相关论文: The Kepler problem and non commutativity
The possibility of measuring the post-Newtonian gravitoelectric correction to the orbital period of a test particle freely orbiting a spherically symmetric mass in the Solar System is analyzed. It should be possible, in principle, to detect…
After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly…
Anisotropic Kepler problem is investigated by perturbation method in both classical and quantum mechanics. In classical mechanics, due to the singularity of the potential, global diffusion in phase space occurs at an arbitrarily small…
A deformed Bianchi type I metric in noncommutative gauge gravity is obtained. The gauge potential (tetrad fields) and scalar curvature are determined up to the second order in the noncommutativity parameters. The noncommutativity correction…
Atmospheric neutrinos at low energies, $E \lsim 500$ MeV, is known to be a rich source of information of lepton mixing parameters. We formulate a simple perturbative framework to elucidate the characteristic features of neutrino oscillation…
Non-Keplerian dynamics of planetary orbits manifest in the transit light-curve as variations of different types. In addition to Transit Timing Variations (TTV's), the shape of the transits contains additional information on variations in…
In this paper, the suggested similarity between micro and macro-cosmos is extended to quantum behavior, postulating that quantum mechanics, like general relativity and classical electrodynamics, is invariant under discrete scale…
We use cosmological perturbation theory to study the backreaction effects of a self-consistent and well-defined cosmological averaging on the dynamics and the evolution of the Universe. Working with a perturbed…
The connection between Lorentz invariance violation and noncommutativity of fields in a quantum field theory is investigated. A new dispersion relation for a free field theory with just one additional noncommutative parameter is obtained.…
Cosmological perturbations of sufficiently long wavelength admit a fluid dynamic description. We consider modes with wavevectors below a scale $k_m$ for which the dynamics is only mildly non-linear. The leading effect of modes above that…
The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…
The Kepler mission provides an exciting opportunity to study the lightcurves of stars with unprecedented precision and continuity of coverage. This is the first look at a large sample of stars with photometric data of a quality that has…
Context. The Sun and solar-like stars undergo activity cycles for which the underlying mechanisms are not well understood. The oscillations of the Sun are known to vary with its activity cycle and these changes provide diagnostics on the…
Light curve modulations in the sample of Kepler planet candidates allows the disentangling of the nature of the transiting object by photometrically measuring its mass. This is possible by detecting the effects of the gravitational pull of…
We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of…
Every theory that modifies gravity at cosmological distances and that is not already ruled out by the Solar system observations must exhibit some nonlinear mechanism that turns off the modification close to a compact matter source. Given…
Inflation predicts that quantum fluctuations determine the large scale structure of the Universe. This raises the striking possibility that quantum mechanics, developed to describe nature at short distances, can be tested by studying nature…
We study relativistic Kepler problems in the plane. At first, using non-smooth critical point theory, we show that under a general time-periodic external force of gradient type there are two infinite families of T-periodic solutions,…
In a previous work, we developed the idea to solve Kepler's equation with a CORDIC-like algorithm, which does not require any division, but still multiplications in each iteration. Here we overcome this major shortcoming and solve Kepler's…
We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative…