Classical central-force problem

<p>In classical mechanics, the central-force problem is to determine the motion of a particle in a single <a href="/facts/Central_force/WT5WWNgq">central potential field</a>. A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.  In a few important cases, the problem can be solved analytically, i.e., in terms of well-studied functions such as <a href="/facts/Trigonometric_functions/czej7ur0">trigonometric functions</a>.
</p><p>The solution of this problem is important to <a href="/facts/Classical_mechanics/ykG8upsN">classical mechanics</a>, since many naturally occurring forces are central. Examples include gravity and electromagnetism as described by <a href="/facts/Newton%27s_law_of_universal_gravitation/F6qH2XC3">Newton's law of universal gravitation</a> and <a href="/facts/Coulomb%27s_law/V0lR5NKv">Coulomb's law</a>, respectively.  The problem is also important because some more complicated problems in classical physics (such as the <a href="/facts/Two-body_problem/YCG4geSH">two-body problem</a> 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 the motion of the planets in the <a href="/facts/Solar_System/QIcLSazQ">Solar System</a>.
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Classical central-force problem open-in-new

Classical central-force problem