Lagrange point (source code)

= Lagrange point
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A <Lagrange point> is a stationary position in the rotating frame of the <circular restricted three-body problem>. The two primaries' <gravitational forces> and the <centrifugal force> balance there. Their gravitational pulls alone need not cancel.

Three <Collinear Lagrange points> lie on the line through the primaries; two <Triangular Lagrange points> complete equilateral triangles with them. Stability requires the full rotating-frame equations, including the <Coriolis force>. The collinear equilibria are unstable, while the triangular equilibria are linearly stable for a sufficiently small secondary mass fraction. Spacecraft can use nearby trajectories with stationkeeping; an equilibrium calculation alone does not make a spacecraft remain there.<The Lagrange Points by Neil J. Cornish>[pp. 1–4: rotating-frame equilibria; pp. 5–8: linear stability and its mass-ratio condition]{ref}