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Astronomers have constructed models of globular clusters for over 100 years. These models mainly fall into two categories: (i) static models, such as King's model and its variants, and (ii) evolutionary models. Most attention has been given…
Most methods of orbit determination are often difficult for numerical implementations since they are developed before the computer era. The recently developed mathematical technique of semi-definite programming (SDP) has been implemented…
A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schr\"{o}dinger equation for this system is obtained. These constraint conditions are now allowed to depend not…
In previous works, entropic gravity and ungravity have been considered as possible solutions to the dark energy and dark matter problems. To test the viability of these models, modifications to planetary orbits are calculated for ungravity…
The study of circular orbits in spacetime is of astrophysical importance. The identification and classification of circular orbits in both static and stationary spacetimes remains an active area of interest. Even in the simplest static…
We numerically investigate the orbital dynamics of a spacecraft, or a comet, or an asteroid in the Pluto-Charon system in a scattering region around Charon using the planar circular restricted three-body problem. The test particle can move…
The analysis of the spatial distribution and kinematics of galaxies in clusters allows one to determine the cluster internal dynamics. In this paper, I review the state of the art of this topic. In particular, I summarize what we have…
In this paper, a surface geometric constraint approach is used in designing the orbits of a solar sail. We solve the solar sail equation of motion by obtaining a generalized Laplace-Runge-Lenz (LRL) vector with the assumption that the cone…
This paper introduces a novel and general algorithm for approximately counting the number of orbits under group actions. The method is based on combining the Burnside process and importance sampling. Specializing to unitriangular groups…
An impressive amount of different astrophysical data converges towards the picture of a spatially flat universe undergoing a today phase of accelerated expansion. The nature of the dark energy dominating the energy content of the universe…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has…
We propose to use a simple observable, the fractional area of "hot spots" in weak gravitational lensing mass maps which are detected with high significance, to determine background cosmological parameters. Because these high-convergence…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
Making mock simulated catalogs is an important component of astrophysical data analysis. Selection criteria for observed astronomical objects are often too complicated to be derived from first principles. However the existence of an…
The knowledge of the redshift of multiple images in cluster-lenses allows to determine precisely the total projected mass within the Einstein radius. The observation of various multiple images in a same cluster is opening new possibilities…
In spite of the promise of new techniques for constraining the mass distribution in galaxy clusters, much remains to be learned from galaxy orbital velocities. This article reviews the theory of potential estimation in hot dynamical systems…
Redshift distortions, both geometrical and kinematical, of quasar clustering are simulated, for the Two-Degree Field QSO Redshift Survey (2QZ), showing that they are very effective to constrain the cosmological density and equation of state…
Knowing the conserved quantities that a galaxy's stellar orbits conform to is important in helping us understand the stellar distribution and structures within the galaxy. Isolating integrals of motion and resonances are particularly…
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…