Related papers: Generalization of a method by Mossotti for initial…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter…
The numerical optimized shooting method for finding periodic orbits in nonlinear dynamical systems was employed to determine the existence of periodic orbits in the well-known R\"ossler system. By optimizing the period $T$ and the three…
The problem of estimating the angular speed of a solid body from attitude measurements is addressed. To solve this problem, we propose an observer whose dynamics are not constrained to evolve on any specific manifold. This drastically…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
In this paper we introduce an algorithm for determining the orbital elements and individual masses of visual binaries. The algorithm uses an optimal point, which minimizes a specific function describing the average length between the…
As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the…
Using the ellipsoidal model for the density configuration, we calculate the equilibrium sequence of the corotating binary stars of the polytropic equation of state in the first post-Newtonian approximation of general relativity. After we…
This paper proposes a dynamic analytical initialization method for spacecraft attitude estimators. In the proposed method, the desired attitude matrix is decomposed into two parts: one is the constant attitude matrix at the very start and…
We investigate the behaviour of two recent methods for the computation of preliminary orbits. These methods are based on the conservation laws of Kepler's problem, and enable the linkage of very short arcs of optical observations even when…
The orbital magnetic moment of a Co adatom on a Pt(111) surface is calculated in good agreement with experimental data making use of the LSDA+U method. It is shown that both electron correlation induced orbital polarization and structural…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
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…
A continuous solution is proposed to the problem of uniform global exponential estimation of the angular velocity for rigid bodies by means of direct attitude measurements. The proposed observer is designed on…
This paper presents a unique approach to the problem of calculating revisit time metrics for different satellite orbits, sensor geometries, and constellation configurations with application to early lifecycle design and optimisation…
This paper develops a robust optimization based method to design orbits on which the sensory perception of the desired physical quantities are maximized. It also demonstrates how to incorporate various constraints imposed by many spacecraft…
We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe…
We describe a new iteration method to estimate asteroid coordinates, which is based on the subpixel Gaussian model of a discrete object image. The method operates by continuous parameters (asteroid coordinates) in a discrete observational…
Relying on the equivalence principle, a first approach of the general theory of relativity is presented using the spacetime metric of an observer with a constant proper acceleration. Within this non inertial frame, the equation of motion of…
We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular…