Related papers: Kepler's Differential Equations
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…
In this work we present a close correlation between third Kepler law and Titius-Bode empirical rule. Concretely, we demonstrate that third Kepler law, or, corresponding equilibrium condition between centrifugal and Newtonian gravitational…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
In 1687, Sir Issac Newton published The Mathematical Principles of Natural Philosophy in which the law of universal gravitation was derived. It is the first inverse-square law discovered in nature, combined with Coulomb's law in 1785, the…
The foundations of Statistical Mechanics can be recovered almost in their entirety from the Principle of Maximum Entropy. In this work we show that its non-equilibrium generalization, the Principle of Maximum Caliber (Jaynes, 1980), when…
Similarities between the non-deterministic nature of quantum theory and the unpredictable patterns of human cognition and decision making have been observed and commented on many times since the invention of Quantum Mechanics in the first…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential…
A succinct chronology is given around Nov 1915, when the explicit field equations of General Relativity have been found. Evidence, unearthed by D.Wuensch, that a decisive document of Hilbert has been mutilated in recent years with the…
We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian…
Closed-form differential equations, including partial differential equations and higher-order ordinary differential equations, are one of the most important tools used by scientists to model and better understand natural phenomena.…
Euler wrote several papers on Astronomy, most of them in Latin. This is a commented translation of E304 'Considerationes de motu corporum coelestium' (Considerations on the motion of celestial bodies). In this publication, Euler essentially…
Wave functions are generally written with arguments consisting of sets of ``particle'' coordinates and quantum numbers. Pauli derived a principle governing the exchange of pairs of sets that differ only in their spatial and spin component…
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…
On incorporating special relativity theory into an extended equivalence principle, post-Newtonian gravitational phenomena beyond that originally predicted by Einstein are predicted (required), such as geodetic and gravitomagnetic…
Newton's laws of motion pose an apparent problem, sometimes referred to as "the independence problem": the first law seems to be a simple consequence of the second law, raising the question of why it was included as a separate law. Numerous…
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between…
I relate some coefficients encountered when computing the functional determinants on spheres to the central differentials of nothing. In doing this I use some historic works, in particular transcribing the elegant symbolic formalism of…
Armed with an astrolabe and Kepler's laws one can arrive at accurate estimates of the orbits of planets.
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…