There are scores of books that give simple Newtonian orbital mechanics. I have several, but right now I'm using one called "Vector Mechanics for Engineers: Dynamics", by Beer and Johnston. In Chapter 12, the development for orbital mechanics is found. I used this book because it makes the simplifying assumption that the orbiting particle's mass is negligible compared to the orbited body, which is true in our case. Equation 12.27 gives the orbital tangential velocity for a circular orbit:

vcirc = sqroot(GM/r0), where:

G is the gravitational constant 6.673x10 raised to the -11 nm2/kg2,

M is the mass of the body, 7.349x10 raised to the 22 kg for the moon,

and r0 is the altitude above the center of mass of the body.

Soving for r0, and subtracting the equatorial radius of the moon (1737.4 km) we get an orbital altitude of 141.87 km. If we want to know the orbital velocity at the equatorial surface of the moon, we use 1737.4 km for r0 and solve for vcirc = 1.6801 km/s = 5512 fps.

Note that these results are for orbital tangential velocity, not for a case where the gun is aimed above the horizon.