Related papers: Description of 4 Spacecraft, Moving on Elliptic Ke…
All four dimensional orbit spaces of compact coregular linear groups have been determined. The results are obtained through the integration of a universal differential equation, that only requires as input the number of elements of an…
A small deformation controlled by four free parameters to the Schwarzschild metric could be referred to a nonspinning black hole solution in alternative theories of gravity. Because such a non-Schwarzschild metric can be changed into a…
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…
Space-based gravitational wave detection is extremely sensitive to disturbances. The Keplerian configuration cannot accurately reflect the variations in spacecraft configuration. Planetary gravitational disturbances are one of the main…
Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…
In addition to its great potential for characterizing extra-solar planetary systems the Kepler mission is providing unique data on stellar oscillations. A key aspect of Kepler asteroseismology is the application to solar-like oscillations…
Spacecraft formation flying serves as a method of astronomical instrumentation that enables the construction of large virtual structures in space. The formation-flying interferometry generally requires very-high control accuracy, and…
We show that the Kepler spacecraft in two-reaction wheel mode of operation is very well suited for the study of eclipsing binary star systems. Continued observations of the Kepler field will provide the most enduring and long-term valuable…
Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…
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…
Accurate gravity field calculations are necessary for landing on planets, moons, asteroids, minimoons, or other irregularly shaped bodies, but current methods become increasingly inaccurate and slow near the surface. We present high…
An algorithm to compute the six distances between particles of a planar Four-Body central configuration is presented according to the following schema. An orthocentric tetrahedron is computed as a function of given masses. Each mass is…
We consider a spacetime singularity at $t = 0$ arising in a Kasner-type metric that solves the gravitational equations modified by quantum effects of a conformal field theory (CFT). The resulting constraints can be solved efficiently when…
With the loss of two reaction wheels, the period of Kepler's ultra-high precision photometric performance is at an end. Yet Kepler retains unique capabilities impossible to replicate from the ground or with existing or future space…
For an algebraic number $\alpha$ we denote by $M(\alpha)$ the Mahler measure of $\alpha$. As $M(\alpha)$ is again an algebraic number (indeed, an algebraic integer), $M(\cdot)$ is a self-map on $\overline{\mathbb{Q}}$, and therefore defines…
We introduce semiclassical methods into the study of the volume spectrum in loop gravity. The classical system behind a 4-valent spinnetwork node is a Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase space and…
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the…
Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and…
In this Note, a new approach to spacecraft positioning based on GGT inversion is presented. The gravity gradient tensor is initially measured in the gradiometer reference frame (GRF) and then transformed to the Earth-Centered Earth-Fixed…