Related papers: Mass distributions for the Kepler problem
We derive the equations of celestial mechanics governing the variations of the orbital elements under a stochastic perturbation generalizing the classical Gauss equations. Explicit formulas are given for the semi-major axis, the…
We discuss the influence of the cosmological constant on the gravitational equations of motion of bodies with arbitrary masses and eventually solve the two-body problem. Observational constraints are derived from measurements of the…
The main effects of the Earth's oblateness on the motion of artificial satellites are usually derived from the variation of parameters equations of an average representation of the oblateness disturbing function. Rather, we approach their…
The widespread prevalence of close-in, nearly coplanar super-Earth- and sub-Neptune-sized planets in multiple-planet systems was one of the most surprising results from the Kepler mission. By studying a uniform sample of Kepler "multis"…
In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can easily…
The orbital parameter space of wide, weakly bound binary stars has been shaped by the still poorly known circumstances of their formation, as well as by subsequent dynamical evolution in parent clusters and in the field. The advance of the…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
The space-time features of the relativistic dynamics are analyzed in the framework of the time dependent propagator theory. The adiabatic hypothesis is substituted by the disturbative adiabatic hypothesis, resulting with the corresponding…
We add to the lore of spherical, stellar-system models a two-parameter family with an anisotropic velocity dispersion, and a central point mass (``black hole''). The ratio of the tangential to radial dispersions, is constant--and…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
One of the fundamental tasks of dynamical astronomy is to infer the distribution of mass in a stellar system from a snapshot of the positions and velocities of its stars. The usual approach to this task (e.g., Schwarzschild's method)…
We discuss some aspects related to the so-called Hilbert space Average Method, as an alternative to describe the dynamics of open quantum systems. First we present a derivation of the method which does not make use of the algebra satisfied…
We present a mathematical method to statistically decouple the effects of unknown inclination angles on the mass distribution of exoplanets that have been discovered using radial-velocity techniques. The method is based on the distribution…
We consider dynamical effects of additional perturbative forces due to the non-point mass nature of stars and planets: effects such as quadrupolar distortion and tidal friction in the systems of exo-planets. It is shown that these forces…
The high-multiplicity exoplanet systems are generally more tightly packed when compared to the solar system. Such compact multi-planet systems are often susceptible to dynamical instability. We investigate the impact of dynamical…
The study of the interior of the planets requires the knowledge of how certain parameters, as radius and mean density, vary according to the planet mass. The aim of this work is to use known data of the Solar System Planets and Transiting…
We derive a formula for the velocity distribution of an axially symmetric galaxy where the mass density is corrected using the mass formula from special relativity. We take some reasonable test mass densities and numerically compute the…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…