Related papers: Long-term planetary integration with individual ti…
In this paper we present our results of numerical integrations of orbits of fictive massless particle in vicinity of resonance. Our goal is to study the dependences of period (frequency) of resonance perturbations and the width of the…
The method of choice for integrating the equations of motion of the general N-body problem has been to use an individual time step scheme. For the sake of efficiency, block time steps have been the most popular, where all time step sizes…
A large sample of planet-planet scattering events for three planet systems with different orbital separations and masses is analyzed with a multiple regression model. The dependence of the time for the onset of instability on the masses of…
(Abridged) The probability of detecting additional companions is essentially unchanged with respect to the single-planet configurations, but after fitting and subtraction of orbits with astrometric signal-to-noise ratio $\alpha/\sigma_d\to…
Long-term integrations of asteroid orbits with high-accuracy numerical integrators are essential for understanding dynamical evolution and ejection from the Solar System, but are computationally expensive. Here, we investigate the dynamical…
Numerical integrations of the Solar System reveal a remarkable stability of the orbits of the inner planets over billions of years, in spite of their chaotic variations characterized by a Lyapunov time of only 5 million years and the lack…
We analyse the potential migration of massive planets forming far away from an inner planetary system. For this, we follow the dynamical evolution of the orbital elements of a massive planet undergoing a dissipative process with a gas disc…
We present a method to study the time variation of the orbital parameters of a Post-Keplerian binary system undergoing a generic external perturbation. The method is the relativistic extension of the planetary Lagrangian equations. The…
We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. We use the symplectic integrator SyMBA to numerically…
We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm. By use of correctable algorithms, we show that the…
We study numerically classical 1-dimensional Hamiltonian lattices involving inter-particle long range interactions that decay with distance like 1/r^alpha, for alpha>=0. We demonstrate that although such systems are generally characterized…
In nominal mission scenarios, geostationary satellites perform end-of-life orbit maneuvers to reach suitable disposal orbits, where they do not interfere with operational satellites. This research investigates the long-term orbit evolution…
The {\it Kepler} mission has detected thousands of planetary systems with 1-7 transiting planets packed within 0.7~au from their host stars. There is an apparent excess of single-transit planet systems that cannot be explained by transit…
Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. These…
In early Solar System numerical simulations, where chaos is a primary driver, it is difficult to explore parameter space in a systematic way. In such simulations, stable configurations are hard to come by, and often require special…
Perturbative Post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the Parameterized Post-Newtonian theoretical framework. The results obtained are applied to the…
The core of every orbit determination process is the comparison between the measured observables and their predicted values, computed using the adopted mathematical models, and the minimization, in a least square sense, of their…
Kepler will monitor a sufficient number of stars that it is likely to detect single transits of planets with periods longer than the mission lifetime. We show that by combining the exquisite Kepler photometry of such transits with precise…
In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such a degeneracy is removed when a post-Keplerian perturbing acceleration enters…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…