Related papers: From Kepler's laws to Newton's law: a didactical p…
An interpretation of selected parts of Newton's Principia, with modern notation and methods. Keplers Laws are derived from an inverse square law using Newton's methods.
We explain the solution of the following two problems: obtaining of Kepler's laws from Newton's laws (so called two bodies problem) and obtaining the fourth Newton's law (the formula for gravitation) as a corollary of Kepler's laws. This…
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…
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…
Newtonian gravity can be regarded as a hypothetic-deductive system where the inverse square law is the starting point from which gravitational phenomena are deduced. This operational form of presenting gravity endorses problem solving and…
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…
In elementary particle physics the philosophy of virtual particles is widely used. We use this philosophy to obtain the famous inverse square law of classical physics. We define a formal model without fields or forces, but with virtual…
Kepler's laws are derived from the inverse square law without the use of calculus and are simplified over previous such derivations.
Newton's "superb theorem" for the gravitational inverse-square-law force states that a spherically symmetric mass distribution attracts a body outside as if the entire mass were concentrated at the center. This theorem is crucial for…
The main purpose of this paper is to seek a mechanical interpretation of gravitational phenomena. We suppose that the universe may be filled with a kind of fluid which may be called the $\Omega (0)$ substratum. Thus, the inverse-square law…
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…
As scientific knowledge expands, science education may not always keep pace with the latest advancements in astrophysics. A solid scientific education is crucial for preparing students for 21st-century challenges. However, science education…
Newton's theorem of revolving orbits states that one can multiply the angular speed of a Keplerian orbit by a factor $k$ by applying a radial inverse cubed force proportional to $(1-k^2)$. In this paper we derive an extension of this…
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…
In this contribution it is shown that the path from Kepler's results to Newtonian motion can be remarkably short and simple. Following this path we also give a straight forward computation of the direction angle of Hamilton's Hodograph.…
We present a new approach to quantum gravity starting from Feynman's formulation for the simplest example, that of a scalar field as the representative matter. We show that we extend his treatment to a calculable framework using resummation…
We propose an interpretation of the Newton's second law that is suggested by Galilean Relativity theory.
In this paper, I outline some problems in the students' understanding of the explanation of recoil motion when introduced to them in the context of Newton's third law. I propose to explain the origin of recoil from a microscopic point of…
Newton's Principia is famous for its investigations of the inverse square force law for gravity. But in this book Newton also did something that remained little-known until fairly recently. He figured out what kind of central force exerted…
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…