Three-body Orbits show four three-body orbits. The Euler example shows a special solution determined by Euler in which all three masses always lie on a straight line. The Lagrange example shows a special solution determined by Lagrange in which the objects maintain a geometric relationship to each other as vertices of a polygon. In this case, the three objects are always at the vertices of an isosceles triangle (whose sides can change length). The Montgomery example shows a stable orbit of three objects that orbit each other in a figure-eight pattern with all three objects tracing out the exact same orbital trajectory. The Restricted Three-body example shows an example of this class of exactly-solvable problems. Two objects with the same mass are in orbit around each other. A third, much less massive, object also orbits, following one object around its orbit.