Related papers: New Solutions for the Planetary Dynamics in HD1606…
The body of work presented here revolves around the investigation of the existence and nature of extra-solar planetary systems. The fitting of stellar radial velocity time series data is attempted by constructing a model to quantify the…
In this letter we report the possible existence of a second planet in the transiting extrasolar planet system HD 17156 and its interactive dynamics with the previously known planet. The analysis is achieved through the \POFP\ optimization…
Over the past years, the amount of detected multi-planet systems significantly grew, an important sub-class of which being the compact configurations. A precise knowledge of them is crucial to understand the conditions with which planetary…
We present a detailed analysis of the orbital stability of the HD 181433 planetary system, finding it to exhibit strong dynamical instability across a wide range of orbital eccentricities, semi-major axes, and mutual inclinations. We also…
We present six years of new radial-velocity data from the Anglo-Australian and Magellan Telescopes on the HD 73526 2:1 resonant planetary system. We investigate both Keplerian and dynamical (interacting) fits to these data, yielding four…
Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…
In this paper we use a Modified Newton's method based on the Continuous analog of Newton's method and high precision arithmetic for a general numerical search of periodic orbits for the planar three-body problem. We consider relatively…
If an orbit is fitted from combined RV and astrometric data, the orbit should be physically consistent with both data sets. The Keplerian orbit of a planet is a highly nonlinear function of seven parameters. The astrometric orbit problem…
The study of multiple extrasolar planetary systems has the opportunity to obtain constraints for the planetary masses and orbital inclinations via the detection of mutual perturbations. The analysis of precise radial velocity measurements…
We implement the geometric method proposed in ([9], [3], [16]) to analytically predict the sequence of bifurcations leading to a change of stability and/or the appearance of new periodic orbits in the secular 3D planetary three body…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
Satellites (topological powers) of the famous figure-eight orbit are special periodic solutions of the planar three-body problem. In this paper we use a modified Newton's method based on the Continuous analog of Newton's method and high…
We present an open-source Python package, Orbits from Radial Velocity, Absolute, and/or Relative Astrometry (orvara), to fit Keplerian orbits to any combination of radial velocity, relative astrometry, and absolute astrometry data from the…
A new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Eulerian configuration is presented. The approach is based on a symmetry property of the solutions at the half period. Depending on…
A small variation of the circular shape of the hodograph theorem states that for every elliptical solution of the two-body problem, it is possible to find an appropriate inertial frame such that the speed of the bodies is constant. We use…
We re-analyze the precision radial velocity (RV) observations of HD160691 (mu Ara) by the Anglo-Australian Planet Search Team. The star is supposed to host two Jovian companions (HD160691b, HD160691c) in long-period orbits about 630 days…
A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion ("acceleration equal force") featuring one-body and two-body velocity-dependent forces "of goldfish type" which determine the…
A new approach is presented for the problem of optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a…
We perform a dynamical analysis of the recently updated set of the radial velocity (RV) measurements of the HD160691 (mu Arae). The kinematic, 2-Keplerian model of the measurements leads to the best-fit solution in which the eccentricity of…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…