Related papers: Approximating Stellar Orbits: Improving on Epicycl…

Cosmological simulations have been used to study interacting galaxies as a function of galaxy pair separation, enabling comparisons with observational studies of galaxy pairs. The study of interacting galaxies as a function of time (i.e.…

We present a practical implementation of the perturbation theory derived by Lynden-Bell (2015) for describing, to arbitrary precision, the orbit of a particle in an arbitrary spherically-symmetric potential. Our implementation corrects…

We use N-body simulations to explore the influence of orbital eccentricity on the dynamical evolution of star clusters. Specifically we compare the mass loss rate, velocity dispersion, relaxation time, and the mass function of star clusters…

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…

Local linearization is highlighted to explain the success of the orbital approximation in positive response to Scerri's comments on the electronic configuration model. The relevance of Rydberg states is made clear.

Simple spherical, non-rotating stellar models are inadequate when describing real stars in the limit of very fast rotation: Both the observable spectrum and the geometrical shape of the star deviate strongly from simple models. We attempt…

In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…

Radial velocity surveys are beginning to reach the time baselines required to detect Jupiter analogs, as well as sub-Saturn mass planets in close orbits. Therefore it is important to understand the sensitivity of these surveys at long…

Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited…

The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to…

Instabilities and strong dynamical interactions between multiple giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities seem…

Low-thrust trajectories play a crucial role in optimizing scientific output and cost efficiency in asteroid belt missions. Unlike high-thrust transfers, low-thrust trajectories require solving complex optimal control problems. This…

Here I review recent work, by other authors and by myself, on some particular topics related to the regular and chaotic motion in elliptical galaxies. I show that it is quite possible to build highly stable triaxial stellar systems that…

It is shown herein that planets with eccentric orbits are more likely to transit than circularly orbiting planets with the same semimajor axis by a factor of (1-e^2)^{-1}. If the orbital parameters of discovered transiting planets are…

We study dynamical models for elliptical galaxies, deriving the projected kinematic profiles in a form that is valid for general surface-brightness profiles and (spherical) total mass profiles, without the need for any explicit…

The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…

We provide an 'effective theory' of tidal dissipation in extrasolar planet systems by empirically calibrating a model for the equilibrium tide. The model is valid to high order in eccentricity and parameterised by two constants of bulk…

Analytic modeling of gravitational waves from inspiraling eccentric binaries poses an interesting mathematical challenge. When constructing analytic waveforms in the frequency domain, one has to contend with the fact that the phase of the…

We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…

We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first order mean motion resonance overlap (Wisdom, 1980). We show that this criterion fits the stability regions in real exoplanet…