4 ms·

Very cool! I was able to get 2 masses to oscillate around each other in a funny way[1]. Seems they keep going like that forever. What is this kind of equilibriu

Very cool! I was able to get 2 masses to oscillate around each other in a funny way[1]. Seems they keep going like that forever. What is this kind of equilibrium called? [1]http://imgur.com/FQYpo9V http://imgur.com/FQYpo9V

xioxox 12y ago
Isn't that a normal orbit around a common centre of mass? As the objects have a similar size the centre of mass appears to wobble as it moves along. In the frame of the centre of mass, the objects would just go round in standard orbits.
- raverbashing 12y ago
  Yeah That's the thing with those kind of simulators (or, actually, with reality), your reference has no relation to the center of mass of the system. Of course, if you "were there" the reference would be the center of mass, like the reference of the solar system is "The Sun" (or a point inside it)
  - jessriedel 12y ago
    The center of mass of the solar system isn't always within the Sun. https://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy) https://en.wikipedia.org/wiki/Barycentric_coordinates_(astro...
    - deleted 12y ago
      [deleted]
- lutusp 12y ago
  > Isn't that a normal orbit around a common centre of mass? If you limit yourself to looking at the position of one body with respect to another, the orbit will be an ellipse. A circular orbit is simply a special-case ellipse with an eccentricity of zero. This is true for any two orbiting masses -- from the perspective of either of them, the other body's orbit will be an ellipse. And yes, it's always with respect to the common center of mass. Interestingly, mostly because of Jupiter, the solar system's common center of mass can sometimes lie outside the sun.
quarterwave 12y ago
Looks like a binary star, similar to the two suns of Tatooine. http://en.wikipedia.org/wiki/Binary_star#mediaviewer/File:Orbit5.gif http://en.wikipedia.org/wiki/Binary_star#mediaviewer/File:Or... OP: This is an amazing tool to learn the sensitivity of dynamical systems to initial conditions. Well done!
jmcmahon443 12y ago
If they were truly rotating around each other in a repeatable way, it would be a harmonic oscillator.
jessriedel 12y ago
Once you change references frames to the center of mass, two bodies that are gravitationally bound are always following ellipses. It looks like this in the case where they have equal mass: https://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#mediaviewer/File:Orbit5.gif https://en.wikipedia.org/wiki/Barycentric_coordinates_(astro... Likewise, two bodies that are not bound will follow hyperbolas in the center of mass frame.
- lutusp 12y ago
  > Likewise, two bodies that are not bound will follow hyperbolas Or parabolas, which also represent unbound solutions. In an orbital system, a parabolic trajectory represents escape velocity (exactly), a solution in which the escaping body's velocity is in progressive decline, and that reaches zero at infinity.
teamonkey 12y ago
An orbit :)
yamaneko 12y ago
I've been playing with it too: http://imgur.com/VAHTfg9 http://imgur.com/VAHTfg9 It took a little bit to generate this one.

xioxox 12y ago

Isn't that a normal orbit around a common centre of mass? As the objects have a similar size the centre of mass appears to wobble as it moves along. In the frame of the centre of mass, the objects would just go round in standard orbits.

raverbashing 12y ago
Yeah That's the thing with those kind of simulators (or, actually, with reality), your reference has no relation to the center of mass of the system. Of course, if you "were there" the reference would be the center of mass, like the reference of the solar system is "The Sun" (or a point inside it)
- jessriedel 12y ago
  The center of mass of the solar system isn't always within the Sun. https://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy) https://en.wikipedia.org/wiki/Barycentric_coordinates_(astro...
  - deleted 12y ago
    [deleted]
lutusp 12y ago
> Isn't that a normal orbit around a common centre of mass? If you limit yourself to looking at the position of one body with respect to another, the orbit will be an ellipse. A circular orbit is simply a special-case ellipse with an eccentricity of zero. This is true for any two orbiting masses -- from the perspective of either of them, the other body's orbit will be an ellipse. And yes, it's always with respect to the common center of mass. Interestingly, mostly because of Jupiter, the solar system's common center of mass can sometimes lie outside the sun.

quarterwave 12y ago

Looks like a binary star, similar to the two suns of Tatooine. http://en.wikipedia.org/wiki/Binary_star#mediaviewer/File:Orbit5.gif http://en.wikipedia.org/wiki/Binary_star#mediaviewer/File:Or... OP: This is an amazing tool to learn the sensitivity of dynamical systems to initial conditions. Well done!

jmcmahon443 12y ago

If they were truly rotating around each other in a repeatable way, it would be a harmonic oscillator.

jessriedel 12y ago

Once you change references frames to the center of mass, two bodies that are gravitationally bound are always following ellipses. It looks like this in the case where they have equal mass: https://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#mediaviewer/File:Orbit5.gif https://en.wikipedia.org/wiki/Barycentric_coordinates_(astro... Likewise, two bodies that are not bound will follow hyperbolas in the center of mass frame.

lutusp 12y ago
> Likewise, two bodies that are not bound will follow hyperbolas Or parabolas, which also represent unbound solutions. In an orbital system, a parabolic trajectory represents escape velocity (exactly), a solution in which the escaping body's velocity is in progressive decline, and that reaches zero at infinity.

teamonkey 12y ago

An orbit :)

yamaneko 12y ago

I've been playing with it too: http://imgur.com/VAHTfg9 http://imgur.com/VAHTfg9 It took a little bit to generate this one.