Related papers: A generalization of the equinoctial orbital elemen…
The Product of Exponentials (PoE) formulation is most commonly used in the field of robotics, but has recently been adapted for use in describing orbital motion. The PoE formula for orbital mechanics is an alternate method for defining and…
We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We study the effect of quantum and relativistic corrections to the gravitational potential of a primary body acting on…
As gravity is a long-range force, one might a priori expect the Universe's global matter distribution to select a preferred rest frame for local gravitational physics. At the post-Newtonian approximation, two parameters suffice to describe…
Ab initio calculations face the challenge of describing a complex multiscale quantum many-body system. The nuclear wave function has both strong short-range correlations and long-range contributions. Natural orbitals provide a means of…
The rosette-shaped motion of a particle in a central force field is known to be classically solvable by quadratures. We present a new approach of describing and characterizing such motion based on the eccentricity vector of the two body…
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the…
In General Relativity, the rotation of a gravitating body like the Earth influences the motion of orbiting test particles or satellites in a non-Newtonian way. This causes, e.g., a precession of the orbital plane known as the Lense-Thirring…
The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if…
The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is…
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…
We consider the motion of uncharged dust grains of arbitrary shape including the effects of electromagnetic radiation and thermal emission. The resulting relativistically covariant equation of motion is expressed in terms of standard…
Mapping exoplanets across phases and during secondary eclipse is a powerful technique for characterizing Hot Jupiters in emission. Since these planets are expected to rotate about axes normal to their orbital planes, with rotation periods…
We consider gravitational scattering of point particles with Planckian centre-of-mass energy and fixed low momentum transfers in the framework of general relativity and dilaton gravity. The geometry around the particles are modelled by…
We study the axial gravitational perturbations of slowly-rotating compact objects which are assumed to be supported by anisotropic fluids. We find that the gravitational perturbations decouple from the matter perturbations for axial…
The force acting on a test particle moving around a body that is gravitating and emitting electromagnetic radiation at the same time is computed up to the second order in $1/c$, and the shift of perihelion is found. The total shift is…
Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited…
When we are fortunate enough to view an exoplanetary system nearly edge-on, the star and planet periodically eclipse each other. Observations of eclipses (transits and occultations) provide a bonanza of information that cannot be obtained…
Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system, and led also to the discovery of chaos in modern science. Nowadays, in light of general relativity,…
The elements of the E\"otv\"os matrix are useful for various geodetic applications, such as the interpolation of the elements of the deflection of the vertical, the determination of gravity anomalies and the determination of geoid heights.…
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…