Mun capture
As soon as the vehicle entered the Mun's sphere of influence (the region where the Mun's gravity dominates), the orbital insertion maneuver was setup:
Coming in along a fast hyperbolic path that would lead the vehicle to escape the Mun's gravity again, a burn at Mun periapsis was required to enter a stable orbit around a Mun.
There was some last-minute debate about the altitude of the final circular orbit. If the current periapsis altitude of 60 km was kept, only one circularization burn would be needed. This was good since the Lunar Module's weight still had to be carried by the Command Module's engine.
However, 60 km is considerably high for the Mun, and the Lunar Module would've needed to cover the extra altitude with its own fuel on its way back.
So, in the end a 30 km orbit was decided (for reference, the delta-v maps figures are for a lower orbit, 14 km); this would require two circularization burns but the CM had fuel to spare. The kerbonauts were finally in stable orbit around the Mun!
Oh, what a sight!
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