dorsal/arxiv
View SchemaTidal pattern instabilities on multi-moon planets
| Authors | Joanna Furno, Kerry Kuehn |
|---|---|
| Categories | |
| ArXiv ID | physics/0701301 |
| URL | https://arxiv.org/abs/physics/0701301 |
| DOI | 10.1016/j.icarus.2007.01.007 |
| Journal | Icarus, Volume 189, Issue 1, July 2007, Pages 246-255 |
Abstract
The equilibrium tide-generating forces in the lunar orbital plane of a planet of radius R are calculated for the case of N moons of mass M_i orbiting the planet at instantaneous polar coordinates (D_i, \alpha_i). For the case of a single moon, there are only two high tides. For the case of two moons, it is found that there can exist a critical lunar orbital distance at which two high tides become unstable with respect to formation of three high tides. Bifurcation diagrams are presented which depict how the angular positions of the high and low tides on the planet vary with the lunar distances and lunar separation angle. Tidal stability diagrams, which illustrate the stability regions for various tidal patterns as a function of lunar distances and lunar separation angle, are presented for various values of D_2/D_1 and M_2/M_1. Generally speaking, the aforementioned tidal instability, and hence the propensity for formation of three high tides on a two-moon planet, exists over a significant range of lunar distances and separation angles provided that M_2/M_1 \sim (D_2/D_1)^3. For the case of N>2 moons, the tidal stability diagram becomes more complex, revealing a diversity of potential tidal patterns.
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"abstract": "The equilibrium tide-generating forces in the lunar orbital plane of a planet\nof radius R are calculated for the case of N moons of mass M_i orbiting the\nplanet at instantaneous polar coordinates (D_i, \\alpha_i). For the case of a\nsingle moon, there are only two high tides. For the case of two moons, it is\nfound that there can exist a critical lunar orbital distance at which two high\ntides become unstable with respect to formation of three high tides.\nBifurcation diagrams are presented which depict how the angular positions of\nthe high and low tides on the planet vary with the lunar distances and lunar\nseparation angle. Tidal stability diagrams, which illustrate the stability\nregions for various tidal patterns as a function of lunar distances and lunar\nseparation angle, are presented for various values of D_2/D_1 and M_2/M_1.\nGenerally speaking, the aforementioned tidal instability, and hence the\npropensity for formation of three high tides on a two-moon planet, exists over\na significant range of lunar distances and separation angles provided that\nM_2/M_1 \\sim (D_2/D_1)^3. For the case of N\u003e2 moons, the tidal stability\ndiagram becomes more complex, revealing a diversity of potential tidal\npatterns.",
"arxiv_id": "physics/0701301",
"authors": [
"Joanna Furno",
"Kerry Kuehn"
],
"categories": [
"physics.ao-ph",
"physics.space-ph"
],
"doi": "10.1016/j.icarus.2007.01.007",
"journal_ref": "Icarus, Volume 189, Issue 1, July 2007, Pages 246-255",
"title": "Tidal pattern instabilities on multi-moon planets",
"url": "https://arxiv.org/abs/physics/0701301"
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