相关论文: Generalized true- and eccentric-anomaly parametriz…
The perturbations of the hyperbolic motion of a test particle due to the general relativistic gravitoelectromagnetic Schwarzschild and Lense-Thirring components of the gravitational field of a rotating massive body are analytically worked…
One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg…
The generalization of Bertrand's theorem to the case of the motion of point particle on the surface of a cone is presented. The superintegrability of such models is discussed. The additional integrals of motion are analyzed for the case of…
The problem of a test body in the Schwarzschild geometry is investigated in a Keplerian limit. Beginning with the Schwarzschild metric, a solution to the limited case of approximately elliptical (Keplerian) motion is derived in terms of…
It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar…
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…
A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by…
A generalized true anomaly-type parametrization, convenient to describe both bound and open orbits of a two-body system in general relativity is introduced. A complete description of the time evolution of both the radial and of the angular…
The Gutzwiller's trace formula for the anisotropic Kepler problem is Fourier transformed with a convenient variable $u=1/\sqrt{-2E}$ which takes care of the scaling property of the AKP action $S(E)$. Proper symmetrization procedure…
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…
The manuscripts provides a novel starting guess for the solution of Kepler's equation for unknown eccentric anomaly E given the eccentricity e and mean anomaly M of an elliptical orbit.
The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A…
To estimate influence of the "dark energy" on the Keplerian orbits, we solve the general relativistic equations of motion of a test particle in the field of a point-like mass embedded in the cosmological background formed by the Lambda-term…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. The present study demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and…
The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by…
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…
Newton famously showed that a gravitational force inversely proportional to the square of the distance, $F \sim 1/r^2$, formally explains Kepler's three laws of planetary motion. But what happens to the familiar elliptical orbits if the…
The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is…
We obtain the generalized quasi-Keplerian parametrization for compact binaries on quasihyperbolic orbits at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories, extending the analogous results for quasielliptic…