Related papers: Keplers's Equation and Angular Momentum: Historica…
We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical…
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…
In this introductory review article, we explore the special relativistic equations of particle motions and the consequent derivation of Einstein's famous formula $E=mc^2$. Next, we study the special relativistic electromagnetic field…
The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the Hyperbolic plane. First, the theory of central potentials on spaces of constant curvature is studied. All the…
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…
We summarize a recent work on the title subject, skipping the detailed calculations but introducing the basic points with enough detail. The theory considered is formulated in a preferred reference frame in a four-dimensional spacetime…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…
Motion of a point mass in gravitational fields of the Sun and of the galactic disk is studied. Fundamental features of the motion are found by investigating the time-averaged differential equations for orbital evolution. Several types of…
The motion of binary star systems is re-examined in the presence of perturbations from the theory of general relativity. The Kepler problem is regularized and linearized with quaternions. In this way first order perturbation results are…
We derive Copernicus's epicycles from Newton's gravitational force law by assuming that a planet's orbit is a perturbed circular orbit, with the perturbation defined to be co-rotating with the said orbit. We substitute this orbit expression…
We show that when we work with coordinate cosmic time, which is not proper time, Robertson-Walker's metric, includes a possible rotational state of the Universe. An exact formula for the angular speed and the temporal metric coefficient, is…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
We analytically work out the long-term, i.e. averaged over one orbital revolution, time variations of some direct observable quantities Y induced by classical and general relativistic dynamical perturbations of the two-body pointlike…
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 consider a geodesic flow on a compact manifold endowed with a Riemannian (or Finsler, or Lorentz) metric satisfying some generic, explicit conditions. We couple the geodesic flow with a time-dependent potential, driven by an external…
Poincar\'e's work more than one century ago, or Laskar's numerical simulations from the 1990's on, have irrevocably impaired the long-held belief that the Solar System should be stable. But mathematical mechanisms explaining this…
The effect of the expanding universe on planetary motion is considered to first order in the Hubble constant H. Orbital elements are shown to be unaffected, but there is a small change in the connection between planetary proper time and…
The meaning and significance of Mach's Principle and its dependence on ideas about relativistic rotating frame theory and the celestial sphere is explained and discussed. Two new relativistic rotation transformations are introduced by using…
The conjecture is considered that every body induces the wave field which imposes oscillations on the gravitational potential of a body. The function for oscillations is chosen to prevent the gravitational collapse of the matter at the…