Related papers: Numerical behavior of the Keplerian Integral metho…

We present results from high-resolution, optical to near-IR imaging of host stars of Kepler Objects of Interest (KOIs), identified in the original Kepler field. Part of the data were obtained under the Kepler imaging follow-up observation…

We present a method for calculating precise distances to asteroids using only two nights of data from a single location --- far too little for an orbit --- by exploiting the angular reflex motion of the asteroids due to Earth's axial…

We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e., constants of the unperturbed…

Since the late 1950s, when the first artificial satellite was launched, the number of Resident Space Objects has steadily increased. It is estimated that around one million objects larger than one cm are currently orbiting the Earth, with…

Reparameterization from the standard set of orbital elements to Cartesian position-velocity vectors can be computationally advantageous for orbit inference problems, particularly when orbital elements are weakly constrained. Here we present…

Here we show how to determine the orbital parameters of a system composed of a star and N companions (that can be planets, brown-dwarfs or other stars), using a simple Fourier analysis of the radial velocity data of the star. This method…

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…

In a Keplerian system, a large number of bodies orbit a central mass. Accretion disks, protoplanetary disks, asteroid belts, and planetary rings are examples. Simulations of these systems require algorithms that are computationally…

The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could have both…

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…

Long-term integrations of asteroid orbits with high-accuracy numerical integrators are essential for understanding dynamical evolution and ejection from the Solar System, but are computationally expensive. Here, we investigate the dynamical…

Orbit-determination programs find the orbit solution that best fits a set of observations by minimizing the RMS of the residuals of the fit. For near-Earth asteroids, the uncertainty of the orbit solution may be compatible with trajectories…

Analyzing the available photometry from the Kepler satellite and other databases, we performed detailed light curve modeling of 10 eclipsing binary systems that were found to exhibit a periodic modulation of their orbital periods. All of…

A mathematical model is given for the occurrence of preferred orbits and orbital velocities in a Keplerian system. The result can be extended into energies and other properties of physical systems. The values given by the model fit closely…

In this article, theory-based analytical methodologies of astrophysics employed in the modern era are suitably operated alongside a test research-grade telescope to image and determine the orbit of a near-earth asteroid from original…

Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…

We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is…

In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…

The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the…

Proper elements are quasi-integrals of motion, meaning that they can be considered constant over a certain timespan, and they permit to describe the long-term evolution with a few parameters. Near-Earth objects (NEOs) generally have a large…