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The problem is also important because some more complicated problems in classical physics (such as the two-body problem with forces along the line connecting the two bodies) can be reduced to a central-force problem. Finally, the solution to the central-force problem often makes a good initial approximation of the true motion, as in calculating ...
In the classical central-force problem of classical mechanics, some potential energy functions () produce motions or orbits that can be expressed in terms of well-known functions, such as the trigonometric functions and elliptic functions. This article describes these functions and the corresponding solutions for the orbits.
1 Classical physics. 2 General relativity. ... There are several types of central-force problems, ... Schwarzschild solution, ...
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details
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 that varies in strength as the inverse square of the distance between them. The force may be either attractive or repulsive.
The problem of two fixed centers conserves energy; in other words, the total energy is a constant of motion.The potential energy is given by =where represents the particle's position, and and are the distances between the particle and the centers of force; and are constants that measure the strength of the first and second forces, respectively.
Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.
In particle physics, the most important hierarchy problem is the question that asks why the weak force is 10 24 times as strong as gravity. [10] Both of these forces involve constants of nature, the Fermi constant for the weak force and the Newtonian constant of gravitation for gravity.