Tidal pattern instabilities on multi-moon planets

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.Comment: 26 pages, 9 figure

Apparatus for real-time acoustic imaging of Rayleigh-Bénard convection

“…Joanna Furno, who graduated from the College with a mathematics major, built and tested the thermometers for the temperature regulations system, and ran initial tests on the newly designed apparatus. Inspired by work on this project, she also co-authored a theoretical paper with the Principle Investigator on tidal instabilities in fluids generated by multiple gravitational sources [6,7]. She is currently a graduate student in the Department of Mathematics at the University of North Carolina in Chapel Hill.…”