Related papers: A general stability-driven approach for the refine…
The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We…
Insufficient instrument thermo-mechanical stability is one of the many roadblocks for achieving 10cm/s Doppler radial velocity (RV) precision, the precision needed to detect Earth-twins orbiting Solar-type stars. Highly temperature and…
Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that…
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…
An automatic Bayesian Kepler periodogram has been developed for identifying and characterizing multiple planetary orbits in precision radial velocity data. The periodogram is powered by a parallel tempering MCMC algorithm which is capable…
We know that planetary systems are just as common around white dwarfs as around main sequence stars. However, self-consistently linking a planetary system across these two phases of stellar evolution through the violent giant branch poses…
To obtain explicit understanding of the behavior of dynamical systems, geometrical methods and slow-fast analysis have proved to be highly useful. Such methods are standard for smooth dynamical systems, and increasingly used for continuous,…
Recent observational campaigns have shown that multi-planet systems seem to be abundant in our Galaxy. Moreover, it seems that these systems might have distant companions, either planets, brown-dwarfs or other stellar objects. These…
More than 450 exoplanets are known and this number increases nearly every day. Only a few constraints on their orbital parameters and physical characteristics can be determined, as most exoplanets are detected indirectly. Measuring the…
The three-planet extrasolar system of HD 181433 has been detected with HARPS. The best-fit solution, announced by the discovery team, describes a highly unstable, self-disrupting configuration. In fact, a narrow observational window, only…
Many of the multi-planet systems discovered to date have been notable for their compactness, with neighbouring planets closer together than any in the Solar System. Interestingly, planet-hosting stars have a wide range of ages, suggesting…
Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method and its variants have been the most widely-used approaches for such systems, but are either confined to low-order approximations or…
The angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criteria to constrain the orbital architectures for exoplanetary systems.…
Population studies of the orbital characteristics of exoplanets in multi-planet systems have highlighted the existence of an anticorrelation between the average orbital eccentricity of planets and the number of planets of their host system,…
We present new radial velocities from Keck Observatory and both Newtonian and Keplerian solutions for the triple-planet system orbiting HD 37124. The orbital solution for this system has improved dramatically since the third planet was…
Inferring planetary parameters from transit timing variations is challenging for small exoplanets because their transits may be so weak that determination of individual transit timing is difficult or impossible. We implement a useful…
Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique…
Planetary systems with multiple giant planets provide important opportunities to study planetary formation and evolution. The HD 45364 system hosts two giant planets that reside within the Habitable Zone (HZ) of their host star and was the…
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.…
Uncovering the formation process that reproduces the distinct properties of compact super-Earth exoplanet systems is a major goal of planet formation theory. The most successful model argues that non-resonant systems begin as resonant…