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A simple general relativity theory for objects moving in gravitational fields is developed based on studying the behavior of an atom in a gravitational field. The theory is applied to calculate the satellite time dilation, light deflection…
Most attempts to unify general relativity with the standard model of particle physics predict violations of the equivalence principle associated in some way with the composition of the test masses. We test this idea by using observational…
Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using…
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…
The gravitational action of the smooth energy-matter components filling in the universe can affect the orbit of a planetary system. Changes are related to the acceleration of the cosmological scale size R. In a universe with significant…
Even though the original Kepler mission ended due to mechanical failures, the Kepler satellite continues to collect data. Using classification models, we can understand the features exoplanets possess and then use those features to…
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,…
Most of the logical objections against the classical laws of motion, as they are usually presented in textbooks, centre on the fact that defining force in terms of mass and acceleration, the first two laws are mere assertions of concepts to…
Planet formation models have been developed during the last years in order to try to reproduce the observations of both the solar system, and the extrasolar planets. Some of these models have partially succeeded, focussing however on…
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…
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on…
A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections in the quantum dynamics governing many-particle systems in a gravitational field. Here we…
We will make the case that \textit{pedal coordinates} (instead of polar or Cartesian coordinates) are more natural settings in which to study force problems of classical mechanics in the plane. We will show that the trajectory of a test…
Within the context of Newton's theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable…
We derive a simple analytical expression for the two-body force in a sub-class of MOND-like theories and make testable predictions in the modification to the two-body orbital period, shape, and precession rate, and escape speed etc. We…
Aristotle has split physics at the sphere of the moon; above this sphere there is no change except eternal spherical motion, below are two different kinds of motion: Natural motion (without specific cause) and enforced motion. In modern…
A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by…
Numerical simulations are playing an increasingly important role in modern science. In this work it is suggested to use a numerical study of the famous perihelion motion of the planet Mercury (one of the prime observables supporting…
The trajectory and the orbital velocity are determined for an object moving in a gravitational system, in terms of fundamental and independent variables. In particular, considering a path on equipotential line, the elliptical orbit is…