what is the Most efficient munar takeoff and return?

[Krenn]

I know of at least two ways to take of from the mun and return to kerbin, assuming you start on the far side of the mun.

my prefferred method is to take off and aim due west, aiming for an escape orbit with a perigee of about 2 kilometers, which shows a final path roughly parallel to, but in the opposite direction of, the mun\'s orbit.

once i shut of the engines, the movement of the mun updates that escape orbit, so it actually alters course \'in\' towards kerbin, and when i leave the mun\'s sphere of influence, I\'m usually on an elliptical orbit, which either impacts kerbin, or passes very close by.

The other method i\'ve heard of involves setting up a 5 km stable orbit EAST, passing in front of the mun\'s orbit. Then you set your course to 40 degrees up pitch when you cross the muns orbit, turn SAS on, and wait until your nose touches the horizon: THEN burn to return to kerbin.

Does anyone know which is more fuel efficient?

[Hypocee]

If I\'m any guide you\'re going to get some bogus answers regarding free-return trajectories assuming an eastward Kerbin launch, which are the lowest-energy overall. Disregarding how you got to the mün and orbital legacies of the Apollo Lunar Orbit Rendezvous architecture, I believe an eastward orbit is theoretically more efficient since its angular momentum both opposes the mün\'s orbital momentum for minimum energy to Kerbin and coincides with its (utterly, utterly negligible) rotational momentum for minimum energy to münar orbit.

I can tell you with much more confidence that the ideal burn takes place at the point in münar orbit exactly opposite Kerbin, and that it doesn\'t actually have to be displayed as an escape trajectory - it only needs to be an ellipse that\'ll take you farther than the münar sphere of influence. The latter part will be much more apparent when conics get patching.

[dashcunning]

The idea behind the 40° thing was to get your trajectory leaving the Mun to be as close to opposite the Mun\'s motion as possible. Which should give you very little velocity relative to Kerbin. Which should result in a highly elliptical orbit that requires very little to get into the atmosphere. And I figured eastwards was better since the Mun is rotating eastwards, giving you some help. But as Hypocee said, it\'s pretty much meaningless. I arrived at 40° below the horizon and 800 m/s @ 5km through trial and error. There\'s no more math or theory behind it than that.