This article is about a special case of the two-body problem in classical mechanics. For the problem of finding the densest packing of spheres in three-dimensional Euclidean space, see Kepler conjecture.
In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force F that varies in strength as the inverse square of the distance r between them. The force may be either attractive or repulsive. The problem is to find the position or speed of the two bodies over time given their masses, positions, and velocities. Using classical mechanics, the solution can be expressed as a Kepler orbit using six orbital elements.
The Kepler problem is named after Johannes Kepler, who proposed Kepler's laws of planetary motion (which are part of classical mechanics and solved the problem for the orbits of the planets) and investigated the types of forces that would result in orbits obeying those laws (called Kepler's inverse problem).[1]
For a discussion of the Kepler problem specific to radial orbits, see Radial trajectory. General relativity provides more accurate solutions to the two-body problem, especially in strong gravitational fields.
^Goldstein, H. (1980). Classical Mechanics (2nd ed.). Addison Wesley.
In classical mechanics, the Keplerproblem is a special case of the two-body problem, in which the two bodies interact by a central force F that varies...
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional...
\theta _{0})} is the initial coordinate of the particle. The traditional Keplerproblem of calculating the orbit of an inverse square law may be read off from...
Johannes Kepler (/ˈkɛplər/; German: [joˈhanəs ˈkɛplɐ, -nɛs -] ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer...
said to be a solution of a special case of the two-body problem, known as the Keplerproblem. As a theory in classical mechanics, it also does not take...
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between the two sheets a "bridge". — A. Einstein, N. Rosen, "The Particle Problem in the General Theory of Relativity" For the combined field, gravity and...
motion of bodies in an orbit'), which provided a physical justification for Kepler's laws of planetary motion. Halley was impressed by the manuscript and urged...
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