Related papers: An Arc-Length Approximation For Elliptical Orbits
We present a new general, complete closed-form solution of the Stark problem in terms of Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our analysis is exact and valid for all values of the…
The manuscript establishes a series expansion of the core integral that relates changes in longitude and latitude along the geodetic line in oblate elliptical coordinates, and of a companion integral which is the path length along this line…
A class of log-trigonometric integrals are evaluated in terms of elliptic functions. From this, by using the elliptic integral singular values, one can obtain closed form evaluations of integrals such as \[…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by…
The propagation time of a signal, emitted by a moving along an elliptical orbit satellite from the GPS (or GLONASS) satellite confi gurations is a very important ingredient of the theory, based on the formalism of the null cone and…
The use of four Lagrange points of the Sun/Earth system for fundamental physics experiments in space is presented. L1, L2, L4 and L5 rotating rigidly together with the Earth form a natural reference frame at the scale of the inner solar…
We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…
The accuracy of astrometric observations conducted via a space-borne optical interferometer orbiting the Earth is expected to approach a few microarcseconds. Data processing of such extremely high-precision measurements requires access to a…
The Hill Restricted 4-Body Problem (HR4BP) is a coherent time-periodic model that can be used to represent motion in the Sun-Earth-Moon (SEM) system. Periodic orbits were computed in this model to better understand the periodic orbit family…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
We obtain $L^p(L^q)$ maximal regularity estimates for time dependent second order elliptic operators in divergence form with rough dependencies in the spatial variables.
We compute the holographic entanglement entropy of a thermalized CFT on a time-dependent background in four dimensions. We consider a slab configuration extending beyond the cosmological horizon of a Friedmann-Lemaitre-Robertson-Walker…
While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained…
We develop a theoretical framework for the calculation of orbits for a system consisting of a spherical object and a non-spherical body, which is then specialized to a prolate ellipsoid. Particular trajectories are presented that illustrate…
Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions…
The four-spacecraft formation is essential for measurements of various physical fields. The use of this formation on substantially elliptical heliocentric Kepler orbits allows measuring gradients of gravitation field in Solar system. The…
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 design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…
In this work we use intersection of different pseudo-orbits obtained by interval extensions to reduce the bounds of the exact solution provided by the toolbox Intlab. The method is applied on the logistic map.