Related papers: On Bode's law
Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using…
We have calculated evolution of neutron star binaries towards the coalescence driven by gravitational radiation. The hydrodynamical effects as well as the general relativistic effects are important in the final phase. All corrections up to…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic…
Recent observations have confirmed the existence of rings around minor bodies in the outer Solar System. These objects may possess satellites as well. Here we analytically investigate the interaction between such rings and satellites. We…
We aim to understand how landslides affect the shape and rotational motion of small rubble planetary bodies. We limit ourselves to axisymmetric global landslides, and take the primordial shape of the body to also be axisymmetric. The…
Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. We suggest in the current research to take into consideration the additional well-known…
The radii of some transiting extrasolar giant planets are larger than would be expected by the standard theory. We address this puzzle with the model of coupled radius-orbit tidal evolution developed by \citet{Ibgui_and_Burrows_2009}. The…
It has been suggested that tidal interaction is important for shaping the orbital configurations of close orbiting giant planets. The excitation of propagating waves and normal modes (dynamical tide) will be important for estimating time…
This work provides, at lower order, general analytical solutions for the orbital separation, merging time, and orbital frequency of binary systems emitting gravitational waves while being submitted to mass variations. Specific features,…
The late-stage formation of giant planetary systems is rich in interesting dynamical mechanisms. Previous simulations of three giant planets initially on quasi-circular and quasi-coplanar orbits in the gas disc have shown that highly…
Gravitational waves emitted in the late inspiral of binary neutron stars are affected by their tidal deformation. We study the tidal dynamics in full general relativity through matched-asymptotic expansions and prove that the dynamical…
This paper is devoted to Radial Orbit Instability in the context of self-gravitating dynamical systems. We present this instability in the new frame of Dissipation-Induced Instability theory. This allows us to obtain a rather simple proof…
Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been…
The majority of star formation results in binaries or higher multiple systems, and planets in such systems are constrained to a limited range of orbital parameters in order to remain stable against perturbations from stellar companions.…
This chapter concerns the long-term dynamical evolution of planetary systems from both theoretical and observational perspectives. We begin by discussing the planet-planet interactions that take place within our own Solar System. We then…
Major (exo)planetary and satellite bodies seem to concentrate at intermediate areas of the radial distributions of all the objects present in each (sub)system. We prove rigorously that the secular evolution of (exo)planets and satellites…
We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose…
Motivated by the large number of extrasolar planetary systems that are near mean motion resonances, this paper explores a related type of dynamical behavior known as "nodding". Here, the resonance angle of a planetary system executes…
The emergence of orbital resonances among planets is a natural consequence of the early dynamical evolution of planetary systems. While it is well-established that convergent migration is necessary for mean-motion commensurabilities to…