4 ms·

Periodic Planar Three-Body Orbits

107 points by jashkenas 7y ago

baliex 7y ago
They're interesting, hypnotic, and beautiful!
317070 7y ago
But do these 'analytically' orbit? I reckon such a proof must be quite intricate? Are there proofs for each of those families?
- 6gvONxR4sf7o 7y ago
  I googled the name of the first set of orbits and found this https://arxiv.org/pdf/1303.0181.pdf https://arxiv.org/pdf/1303.0181.pdf
  - JadeNB 7y ago
    Routine plea: please link to abstracts (Šuvakov and Dmitrašinović - Three classes of Newtonian three-body planar periodic orbits - https://arxiv.org/abs/1303.0181 https://arxiv.org/abs/1303.0181) rather than directly to PDFs. (It is an easy click to get from abstract to PDF, but not vice versa.)
    - rreusser 7y ago
      That's good advice. Thanks! I've switched a couple of the links to abstracts instead of PDFs, though what I really need is a proper references section since direct links are also convenient—if they work.
j16sdiz 7y ago
This notebook sharing website look nice. Why we haven't seen this before?
- dang 7y ago
  Previous submissions may be of interest: https://news.ycombinator.com/from?site=observablehq.com https://news.ycombinator.com/from?site=observablehq.com
raverbashing 7y ago
I wonder how many of those would be feasible in real life situations For example, a celestial body coming in proximity to another will impart tidal forces, might involve some kind of mass exchange or simply find form of atmospheric drag.
- p1mrx 7y ago
  The three-body problem has very few stable solutions, which include an equilateral triangle and a figure eight: https://sites.math.washington.edu/~morrow/336_12/papers/adrian.pdf https://sites.math.washington.edu/~morrow/336_12/papers/adri... "The actual probability of finding such a [figure eight] star system is somewhere between one per galaxy and one per universe."
  - garmaine 7y ago
    This is an extremely misleading statement. The Earth-Sun-Moon is a 3 body system and quite stable. Obviously moons and multi-planet systems are quite common. As are 3-star systems. Our nearest neighbor is one: Proxima/Alpha Centauri. And Proxima Centauri has a planet too. What is difficult to find stable solutions for is 3 body movements where the three objects are of similar mass. But that is an improbable circumstance to start with. Also that citation seems to be totally disregarding the fact that multi-body systems never start in stable systems but instead naturally align into them.
Myrmornis 7y ago
If I work on an observable notebook, is it (or can it be) backed by a git repo? Is it convenient to edit the code in a traditional text editor?
- jashkenas 7y ago
  Not too easily, and no. With Observable notebooks we're trying to expand the boundaries of how live, networked and interactive a notebook can be. So, to that end, the notebook is the editor, visualizations update reactively with your changes to the code just as they would update to changes in the data, you can inspect and autocomplete actual values flowing through your program, and you can fork someone else's notebook or merge their changes with a single click. There's built-in history too (live, every version reproducible), as seen in 15 seconds with an animated gif here: https://observablehq.com/@observablehq/history https://observablehq.com/@observablehq/history In the future, we're thinking about working on APIs for better git and generic text editor integration; but for the reasons listed above, the primary focus for now is on making working directly in a notebook on the web the best experience possible.
  - Myrmornis 7y ago
    Thanks! I have another question about observable: are you aware of anyone using mathbox in conjunction with observable? Do you think that could be a fruitful direction? https://github.com/unconed/mathbox https://github.com/unconed/mathbox
    - jashkenas 7y ago
      I'm not aware of anyone using Mathbox in Observable, although it certainly seems promising! On the other hand, I have seen quite a lot of neat Ganja.js notebooks float by, for plotting explorations of algebraic spaces in notebooks: https://observablehq.com/search?query=ganja https://observablehq.com/search?query=ganja
NotSammyHagar 7y ago
I searched around for observablehq. I hadn't see it before. Checkout https://observablehq.com/@observablehq/five-minute-introduction https://observablehq.com/@observablehq/five-minute-introduct... and https://news.ycombinator.com/item?id=20184181 https://news.ycombinator.com/item?id=20184181.

