[derobert]

I'm pretty sure that said hypothetical impact can't exist. The object either has far too little energy to significantly change its orbit, or alternatively has enough energy but there is nothing moon-like left after that collision.

The moon has a mass of 7.349×10²² kg. Its mean orbital velocity is 1023m/s. So, with a perfectly-aligned impact, and perfect efficiency, to add velocity, you'd need to add energy equal to difference in kinetic energy. For 1m/s, that'd be 10²⁵J (assuming the change in mass is negligible). That's an incredible amount of energy, about 20 times greater than the Chicxulub impact (believed to have triggered the mass extinctions at the K-T boundary).

That's 1 m/s. You need far more than that. Earth escape velocity is 11200m/s. So, that would seem to need 10³⁰ J. And an impact would deliver that in well under a minute. Which would be a problem, since that's an order of magnitude greater than the gravitational binding energy of the moon.

Conclusion: impact required would fully obliterate moon.

(Moon mass and velocity, and escape velocity from http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html. Gravitational binding energy and estimate of Chicxulub from Wolfram Alpha)