Question

When you jump off the earth, your momentum changes, but the Earth does not move. 1)If momentum is always conserved, why do we not feel the earth moving every time someone jumps? 2) If we were to get everyone to jump at once, could we change the momentum of the earth?

Answer 1

This question is off-base and misleading from the beginning.

When you jump off the Earth, your momentum changes, and the Earth moves away from you with an equal change of momentum in the opposite direction.

1). Momentum is conserved when you jump.  But we don't feel the Earth moving. Since the Earth's mass is a bazillion times greater than YOUR mass, the speed with which the Earth moves away from you is only one bazillionth of your speed.  That way, the product of (mass) x (speed) is the SAME for you and for the Earth, and momentum is conserved.

2). Of course !  If everyone jumped at the same time, the Earth's momentum would change.  In answer-(1), I explained that the Earth's momentum changes whenever ONE PERSON jumps.  So 7 billion people all jumping at the same time would certainly make it change.