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The N1 is a bear to fly and has a tendency to flip. I found that starting the gravity turn immediately at launch helps by getting the craft heeled over to 45 degrees by the time it reached 15,000 meters. It’s inefficient and has atmospheric heating effects pushing through all that air but there is delta-V to spare. Setting SAS to prograde also helps to keep you from oversteering. Keep the Angle of Attack right at the edge of the prograde circle for the bulk of the ascent.
The third stage (Block V) is used to circularize your orbit. Shut it down and discard it just as your periapsis goes above zero and use the Block G for the last 100 m/s or so to circularize. That way you don’t leave boosters in orbit.
Set up your Munar transfer to impact the Mun. Then, turn around and activate the staging. The discarded Block G stage will crash into the Mun and a tiny thrust with RCS will adjust your trajectory to miss.
Block D is used to enter Munar orbit and for the descent of the LK module. It has a lot of fuel so don’t feel bad about using it up for a cautious landing approach.
For all the other stages that are overpowered with delta-V to spare, the LK lander has just enough fuel for it to descend from orbit and reascend to dock with the orbiting Soyuz 7K-LOK. But only if your flight path is absolutely perfect and super efficient. Better to use up the fuel in the Block D for the descent so you can return to orbit.
After rendezvous, the Soyuz 7K-LOK has plenty of fuel for the return to Kerbin. Don’t forget to EVA your scientist with the science data you collected before leaving the LK module behind.
