Thus we have reduced the two-body problem to that of one body.

An example of this is the two-body problem with circular orbits.

Any classical system of two particles is, by definition, a two-body problem.

The centripetal force is provided by gravity, see also two-body problem.

Kepler's laws apply only in the limited case of the two-body problem.

In this case, the problem is simplified to the two-body problem.

And these only work for the simple situation of one electron and the nucleus (two-body problems).

This is called a two-body problem, or an unperturbed Keplerian orbit.

Even the two-body problem becomes insoluble if one of the bodies is irregular in shape.

Specific relative angular momentum plays a pivotal role in the analysis of the two-body problem.

This changes the three-body problem into a restricted two-body problem.

This is an important concept in the fields of astronomy, astrophysics, and the like (see two-body problem).

Simple two-body problems, for example, can be solved analytically.

And then there was the two-body problem.

Reduced mass occurs in a multitude of two-body problems, where classical mechanics is applicable.

In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other.

Solving the equation for r(t) is the key to the two-body problem; general solution methods are described below.

Note on uniqueness for a one-dimensional two-body problem of classical electrodynamics.

The Stumpff functions, used in the universal variable formulation of the two-body problem, are named after him.

Imagine the two of them tumbling about each other in the classic two-body problem of astrophysics.

"Most court cases are a two-body problem.

See centrifugal force, two-body problem, orbit and Kepler's laws of planetary motion.

In the more general case where the bodies need not be a large one and a small one (the two-body problem), we define:

When this method is applied to the two-body problem without restriction on their masses, the result is remarkably simple.

It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem.