The answer of Damon is close to what I have in mind, never mentioned in the "orthodox" , or rather conventional thoughts of the bulk. That was my point 2 in the first answer. If you somehow added a 10cm/sec or 0,1m/sec vector towards earth, you would think this is small but would have devastating effects in the course of a thousand years, which is more familiar to our timescale.
People are used to say huh.. what's the mass of the moon ah ~10^22 kg,
wait what it is its speed ahhh about 10^3m/sec, soooo you would have to
add about 10^ 28 joules to the kinetic energy of the moon, right?
WRONG! This is what happens when you reiterate answers "taught" and not looking scholastically into the details. (Been caught myself doing exactly that many times) You can put just 10^22 or 10^21 joules to the kinetic energy of the moon in such a direction that the moon would acquire a lateral velocity vector of about say 1m/sec or 0.1 m/sec. This would be enough to move the moon the equivalent of its current distance from the earth towards that lateral direction in the course of 100 to 1000 years.
And some would say: now If I had infinite money and time, sure why not. Pointing sarcastically to the fact that it maybe theoretically possible, but not practically, because it would require much time and money, right?
VERY WRONG AGAIN! Thank you very much. The "megatonnage" of the nuclear arsenal
of just 2 countries developed in practically 2 decades by Russia and U.S.A. was about 12 000 megatons or about 5x 10^19 joule. But people this was an arms race half a century ago. Now the whole planet is into building nukes and with a better know-how, meaning much shorter times building a certain amount of destructive power and far more powerful warheads.
If an arms race were to break out again be sure , the "superpowers"(U.S.A., Russia, China, U.K. Canada, Australia France, Korea,Iran, Pakistan , India etc)
would build 10^ 22 "joules of destruction" in far less than a century with a hardly noticeable effect on their budgets, or alternatively they could build the same force in 150 or 200 years, seemingly a lot but nothing in the grand scope of things.
So, can we build enough nukes to change the course of the moon or other heavenly bodies. Sure it's a certain stretch but very doable within the capacities of the current technology.
P.S. The release of the 10^22 joules by an explosion would not necessarily mean that this would translate into a velocity to a certain direction. The help of a supercomputer would be needed in calculating distance and other parameters so we would maximally utilize this energy as motion.