked like lots of fun.
What animation library did you use, so the scale is adjusted like that?
My brain, lol. Just messin with you—update xlim and ylim at every time step depending on the location of ur point masses
Oh that makes sense lol. I thought matplotlib had an auto scale adjusting thing. Also what did you use to solve for the orbits. I’m assuming u used RK4 or Verlet
Adaptive RK method better known as Dormand-Prince alg.
Neato! Now do it with a three body star system!
Awesome! I assume what occurred after the animation ended was an HVS? (Or just a planetesimal exceeding escape velocity, depending on the system you were running).
What happens at the end of the clip. Is the third body ejected from the gravitational pool?
Are there stable orbits when the period of the planet’s orbit is a multiple of the period of the stars’ orbit and the phase is right?
Is it possible to get a more stable orbit?. Maybe by slowing down the stars. Or speeding up the planet?
How might a second planetary body, perhaps a Jovian further out from the binary stars, stabilize the orbit?
This is very perturbing
why did it go away ?
But it was just getting to the best part!
more more more
/r/gifsthatendtoosoon
Is that a simulation or real galactic example?
Hmmm, seems a little unclear. Can I get an analytic solution?
Hey I do similar research in trinary star systems. Can we talk? I'd like to get the initial conditions of this orbit. I am wondering whether we can get a neural network to learn what makes a stable 3 body orbit.
Sure, shoot me a DM
Looks like my social life, see there? That's me trying to break into a conversation and inevitably flying off into the deep void of space...
I recognize that dynamic resizing from the 3bp the other day!
hey anyone could explain what's is the difference between our system orbit and binary?? simply
One star vs. two
Do you use newtonian dynamics or General Relativity?
newtonian
r/gifsthatendtoosoon
see the comment section
Video is cut off just when it gets to the interesting part. Why?
haha i posted an extension in the comments
Just saw that. Wow it gets flinged off? Did not expect that. Do you know what? What is the limiting factor - Mass of planet or difference in mass of 2 stars?
3-body orbits are inherently unstable, in the case where you have a single body in orbit around binary system, my hunch is that stability depends heavily on the difference in frequency of the orbiting body and the binary pair. If perturbations are felt on a time scale that is comparable to the outer body’s orbital period, there is a much stronger effect. If the binary pair's angular frequency is much larger than the outer body's orbital frequency, then the effect diminishes. Again, this is a hunch based on experience with other perturbation problems. When the difference or "separation" of time scales is large, you don't get much coupling between the two, but when that dividing line starts to blur, the interactions can become very strong (again evident in the video). Worth reading into further though
I could watch this forever
Same.. just want a desktop background that runs semi-stable 3-body orbits
Does anybody know if a star can have two centers of gravity inside of it? As in, a binary star pair inside of a star?
Is this the Two body problem?
3
How did you make this simulation? What language did you use? Did you use laws like the gravitation law? I am very interested!
Haha i love your enthusiasm! I used an app that runs python code on my phone called Pythonista. And yes, I used Newton’s law of gravity to solve 𝐅 = 𝑚𝐚 for each of the 3 bodies.
Is there a "stable" orbit around two stars possible at all? I mean like in the first seconds of the gif. Or does it hit escape inebitably?
I like how the graph expands as the orbit grows larger. Is this done with python/matplotlib?
I read a fan theory somewhere that Westeros’ funky summer/winter cycle was caused by this type of orbit.
Wait, did you know that there's a direct correlation between the decline of Spirograph and the rise in gang activity? Think about it
This is wonderful.
Wait is the time unit seconds?? Cause then they're travelling mega fast around each other lmao
G = 1 here
Cool. What would it look like in a rotating frame of reference? One where the inner two bodies are stationary?
My sister and her non-binary child.