相关论文: The Kepler problem and non commutativity

The stellar obliquity of a transiting planetary system can be constrained by combining measurements of the star's rotation period, radius, and projected rotational velocity. Here we present a hierarchical Bayesian technique for recovering…

In this paper we present noncommutative version of scalar field cosmology. We find the noncommutative Friedmann equations as well as the noncommutative Klein-Gordon equation. Interestingly the noncommutative contributions are only present…

The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a…

The true- and eccentric-anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A…

We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales…

The model of the Universe in this paper uses equations of the unperturbed Keplerian motion. They have been updated, complementied and generalized when the solution of these equations is the characteristic function of a random value from the…

It is shown that quantum uncertainty of motion in systems controlled mainly by gravity generally grows with orbital timescale $H^{-1}$, and dominates classical motion for trajectories separated by distances less than $\approx H^{-3/5}$ in…

An heuristic semiclassical procedure that incorporates quantum gravity induced corrections in the description of photons and spin 1/2 fermions is reviewed. Such modifications are calculated in the framework of loop quantum gravity and they…

Usually we consider the symmetry of action as the symmetry of the theory, however, in the Keplar problem the scaling symmetry existing in equa tion of motion is not the ones for action. It changes the multiplicative c onstant of action and…

Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form,…

Noncommutative solitons are easier to find in a noncommutative field theory. Similarly, the one-loop quantum corrections to the mass of a noncommutative soliton are easier to compute, in a real scalar theory in 2+1 dimensions. We carry out…

The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses…

The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the Heisenberg group, thought of as a three-dimensional sub-Riemannian manifold. The sub-Riemannian Hamiltonian provides the kinetic energy, and the…

We examine the equant model for the motion of planets, which has been the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for…

It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…

Dynamical similarities are non-standard symmetries found in a wide range of physical systems that identify solutions related by a change of scale. In this paper we will show through a series of examples how this symmetry extends to the…

Our experience shows that dealing with noncommutative objects one should not imitate the classical commutative mathematics, but follow "the way it is" starting with basics. In this paper we consider mainly two such problems: noncommutative…

Many multiple-planet systems have been found by the Kepler transit survey and various radial velocity (RV) surveys. Kepler planets show an asymmetric feature, namely, there are small but significant deficits/excesses of planet pairs with…

We study a classical, noncommutative (NC), Friedmann-Robertson-Walker cosmological model. The spatial sections may have positive, negative or zero constant curvatures. The matter content is a generic perfect fluid. The initial…

We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do…