Computing Lagrange points L1-L3

Detailed computation and discussion of Lagrange Points L1-L3 and a few words about L4-L5.

The placement of the JWST (Hubble follow-on telescope) at Lagrange Point L2 has increased interest in these unusual points in space. They were first mentioned by Euler and carefully analyzed by Lagrange as part of a restricted 3-body problem. The advantage of L2 is that objects there will naturally orbit the Sun at the same speed as Earth, which in turn keeps the orbiting objects "close to home".

The January 2022 Scientific American presented a diagram and explanation of the L2 placement. This is my response to that presentation. I expect my function to be read by people and exectuted by MATLAB, perhaps at the same time using DBSTEP. The bottom line is the various distances involved.