Related papers: Revisiting Kepler's Laws of Equal Areas and Ellips…
The Earth itself is not stationary but keeps revolving, and its motion further satisfies the law of equal area according to the heliocentric doctrine. That satisfaction can be used to construct the mathematical relationships between the…
Newton's deduction of the inverse square law from Kepler's ellipse and area laws together with his "superb theorem" on the gravitation attraction of spherically symmetric bodies, are the major steps leading to the discovery of the law of…
In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can easily…
After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly…
An elementary proof of Kepler's first law, i.e. that bounded planetary orbits are elliptical, is derived without the use of calculus. The proof is similar in spirit to previous derivations, in that conservation laws are used to obtain an…
Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that…
In this article, we review the main results of Volume I of Newton's Principia which relates Kepler's law of planets and universal gravitation. In order to clarify the reasoning of Newton, elementary and simple proofs are given to inspire…
An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed…
We examine the equant model for the motion of planets, which has been the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for…
Kepler's laws of planetary motion are deduced from those of a harmonic oscillator following Arnold. Conversely, the circular orbits through the Earth's center suggested by Galilei are consistent with an $r^{-5}$ potential as found before by…
The law of centripetal force governing the motion of celestial bodies in eccentric conic sections, has been established and thoroughly investigated by Sir Isaac Newton in his Principia Mathematica. Yet its profound implications on the…
The Equivalence Principle (EP) is at the heart of General Relativity (GR), tested in many aspects. It is often used to discuss qualitatively the influence of gravity on physical phenomena. But can this be made more precise? We compare clock…
It is shown that a recent result regarding the average rate of evolution of a dynamical system at equilibrium in combination with the quantization of geometric areas coming from LQG, implies the validity of Kepler's Second Law of planetary…
Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls…
With only five photographs of the Sun at different dates we show that the mass of Sun can be calculated by using a telescope, a camera, and the Kepler's third law. With these photographs we are able to calculate the distance between Sun and…
The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a…
Kepler's 2nd law, the law of the areas, is usually taught in passing, between the 1st and the 3rd laws, to be explained "later on" as a consequence of angular momentum conservation. The 1st and 3rd laws receive the bulk of attention; the…
The true- and eccentric-anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A…
The Kepler map was derived by Petrosky (1986) and Chirikov and Vecheslavov (1986) as a tool for description of the long-term chaotic orbital behaviour of the comets in nearly parabolic motion. It is a two-dimensional area-preserving map,…
We present a natural proof of Kepler's law of ellipses in the spirit of Euclidean geometry. Moreover we discuss two existing Euclidean geometric proofs, one by Feynman in hist Lost Lecture from 1964 and the other by Newton in the Principia…