Timeline for Conjecture: Finitely many points where gravitational field due to N masses vanishes
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2017 at 13:51 | comment | added | Alexandre Eremenko | @KlausDraeger: This is what I referred to as "general considerations" in my answer: arguments which use very little of the nature of the potential. | |
| Oct 6, 2017 at 13:00 | comment | added | Klaus Draeger | @JoshuaBenabou How about the following? If you consider a sufficiently large ball $B$ which contains all the points in its interior, it is clear that the gravitational field $F$ is continuous on $B$ and pointing into $B$ everywhere on its surface. Then for a sufficiently small $\varepsilon$, $x+\varepsilon F(x)$ is in $B$ for all $x\in B$. As an endomorphism of a convex compact subset, it has a fixpoint (where $F$ has to be $0$) by the Schauder fixpoint theorem. | |
| Oct 6, 2017 at 8:51 | comment | added | math_lover | @AlexandreEremenko: Why is it obvious that the number of points is nonzero? For example even with $N=3$, if the configuration does not consist of 3 collinear points or an equilateral triangle, the existence of a point $P$ where the field vanishes is not obvious. | |
| Oct 6, 2017 at 3:09 | comment | added | Steven Stadnicki | @KonstantinosKanakoglou At its root, the question is just about Newtonian $r^{-2}$ potential fields; aside from charge, there's no real difference between gravity and EM fields in that regard. | |
| Oct 6, 2017 at 3:08 | comment | added | zibadawa timmy | @KonstantinosKanakoglou Depends on your definition of positive and the scalar potential. | |
| Oct 6, 2017 at 2:56 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Oct 5, 2017 at 23:32 | comment | added | Konstantinos Kanakoglou | "Since you are talking about gravitation (rather than electrostatics) I assume that all charges are positive": isn't this statement a little shady? Given that gravitational forces are always attractive? | |
| Oct 5, 2017 at 23:01 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Oct 5, 2017 at 22:54 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |