# Acceleration to enter into orbit around the Moon

I know that the escape velocity of the Moon is of 2.38 km/s. That is the velocity required to put any object of any size or mass out of the gravitational effect of the Moon (correct me if anything I am saying is wrong). My question is: what acceleration would be required to put any object in orbit around the Moon, not out of the Moon's gravitational influence? Also: what would be the required height and momentum of an object to orbit around the Moon for long period of time?

I think you mean what velocity is required to put an object in orbit. Well that can be a complicated question. But assuming you want to be in a circular orbit, the formula is simply $v = \sqrt{\frac{GM}{r}}$ This is when centrifugal acceleration matches the acceleration due to gravity.You can orbit at several distances that's the "r" in the formula, the distance from the center of the moon. G is the gravitational constant. M is the mass of the moon. You should read up on "Orbital Mechanics." In light of Chris' answer, I'd like to mention the velocity I'm referring to would be the burnout velocity. The final velocity at height(r) tangent to the moon that would be needed for that orbit. How exactly you accelerate and get to that point requires a more complicated transfer ellipse when leaving from the surface via spacecraft.