Related papers: Numerical behavior of the Keplerian Integral metho…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
Observations of the Kuiper Belt indicate that a larger than expected percentage of KBO's (approximately 8 out of 500) are in binary pairs. The formation and survival of such objects presents a conundrum [1]. Two competing theories have been…
The Doppler technique measures the reflex radial motion of a star induced by the presence of companions and is the most successful method to detect exoplanets. If several planets are present, their signals will appear combined in the radial…
If an orbit is fitted from combined RV and astrometric data, the orbit should be physically consistent with both data sets. The Keplerian orbit of a planet is a highly nonlinear function of seven parameters. The astrometric orbit problem…
Short-period super-Earths and mini-Neptunes encircle more than $\sim50\%$ of Sun-like stars and are relatively amenable to direct observational characterization. Despite this, environments in which these planets accrete are difficult to…
We investigate the distributions of the orbital period ratios of adjacent planets in high multiplicity \kepler\ systems (four or more planets) and low multiplicity systems (two planets). Modeling the low multiplicity sample as essentially…
Numerical solutions of Kepler's Equation are critical components of celestial mechanics software, and are often computation hot spots. This work uses symbolic regression and a genetic learning algorithm to find new initial guesses for…
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…
We present a simple method for determination of the orbital parameters of binary pulsars, using data on the pulsar period at multiple observing epochs. This method uses the circular nature of the velocity space orbit of Keplerian motion and…
We investigated the underlying architecture of planetary systems by deriving the distribution of planet multiplicity (number of planets) and the distribution of orbital inclinations based on the sample of planet candidates discovered by the…
We introduce a new method to perform preliminary orbit determination for space debris on low Earth orbits (LEO). This method works with tracks of radar observations: each track is composed by $n\ge 4$ topocentric position vectors per pass…
We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are…
We consider different choices of Keplerian conservation laws for the computation of preliminary orbits with two very short arcs (VSAs) of astrometric observations. In total we have 7 equations in 4 unknowns. Adding two auxiliary variables…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…
An elementary proof of Kepler's first law, i.e. that bounded planetary orbits are elliptical, is derived without the use of calculus. The proof is similar in spirit to previous derivations, in that conservation laws are used to obtain an…
Knowledge of the orbits of visual binary stars has always been one of the fundamentals of astronomy. Based historically on the visual measures, nowadays the orbits rely more (or exclusively) on the accurate speckle data. This prompts…
The mutual orbital alignment in multiple planetary systems is an important parameter for understanding their formation. There are a number of elaborate techniques to determine the alignment parameters using photometric or spectroscopic…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are…