What is "two-body problem"

n. 1 The problem of find the motion, relative to one another, of two objects, where the position of each affects the motion of the other. 2 (context humorous English) The problem of obtaining employment for two people who wish to reside near one another.

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 (although to solve the electron/nucleus 2-body system correctly a quantum mechanical approach must be used).

The two-body problem can be re-formulated as two one-body problems, a trivial one and one that involves 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 n-body problem for n ≥ 3) cannot be solved in terms of first integrals, except in special cases.

The two-body problem is a dilemma for life partners (for e.g. spouses or any other couple) in academia, relating to the difficulty of both spouses obtaining jobs at the same university or within a reasonable commuting distance from each other. The central dilemma is thus a no-win situation in which if the couple wishes to stay together one of them may be forced to abandon an academic career, or if both wish to pursue academic careers the relationship may falter due to the spouses being constantly separated. The term "two body problem" has been used in the context of working couples since at least the mid-1990s. It alludes to the insolvable three-body problem in classical mechanics.

More than 70 percent of academic faculty have a working partner, while more than a third of faculty have an academic partner.