Timeline for Infinitely many planets on a line, with Newtonian gravity
Current License: CC BY-SA 3.0
11 events
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| May 27, 2018 at 20:30 | comment | added | Alexandre Eremenko | @Anthony Quas and Jon: I think this is not what he means. He does not "live in 1D world" but in 3-space. Just the planets happen to be on the line. The gravity law must be inverse squares. Otherwise the questions make no sense. | |
| Jun 15, 2017 at 12:21 | comment | added | Jon | @AnthonyQuas is correct. The Poisson equation in one dimension in this case is $\phi''(x)=\delta(x)$ that has as a solution $\theta(x) x$. So, the potential between two bodies is not decaying in this case. | |
| Apr 13, 2017 at 12:40 | history | edited | CommunityBot |
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| Apr 26, 2013 at 20:39 | comment | added | Liviu Nicolaescu | Excellent question! Perhaps You should start as in thermodynamics with a large number $N$ of particles located at $-N,\dotsc,-1, \epsilon, 1,\dotsc, N$ and see what happens then. At least in this case the total energy is finite, which is not the case when infinitely many particles are present. | |
| Apr 26, 2013 at 7:59 | comment | added | user5810 | point masses $\:$ | |
| Apr 26, 2013 at 7:56 | comment | added | David Roberts♦ | Are the planets point masses, or some radius $r \lt \frac{1}{2}$? | |
| Apr 26, 2013 at 7:42 | comment | added | Douglas Zare | Yes, particles clump together, typically forming smaller systems first. This is studied extensively in cosmology, both analytically and numerically. Gravitational effects are easy to model, and affect dark matter. youtube.com/watch?v=8C_dnP2fvxk However, dissipative effects such as the inelastic contraction of gas clouds are important, too. | |
| Apr 26, 2013 at 7:10 | comment | added | Anthony Quas | I think that as long as each planet is at most $\delta$ from its nearest integer, the total force on each planet is $O(\delta)$. This can be used to prove rigorously that there's a positive $\tau>0$ before any collision can occur. | |
| Apr 26, 2013 at 7:07 | comment | added | Anthony Quas | Of course if you really live in a 1D world, gravitational force presumably doesn't decay at all? | |
| Apr 26, 2013 at 7:06 | comment | added | Anthony Quas | I read recently about a very similar problem that appeared in a 1949 letter from Ulam to von Neumann. (In that case the particles started at points of $\mathbb Z$ with each node being occupied with probability 1/2). He showed(?) that something analogous to the universe happens: nearby groups of particles come together; and then those "solar systems" form galaxies etc. | |
| Apr 26, 2013 at 3:31 | history | asked | user5810 | CC BY-SA 3.0 |