A new expansion of planetary disturbing function and applications to interior, co-orbital and exterior resonances with planets

In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around circular orbits in the first step and then, in the second step, the resulting mutual interaction between circular orbits is expanded around a reference point. As usual, the resulting expansion is presented in the Fourier series form, where the force amplitudes are dependent on the semimajor axis, eccentricity and inclination, and the harmonic arguments are linear combinations of the mean longitude, longitude of pericenter and longitude of ascending node of each mass. The resulting new expansion is valid for arbitrary inclinations and semimajor axis ratios. In the case of mean motion resonant configuration, the disturbing function can be easily averaged to produce the analytical expansion of resonant disturbing function. Based on the analytical expansion, the Hamiltonian model of mean motion resonances is formulated, and the resulting analytical developments are applied to Jupiter’s inner and co-orbital resonances and Neptune’s exterior resonances. Analytical expansion is validated by comparing the analytical results with the associated numerical outcomes.

Magnetic Topology in Coupled Binaries, Spin-orbital Resonances, and Flares

We consider topological configurations of the magnetically coupled spinning stellar binaries (e.g., merging neutron stars or interacting star–planet systems). We discuss conditions when the stellar spins and the orbital motion nearly “compensate” each other, leading to very slow overall winding of the coupled magnetic fields; slowly winding configurations allow gradual accumulation of magnetic energy, which is eventually released in a flare when the instability threshold is reached. We find that this slow winding can be global and/or local. We describe the topology of the relevant space F = T 1 S 2 as the unit tangent bundle of the two-sphere and find conditions for slowly winding configurations in terms of magnetic moments, spins, and orbital momentum. These conditions become ambiguous near the topological bifurcation points; in certain cases, they also depend on the relative phases of the spin and orbital motions. In the case of merging magnetized neutron stars, if one of the stars is a millisecond pulsar, spinning at ∼10 ms, the global resonance ω 1 + ω 2 = 2Ω (spin-plus beat is two times the orbital period) occurs approximately one second before the merger; the total energy of the flare can be as large as 10% of the total magnetic energy, producing bursts of luminosity ∼1044 erg s−1. Higher order local resonances may have similar powers, since the amount of involved magnetic flux tubes may be comparable to the total connected flux.

On the divergence of first-order resonance widths at low eccentricities

ABSTRACT Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first-order mean motion resonances diverge for nearly circular orbits. Here, we examine the nature of this divergence with a non-perturbative analysis of a few first-order resonances interior to a Jupiter-mass planet. We show that a first-order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centres of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of ‘bridges’ between adjacent first-order resonances: at low eccentricities, the apocentric libration zone of a first-order resonance smoothly connects with the pericentric libration zone of the neighbouring first-order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low-eccentricity regime.

Single-molecule functionality in electronic components based on orbital resonances

A gateable single-molecule diode and resonant tunneling diode are realized using molecular orbital engineering in multi-site molecules.

Monitoring Jovian Orbital Resonances of a Spacecraft: Classical and Relativistic Effects

Orbital resonances continue to be one of the most difficult problems in celestial mechanics. They have been studied in connection with the so-called Kirkwood gaps in the asteroid belt for many years. On the other hand, resonant trans-Neptunian objects are also an active area of research in Solar System dynamics, as are the recently discovered resonances in extrasolar planetary systems. A careful monitoring of the trajectories of these objects is hindered by the small size of asteroids or the large distances of the trans-Neptunian bodies. In this paper, we propose a mission concept, called CHRONOS (after the greek god of time), in which a spacecraft could be sent to with the initial condition of resonance with Jupiter in order to study the future evolution of its trajectory. We show that radio monitoring of these trajectories could allow for a better understanding of the initial stages of the evolution of resonant trajectories and the associated relativistic effects.

Does Io Have a Magma Ocean?

Future space missions will further our knowledge of tidal heating and orbital resonances, processes thought to create spectacular volcanism and oceans of magma or water on other worlds.

Survey of asteroids in retrograde mean motion resonances with planets

Aims. Asteroids in mean motion resonances (MMRs) with planets are common in the solar system. In recent years, increasingly more retrograde asteroids are discovered, several of which are identified to be in resonances with planets. We here systematically present the retrograde resonant configurations where all the asteroids are trapped with any of the eight planets and evaluate their resonant condition. We also discuss a possible production mechanism of retrograde centaurs and dynamical lifetimes of all the retrograde asteroids. Methods. We numerically integrated a swarm of clones (ten clones for each object) of all the retrograde asteroids (condition code U < 7) from −10 000 to 100 000 yr, using the MERCURY package in the model of solar system. We considered all of the p/−q resonances with eight planets where the positive integers p and q were both smaller than 16. In total, 143 retrograde resonant configurations were taken into consideration. The integration time was further extended to analyze their dynamical lifetimes and evolutions. Results. We present all the meaningful retrograde resonant configurations where p and q are both smaller than 16 are presented. Thirty-eight asteroids are found to be trapped in 50 retrograde mean motion resonances (RMMRs) with planets. Our results confirm that RMMRs with giant planets are common in retrograde asteroids. Of these, 15 asteroids are currently in retrograde resonances with planets, and 30 asteroids will be captured in 35 retrograde resonant configurations. Some particular resonant configurations such as polar resonances and co-orbital resonances are also identified. For example, Centaur 2005 TJ50 may be the first potential candidate to be currently in polar retrograde co-orbital resonance with Saturn. Moreover, 2016 FH13 is likely the first identified asteroid that will be captured in polar retrograde resonance with Uranus. Our results provide many candidates for the research of retrograde resonant dynamics and resonance capture. Dynamical lifetimes of retrograde asteroids are investigated by long-term integrations, and only ten objects survived longer than 10 Myr. We confirmed that the near-polar trans-Neptunian objects 2011 KT19 and 2008 KV42 have the longest dynamical lifetimes of the discovered retrograde asteroids. In our long-term simulations, the orbits of 12 centaurs can flip from retrograde to prograde state and back again. This flipping mechanism might be a possible explanation of the origins of retrograde centaurs. Generally, our results are also helpful for understanding the dynamical evolutions of small bodies in the solar system.