Editing Lagrange point (section)

==={{L4|nolink=yes}} and {{L5|nolink=yes}}===
{{Further|Trojan (celestial body)}}

The reason these points are in balance is that at {{L4|nolink=yes}} and {{L5|nolink=yes}} the distances to the two masses are equal. Accordingly, the gravitational forces from the two massive bodies are in the same ratio as the masses of the two bodies, and so the resultant force acts through the [[Barycentric coordinates (astronomy)|barycenter]] of the system.  Additionally, the geometry of the triangle ensures that the [[Parallelogram law|resultant]] acceleration is to the distance from the barycenter in the same [[ratio]] as for the two massive bodies. The barycenter being both the [[center of mass]] and center of rotation of the three-body system, this resultant force is exactly that required to keep the smaller body at the Lagrange point in orbital [[Dynamic equilibrium|equilibrium]] with the other two larger bodies of the system (indeed, the third body needs to have negligible mass). The general triangular configuration was discovered by Lagrange working on the [[three-body problem]].