Everything about Two-body Problem totally explained
In
classical mechanics, the
two-body problem is to determine the motion of two point particles that interact only with each other. Common examples include a
satellite orbiting a
planet, a
planet orbiting a
star, two
stars orbiting each other (a
binary star), and a classical
electron orbiting an
atomic nucleus.
The two-body problem can be re-formulated as two independent
one-body problems, which involve solving for the motion of one particle in an external
potential. Since many one-body problems can be solved exactly, the corresponding two-body problem can also be solved. By contrast, the
three-body problem (and, more generally, the
-body problem for
) can't be solved, except in special cases.
Statement of problem
Let
, and a straight line for
.
This inverse-square law case of the two-body problem is called the
Kepler problem.
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