107 points by jashkenas 7y ago

They're interesting, hypnotic, and beautiful!

But do these 'analytically' orbit? I reckon such a proof must be quite intricate? Are there proofs for each of those families?

6gvONxR4sf7o 7y ago
I googled the name of the first set of orbits and found this https://arxiv.org/pdf/1303.0181.pdf https://arxiv.org/pdf/1303.0181.pdf
- JadeNB 7y ago
  Routine plea: please link to abstracts (Šuvakov and Dmitrašinović - Three classes of Newtonian three-body planar periodic orbits - https://arxiv.org/abs/1303.0181 https://arxiv.org/abs/1303.0181) rather than directly to PDFs. (It is an easy click to get from abstract to PDF, but not vice versa.)
  - rreusser 7y ago
    That's good advice. Thanks! I've switched a couple of the links to abstracts instead of PDFs, though what I really need is a proper references section since direct links are also convenient—if they work.

j16sdiz 7y ago

This notebook sharing website look nice. Why we haven't seen this before?

dang 7y ago
Previous submissions may be of interest: https://news.ycombinator.com/from?site=observablehq.com https://news.ycombinator.com/from?site=observablehq.com

raverbashing 7y ago

I wonder how many of those would be feasible in real life situations For example, a celestial body coming in proximity to another will impart tidal forces, might involve some kind of mass exchange or simply find form of atmospheric drag.

p1mrx 7y ago
The three-body problem has very few stable solutions, which include an equilateral triangle and a figure eight: https://sites.math.washington.edu/~morrow/336_12/papers/adrian.pdf https://sites.math.washington.edu/~morrow/336_12/papers/adri... "The actual probability of finding such a [figure eight] star system is somewhere between one per galaxy and one per universe."
- garmaine 7y ago
  This is an extremely misleading statement. The Earth-Sun-Moon is a 3 body system and quite stable. Obviously moons and multi-planet systems are quite common. As are 3-star systems. Our nearest neighbor is one: Proxima/Alpha Centauri. And Proxima Centauri has a planet too. What is difficult to find stable solutions for is 3 body movements where the three objects are of similar mass. But that is an improbable circumstance to start with. Also that citation seems to be totally disregarding the fact that multi-body systems never start in stable systems but instead naturally align into them.

Myrmornis 7y ago

If I work on an observable notebook, is it (or can it be) backed by a git repo? Is it convenient to edit the code in a traditional text editor?

jashkenas 7y ago
Not too easily, and no. With Observable notebooks we're trying to expand the boundaries of how live, networked and interactive a notebook can be. So, to that end, the notebook is the editor, visualizations update reactively with your changes to the code just as they would update to changes in the data, you can inspect and autocomplete actual values flowing through your program, and you can fork someone else's notebook or merge their changes with a single click. There's built-in history too (live, every version reproducible), as seen in 15 seconds with an animated gif here: https://observablehq.com/@observablehq/history https://observablehq.com/@observablehq/history In the future, we're thinking about working on APIs for better git and generic text editor integration; but for the reasons listed above, the primary focus for now is on making working directly in a notebook on the web the best experience possible.
- Myrmornis 7y ago
  Thanks! I have another question about observable: are you aware of anyone using mathbox in conjunction with observable? Do you think that could be a fruitful direction? https://github.com/unconed/mathbox https://github.com/unconed/mathbox
  - jashkenas 7y ago
    I'm not aware of anyone using Mathbox in Observable, although it certainly seems promising! On the other hand, I have seen quite a lot of neat Ganja.js notebooks float by, for plotting explorations of algebraic spaces in notebooks: https://observablehq.com/search?query=ganja https://observablehq.com/search?query=ganja

NotSammyHagar 7y ago

I searched around for observablehq. I hadn't see it before. Checkout https://observablehq.com/@observablehq/five-minute-introduction https://observablehq.com/@observablehq/five-minute-introduct... and https://news.ycombinator.com/item?id=20184181 https://news.ycombinator.com/item?id=20184181.