Related papers: Kepler's laws without calculus
Conservation laws are formulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples. The formulation does not…
We illustrate a simple derivation of the Schrodinger equation, which requires only knowledge of the electromagnetic wave equation and the basics of Einstein's special theory of relativity. We do this by extending the wave equation for…
There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson…
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the…
We discuss the numerous advantages of using dimensionless equations in non-relativistic quantum mechanics. Dimensionless equations are considerably simpler and reveal the number of relevant parameters in the models. They are less prone to…
By a suitable transformation, we derive the rotating Goedel universe from a static one and we show, how rotation may be implemented geometrically. The rotation law turns out to be a differential one. By increasing distance from the rotation…
The Kepler's third law is a relation between the period and the energy of two classical particles interacting via a gravitational potential. Recent works showed that this law could be extended, at least approximately, to classical…
It is shown that Kepler problem in deformed (quantum) four-dimensional space in non relativistic limit is integrable in quadratures. In non relativistic limit group of motion of quantum space coincide with Galilei one.
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…
The Kepler problem is a physical problem about two bodies which attract each other by a force proportional to the inverse square of the distance. The MICZ-Kepler problems are its natural cousins and have been previously generalized from…
This article presents simple and easy proofs of the Implicit Function Theorem and the Inverse Function Theorem, in this order, both of them on a finite-dimensional Euclidean space, that employ only the Intermediate Value Theorem and the…
Derivations of Borns Rule are of interest because they tell us what's connected to what in quantum mechanics if we ever need to change or modify it.
We classify gentle algebras defined by quivers with two cycles under derived equivalence in a non degenerate case, by using some combinatorial invariants constructed from the quiver with relations defining these algebras. We also present a…
Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from…
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the…
The critics of P. Lipavsky on the derivation of conservation laws including gradient corrections is refuted since his counterexample is based on a mathematical error. Instead, the derived conservation laws for density, momentum and energy…
The equations for a self-similar solution of an inviscid incompressible fluid are mapped into an integral equation which hopefully can be solved by iteration. It is argued that the exponent of the similarity are ruled by Kelvin's theorem of…
In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
The effect of the cosmological constant on the curvature of light due to an isolated spherical mass is recalculated without using the lens equation and compared to a lensing cluster.