What (very simply) is a lagrangian point?

Answer 1

A Lagrange point is one of five in an orbit of a small object around a larger one that is also affected by a second massive object. Each of these points is where the small object's orbit is stable due to the balance of the gravitational forces of the two larger objects, such that the small object orbits precisely with them in the equivalent of a geosynchronous orbit.

Answer 2

The Lagrangian points (pronounced [ləˈgɹɒn.dʒi.ən] or [laˈgʀɑ̃.ʒjɑ̃]); also Lagrange point, L-point, or libration point), are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with respect to the Earth and Moon). The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to rotate with them. They are analogous to geosynchronous orbits in that they allow an object to be in a "fixed" position in space rather than an orbit in which its relative position changes continuously.

A more precise but technical definition is that the Lagrangian points are the stationary solutions of the circular restricted three-body problem. For example, given two massive bodies in circular orbits around their common center of mass, there are five positions in space where a third body, of comparatively negligible mass, could be placed which would then maintain its position relative to the two massive bodies. As seen in a frame of reference which rotates with the same period as the two co-orbiting bodies, the gravitational fields of two massive bodies combined with the centrifugal force are in balance at the Lagrangian points, allowing the third body to be stationary with respect to the first two bodies.

Answer 3

Try searching wikipedia - they have a good answer.