Timeline for Random N-body problem
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 22, 2017 at 22:47 | comment | added | Douglas Zare | Why is the solar system bounded? Isn't it expected that the solar system is unstable and will eject planets, say every few billion years? I can believe that there are stable solar systems, but why would every small perturbation also be bounded, wouldn't you expect to be able to get a planet ejected with arbitrarily small perturbations? | |
| Jun 19, 2017 at 8:52 | comment | added | Alexandre Eremenko | Open set has positive volume. Or you are asking about $n\to\infty$? | |
| Jun 18, 2017 at 23:11 | comment | added | Joseph O'Rourke | "there is an open set of initial positions when the motion is bounded": May I ask: Does this open set have volume a positive fraction of the volume of the space of all initial positions? | |
| Jun 17, 2017 at 10:30 | comment | added | aglearner | I agree, such case should be doable by KAM theory. But in the case under consideration the masses are equal... | |
| Jun 17, 2017 at 10:09 | comment | added | Alexandre Eremenko | The case when one mass is large, second much smaller, and the third much smaller than the second, so that the first is in the center, second moves approximately on Kepler orbit and the third (satellite) around the second, I suppose this case is stable. Like for example Sun-Mars-Fobos. | |
| Jun 17, 2017 at 9:31 | comment | added | aglearner | Alexandre, could you please give some details for the case of three bodies? The case of two bodies is clear, since it is integrable. By the way, I forgot, is it proven by now the the solar system is stable? (I remember Arnold had some ideas of how to prove this using KAM theory but not sure if he was successful). | |
| Jun 17, 2017 at 6:45 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |