Brief Report
Version 1
Preserved in Portico This version is not peer-reviewed
On Some Damped 2 Body Problems
Version 1
: Received: 19 December 2020 / Approved: 21 December 2020 / Online: 21 December 2020 (11:19:42 CET)
Version 2 : Received: 23 December 2020 / Approved: 23 December 2020 / Online: 23 December 2020 (17:25:05 CET)
Version 3 : Received: 4 January 2021 / Approved: 5 January 2021 / Online: 5 January 2021 (10:07:44 CET)
Version 2 : Received: 23 December 2020 / Approved: 23 December 2020 / Online: 23 December 2020 (17:25:05 CET)
Version 3 : Received: 4 January 2021 / Approved: 5 January 2021 / Online: 5 January 2021 (10:07:44 CET)
How to cite: Haraux, A. On Some Damped 2 Body Problems. Preprints 2020, 2020120510. https://doi.org/10.20944/preprints202012.0510.v1. Haraux, A. On Some Damped 2 Body Problems. Preprints 2020, 2020120510. https://doi.org/10.20944/preprints202012.0510.v1.
Abstract
The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear. It is shown that whenever the momentum is not zero, the moving particle does not reach the center in finite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover we prove that all bounded solutions tend to $0$ for $t$ large, and some formal calculations suggest the existence of special orbits with an asymptotically spiraling exponentially fast convergence to the center. A related model with exponentially damped central charge or mass gives some explicit exponentially decaying solutions which might help future investigations. An atomic contraction hypothesis related to the asymptotic dying off of solutions proven for the dissipative model might give a solution to some intriguing phenomena observed in paleontology, familiar electrical devices and high scale cosmology.
Keywords
gravitation; singular potential; global solutions; spiraling orbit
Subject
PHYSICAL SCIENCES, Atomic & Molecular Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)