The gravitational motion of three interacting bodies under their coupled Newtonian mechanics equations. When one body's mass is negligible, the restricted three-body problem neglects its influence on the other two while retaining both forces on its trajectory.
A trajectory whose dynamics require gravitational forces from more than one attracting body. Around a synchronously rotating moon, a maintained trajectory involving the planet–moon system is distinct from a simple moon-centred stationary Kepler orbit; the moon's Hill sphere limits the latter approximation.
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The three-body problem is a classic problem in physics and mathematics that involves predicting the motion of three celestial bodies as they interact with one another through gravitational forces. The challenge of the three-body problem arises from the fact that while the gravitational interactions between two bodies can be described by simple equations (the two-body problem), adding a third body leads to a complex and chaotic system that generally cannot be solved analytically.