Related papers: Optimizing the Ptolemaic Model of Planetary and So…
In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…
The problem of fitting concentric ellipses is a vital problem in image processing, pattern recognition, and astronomy. Several methods have been developed but all address very special cases. In this paper, this problem has been investigated…
In previous papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. We considered systems with well separated components and different initial…
Construction of a theory of orbits about a precessing oblate planet, in terms of osculating elements defined in a frame of the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2005, 2006). We now combine that…
The calculation of the trajectories in the Sun-Earth-Mars system will be performed in two different models, both in the framework of Newtonian mechanics. First model is well-known Copernican system, which assumes the Sun is at rest and all…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
Spider millisecond pulsars are, along with some eclipsing post-common envelope systems and cataclysmic variables, part of an expanding category of compact binaries with low-mass companions for which puzzling timing anomalies have been…
Cosmology can be viewed as geodesic motion in an appropriate metric on an `augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application, we find some exact (flat and curved)…
Studies of future space- and ground-based exoplanet surveys often rely on models of planetary systems to simulate instrument response, estimate scientific yields, perform trade analyses, and study efficient observation strategies. Until…
Starting with an entropy that includes volumetric, area and length terms as well as logarithmic contributions, we derive the corresponding modified Newtonian gravity and derive the expression for planetary orbits. We calculate the shift of…
The complexity and accuracy of current and future precision cosmology observational campaigns has made it essential to develop an efficient technique for directly combining simulation and observational datasets to determine cosmological and…
Euler wrote several papers on Astronomy, most of them in Latin. This is a commented translation of E304 'Considerationes de motu corporum coelestium' (Considerations on the motion of celestial bodies). In this publication, Euler essentially…
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…
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
In this paper we study the orbits of massive bodies moving in the spacetime generated by a spherically symmetric and non-rotating distribution of mass. More specifically, our treatment discusses the more accurate calculation of the…
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
A metric-field approach to gravitation is presented. It is based on an idea of dependency of space-time properties on measuring instruments. Some bimetric equations that realize this idea are considered. They were tested by the binary…
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We…
Several different factors influence the seasonal cycle of a planet. This study uses a general circulation model and an energy balance model (EBM) to assess the parameters that govern the seasonal cycle. We define two metrics to describe the…
The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. The corresponding corrections must be…