Lagrange Points 1 Potential Function Plot

This example demonstrates the positions and properties of Lagrange points by plotting the potential function in a multi-body gravitational system. Key math concepts include gravity, potential energy, multi-body problems, and optimization. GeoGebra commands/objects used in construction are: Max (to find maxima), Min (to find minima), uoff (offset), massrat (mass ratio), mu1, mu2 (mass parameters), d (distance), xcm (center of mass), Te (total energy), m (mass), u (potential energy), Lag4, lag3max, Lag3, lag1max, Lag1, lag2max, Lag2 (Lagrange point calculations), f1, f2, f1x, f1y, f2x, f2y (force vectors), fc, fcx, fcy (central force), fx, fy, fmag (net force magnitude), zhoz, hoz (height), umax (maximum potential energy), minlags (minimum Lagrange points), Lag5, maxlags (other Lagrange points), zscale (scaling), text1, text2, text3 (text annotations). Suitable for high school and above students studying multi-body dynamics and celestial mechanics.