相关论文: A Modern Interpretation of Newton's Theorem of Rev…

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 Book 1, Proposition 7, Problem 2 of his 1687 Philosophiae Naturalis Principia Mathematica, Isaac Newton poses and answers the following question: Let the orbit of a particle moving in a central force field be an off-center circle. How…

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…

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…

This is a comment on the recent paper by G. S. Adkins and J. McDonnell ``Orbital precession due to central-force perturbations'' published in Phys. Rev. D75 (2007), 082001 [arXiv:gr-qc/0702015]. We show that the main result of this paper,…

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…

Euler's rotation theorem states that any reconfiguration of a rigid body with one of its points fixed is equivalent to a single rotation about an axis passing through the fixed point. The theorem forms the basis for Chasles' theorem which…

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…

We derive the first-order orbital equation employing a complex variable formalism. We then examine Newton's theorem on precessing orbits and apply it to the perihelion shift of an elliptic orbit in general relativity. It is found that…

We present a new simple relativistic model for planetary motion describing accurately the anomalous precession of the perihelion of Mercury and its origin. The model is based on transforming Newton's classical equation for planetary motion…

General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the…

When a test particle moves about an oblate spheroid, it is acted upon, among other things, by two standard perturbing accelerations. One, of Newtonian origin, is due to the quadrupole mass moment $J_2$ of the orbited body. The other one, of…

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure…

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…

This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic…

Each observable ballistic phenomenon of a spin-stabilized rifle bullet can be explained in terms of the acceleration of gravity and the total aerodynamic force acting on that bullet. In addition to the coning motion itself, Coning Theory…

An apparent paradox in Einstein's Special Theory of Relativity, known as a Thomas precession rotation in atomic physics, has been verified experimentally in a number of ways. However, somewhat surprisingly, it has not yet been demonstrated…

Based on Propostion 6 of his Principia, Newton's geometrical derivation in Propositions 10 and 11 for the radial dependence of the two central forces that lead to elliptical orbits is notoriously difficult. An alternate and more transparent…

The motion of rockets is part of the study devoted to the motion of variable mass systems. Notably those in which the mass leaves permanently the considered system. Rockets are propelled forward by the reaction force produced by the hot…

With consideration of quantization of space, we relate Newton's gravitation with the Second Law of thermodynamics. This leads to a correction to its original form, which takes into consideration the role of classical measurement. Our…