Newton's Laws - Pushing on a heavy object

Einstein

I'm trying to understand if a really heavy object on earth, say a mountain, would move if I push it with my bare hands. This sounds absurd but according to Newton's Laws, if I push against the mountain it will exert an equal and opposite force. I understand there are other forces like gravity and friction involved but does it mean that me pushing on it will effectively move the mountain and because of the astronomical difference in the mass between me and the mountain, the effect will be infinitesimally small? or is it that there will be absolutely zero displacement?

Drakkith

You will be pushing on the mountain, which will exert a force back on you, and all you will end up doing is moving a little bit of dirt around as you hands and feet slide around. Other than the dirt there will be no displacement because the mountain is part of the ground and is held there through atomic/molecular forces. If you were both floating in space and you pushed off the mountain then both you and the mountain would begin to move apart.

Nugatory

How about running this experiment on a really heavy object, in fact the most massive object on earth? That most massive object is... The earth itself!

All you need to to do is to jump. Your feet are pushing on the earth, and the earth is pushing back with an equal and opposite force. The force of the earth pushing against your feet will throw you into the air (how high can you jump?). Meanwhile your feet pushing on the earth will move it ever so slightly in the opposite direction. How slightly? Well for reasonable assumptions about your weight and strength, maybe 10^-21 centimeters, which is well and thoroughly undetectable.

So to answer your question: not truly zero, but infinitesimally small.