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About 1,305 papers for “Kepler problem”

THE KEPLER PROBLEM

Jamila Alieva, Nigora Akbarova · Zenodo (CERN European Organization for Nuclear Research) · 2026

This paper examines the Kepler problem as a special case of the motion of bodies in a central force field. It presents Kepler's fundamental laws, which describe the motion of planets around the Sun, and discusses their physical meaning and significance for modern science. Particular attention is paid to the analytical solution of the two-body problem and the impossibility of obtaining an exact solution for systems with three or more bodies. In this regard, numerical methods for solving equations of motion are considered, specifically the use of the MATLAB environment for modeling orbital motion. An algorithm is presented for reducing a system of differential equations to first-order form and their subsequent numerical solution. The paper emphasizes the importance of the Kepler problem for the development of astronomy, mechanics, and space exploration.

Cited by 0Open access

Linearized Kepler problem

BENTHAM SCIENCE PUBLISHERS eBooks · 2010

Our first objective is to reformulate the age-old problem of a satellite orbiting a primary (of a substantially bigger mass) by means of quaternion algebra.1 In subsequent chapters, this will facilitate a relatively simple construction of the problem’s iterative solution. Here we also review some details of constructing the unperturbed solution.

Cited by 0

THE KEPLER PROBLEM

Jamila Alieva, Nigora Akbarova · Zenodo (CERN European Organization for Nuclear Research) · 2026

This paper examines the Kepler problem as a special case of the motion of bodies in a central force field. It presents Kepler's fundamental laws, which describe the motion of planets around the Sun, and discusses their physical meaning and significance for modern science. Particular attention is paid to the analytical solution of the two-body problem and the impossibility of obtaining an exact solution for systems with three or more bodies. In this regard, numerical methods for solving equations of motion are considered, specifically the use of the MATLAB environment for modeling orbital motion. An algorithm is presented for reducing a system of differential equations to first-order form and their subsequent numerical solution. The paper emphasizes the importance of the Kepler problem for the development of astronomy, mechanics, and space exploration.

Cited by 0Open access

The Kepler problem

Bruno Cordani · 2002

In this chapter, we will study the group-geometrical structure of the Kepler problem and point out how this structure also turns out to be useful in the study of the perturbed case.

Cited by 34

The Kepler Problem

Bruno Cordani · Birkhäuser Basel eBooks · 2003

Because of the correspondences existing among all levels of reality, truths pertaining to a lower level can be considered as symbols of truths at a higher level and can therefore be the "foundation" o

Cited by 73Open access

SOLVING THE KEPLER PROBLEM

Steven C. Frautschi, Richard P. Olenick, Tom M. Apostol et al. · Cambridge University Press eBooks · 1986

Therefore, during the whole time of their appearance, comets fall within the sphere of activity of the circumsolar force, and hence are acted upon by its impulse and therefore (by Corollary 1, Proposition XII) describe conic sections that have their foci in the center of the sun, and by radii drawn from the sun describe areas proportional to the times. For that force propagated to an immense distance, will govern the motions of bodies far beyond the orbit of Saturn.Isaac Newton, Principia (1687)

Cited by 0

Kepler and his problem

Τ. Padmanabhan · 2009

The major contribution of Kepler was in discovering his laws of planetary motion, one of which states that planets move in elliptical orbits around the Sun which is located at one of the foci of the ellipse. The motion of a test particle in an inverse square force law is usually called the Kepler problem. We will examine several aspects of this motion in this last installment of Snippets in Physics.

Cited by 1

The Universal Kepler problem

Rare & Special e-Zone (The Hong Kong University of Science and Technology) · 2014

Elsevier’s Scopus, the largest abstract and citation database of peer-reviewed literature. Search and access research from the science, technology, medicine, social sciences and arts and humanities fields.

Cited by 0

Planetary orbits - the Kepler problem

Stammberger, W. · OpenGrey (Institut de l'Information Scientifique et Technique)

Copy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informationsbibliothek

Cited by 0

Perturbations of the Kepler Problem

Bruno Cordani · Birkhäuser Basel eBooks · 2003

In this chapter we study the perturbations of the Kepler problem, i.e., the motion of a particle with mass m and Hamiltonian $$H(\vec{Q},\vec{P}) = \frac{1}{{2m}}{{P}^{2}} - \frac{k}{Q} + \varepsilon {{H}_{p}}(\vec{Q},\vec{P}),$$ where $${{H}_{p}}(\vec{Q},\vec{P})$$ the perturbation Hamiltonian and E a dimension-less, “small” parameter. The canonical variables $$\vec{Q},\vec{P}$$ differ from the previously defined, $$\vec{q},\vec{p}$$ and $$\vec{x},\vec{y}$$ by resealing factors; see (12.1.3) and Remark 12.2 below.

Cited by 1

On the inverse Kepler problem

Jean Sivardière · European Journal of Physics · 1985

Much useful information-and not only the inverse square law force-can be extracted from Kepler's law. A very simple treatment is proposed.

Cited by 9