It's not even guaranteed to be a straight line if you drop it, due to variations in the density of different parts of the moon, radiation pressure, particles in

It's not even guaranteed to be a straight line if you drop it, due to variations in the density of different parts of the moon, radiation pressure, particles in the way (yes, the vacuum isn't absolute), any magnetic effects, gravitational gradient caused by other celestial bodies, etc. The arc will approximate a conic section of some kind, depending on how hard you throw it. Within the usual level of ability of a space-suited human throw, it will approximate to an ellipse so close to parabolic as to be impossible to tell the difference before it hits the moon. Throw it harder and it'll approximate to an ellipse. You are only going to be able to approximate a circle if you stand on the highest point on the Moon and throw at exactly the circular orbital speed horizontally, although gravitational perturbations will usually break the orbit. It'll approximate a parabola if you throw at exactly the escape velocity, and a hyperbola if you throw even harder than that.