Related papers: The true and eccentric anomaly parametrizations of…
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…
The angular and the radial parts of the dynamics of the perturbed Kepler motion are separable in many important cases. In this paper we study the radial motion and its parametrizations. We develop in detail a generalized eccentric anomaly…
Observations of astrophysical binaries may reveal departures from pure Keplerian orbits due to environmental influences, modifications to the underlying gravitational dynamics, or signatures of new physics. In this work, we develop a…
Compact binaries consisting of neutron stars / black holes on eccentric orbit undergo a perturbed Keplerian motion. The perturbations are either of relativistic origin or are related to the spin, mass quadrupole and magnetic dipole moments…
The radial component of the motion of compact binary systems composed of neutron stars and/or black holes on eccentric orbit is integrated. We consider all type of perturbations that emerge up to second post-Newtonian order. These…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
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 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…
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…
The motion of binary star systems is re-examined in the presence of perturbations from the theory of general relativity. The Kepler problem is regularized and linearized with quaternions. In this way first order perturbation results are…
We investigate perturbations in the Kepler problem. We offer an overview of the dynamical system using Newtonian, Lagrangian and Hamiltonian Mechanics to build a foundation for analyzing perturbations. We consider the effects of a…
The pulsar timing residuals induced by gravitational waves from non-evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will fully analyze the…
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.
A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…
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 orbital motion of a binary system is characterized by various characteristic temporal intervals which, by definition, are different from each other: the draconitic, anomalistic and sidereal periods. They all coincide in the Keplerian…
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…
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…
We revisit the Ligon--Schaaf regularization of the Kepler problem and identify the geometric origin of the rotation appearing in their transformation. We show that this rotation is determined by the eccentric anomaly of the Kepler motion,…
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…