Thank you, the screen shot is exactly what I experienced.
About the Lagrange points, if I recall correctly my space dynamic university course (alas, 20 years have gone by) you can't in any case orbit around them like you orbit around a mass. If you are at the stable one you stay fixed at it, with some slight oscillation around it dampened by the gravity itself. The point is located somewhere between the main and secondary body, and if you assume as fixed the main body, you see the L point travelling around it together with the secondary body (L1 leading, L2 trailing) . So, if you are at L1, you are actually travelling around the maon body. This is actually been thought of by Nasa to locate a base between earth and moon to prepare the launch to Mars, but actually been discarded because of all the debris that a stable L point tends to collect. If you are at L2 (the unstable one) you don't otbit around it either. You freefall on one side ore the other, entering a normal orbit around the main or secobdary body.