Related papers: Kepler's laws with introduction to differential ca…
This article studies the application of the Jacobi-Eisenhart lift, Jacobi metric and Maupertius transformation to the Kepler system. We start by reviewing fundamentals and the Jacobi metric. Then we study various ways to apply the lift to…
This is a translation from Latin of E348 'Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi', in which Euler develops a method to alleviate the astronomical computations in a typical…
A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with…
One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and…
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…
Starting from the action function, we have derived a theoretical background that leads to the quantization of gravity and the deduction of a correlation between the gravitational and the inertial masses, which depends on the kinetic…
Based on the kinetic energy theorem, as one of the fundamental theorems from the classical mechanics, throughout the first part of the article an attempt has been made to derive the mathematical model of a material point motion in the…
A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way…
This is a pedagogical paper which explains some ideas in cosmology at a level accessible to undergraduate students. It does not use general relativity, but uses the ideas of Newtonian cosmology worked out by Milne and McCrea. The…
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…
We show that a slowly varying Newton's constant, consistent with existing bounds, can potentially explain a host of observations pertaining to gravitational effects or phenomena across distances spanning from planetary to the cosmological,…
A generalization of the Kepler's third law has been proposed by BoHua Sun for $N$-body periodic orbits in a Newtonian gravitation field. In this paper, it is shown that this formula can apply for a quantum system of $N$ self-gravitating…
We start with the cosmic Friedmann equations, where we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that…
I review the elementary theory of gravitational waves on a Minkowski background and the quadrupole approximation. The modified conservation laws for energy and momentum keeping track of the gravitational-wave flux are presented. The theory…
Kepler's first law states that the orbit of a point mass with negative energy in a classical gravitational potential is an ellipse with one of its foci at the gravitational center. In numerical simulations of this system one often observes…
The fact that mass has an effect on surrounding space is the first essential element of general relativity. This paper unifies this mass/space distinction of general relativity with Newtonian gravity at a subatomic scale and with reported…
In this short letter we calculate separately the generalized uncertainty principle (GUP) and self gravitational corrections to the Newton's gravitational formula. We show that for a complete description of the GUP and self-gravity effects,…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
We construct a general relativity formula for the law of gravity for material bodies. The formula contains three numeric parameters that are to be determined experimentally. If they are chosen from symmetry considerations, then the theory…
We derive an action whose equations of motion contain the Poisson equation of Newtonian gravity. The construction requires a new notion of Newton--Cartan geometry based on an underlying symmetry algebra that differs from the usual Bargmann…