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Novel method for semi-analytical solving of equations of a trapped dynamics for a planetoid m4 close to the plane of mutual motion of main bodies around each other (in case of a special type of Bi-Elliptic Restricted 4-Bodies Problem) is…
In the case of a constant uniform magnetic field it can be assumed, without the loss of generality, that the vector potential (the gauge) is a linear function of position, i.e. it could be considered as a three-dimensional real matrix or,…
A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near asteroids are very…
A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…
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…
Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large…
A metric-field approach to gravitation is presented. It is based on an idea of dependency of space-time properties on measuring instruments. Some bimetric equations that realize this idea are considered. They were tested by the binary…
The Solar System Odyssey mission uses modern-day high-precision experimental techniques to test the laws of fundamental physics which determine dynamics in the solar system. It could lead to major discoveries by using demonstrated…
Oscillations occur in stars of most masses and essentially all stages of evolution. Asteroseismology is the study of the frequencies and other properties of stellar oscillations, from which we can extract fundamental parameters such as…
A point mass at the center of an ellipsoidal homogeneous fluid is used as a simple model to study the effect of rotation on the shape and external gravitational field of planets and stars. Maclaurin's analytical result for a homogenous body…
LETSGO (LEnse-Thirring Sun-Geo Orbiter) is a proposed space-based mission involving the use of a spacecraft moving along a highly eccentric heliocentric orbit perpendicular to the ecliptic. It aims to accurately measure some important…
The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. The corresponding corrections must be…
The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…
This white paper discusses a repurposed mission for the Kepler spacecraft that focusses on solving outstanding problems in planet formation and evolution by targeting the study of the hot Jupiter population of young stars. This mission can…
We discuss the leading term in the semi-classical asymptotics of Newtonian quantum gravity for the Kepler problem. For dark matter, ice or dust particles in the gravitational field of a star or massive planet this explains how rapidly…
We define and analyze the photometric orbit (PhO) of an extrasolar planet observed in reflected light. In our definition, the PhO is a Keplerian entity with six parameters: semimajor axis, eccentricity, mean anomaly at some particular time,…
We investigate the motion in space of an infinitesimal particle in the gravitational field generated by three primary bodies positioned at the vertices of a fixed equilateral triangle. We assume that the distances between the primaries are…
Collisionless N-body simulations of merging disk-galaxies with mass ratios ($\eta$) of 1:1, 2:1, 3:1, and 4:1 have been performed using direct summation with the special purpose hardware GRAPE. The simulations are used to examine whether…
The nearby (50 pc) K7V dwarf HIP~41431 (EPIC 212096658) is a compact 3-tier hierarchy. Three K7V stars with similar masses, from 0.61 to 0.63 solar, make a triple-lined spectroscopic system where the inner binary with a period of 2.9 days…
The Kepler Mission, launched on Mar 6, 2009 was designed with the explicit capability to detect Earth-size planets in the habitable zone of solar-like stars using the transit photometry method. Results from just forty-three days of data…