Final answer:
The Earth doesn't accelerate away when you stand on it because it exerts an equal and opposite force on you according to Newton's third law of motion, and its massive mass means the force of your weight results in negligible acceleration.
Step-by-step explanation:
When you stand on Earth, the reason the Earth doesn’t accelerate away from you, despite the force you exert on it, is primarily because the Earth exerts an equal and opposite force on you. This is in accordance with Newton's third law of motion, which states that for every action there is an equal and opposite reaction.
The Earth is also extremely massive, so the force you apply when you stand (equal to your weight) causes an incredibly small acceleration of the Earth that is not noticeable; hence the Earth seems to not move at all. We consider that F = ma, where 'F' is force, 'm' is mass and 'a' is acceleration. Given the massive mass of the Earth, the acceleration ('a') produced by the force of your weight is negligible.
When you stand on Earth, the Earth exerts a force on you due to gravity, pulling you towards it. According to Newton's third law of motion, you also exert a force on the Earth that is equal in magnitude, but opposite in direction. However, the mass of the Earth is so massive compared to your mass that the acceleration of the Earth towards you is negligible. This is why the Earth doesn't accelerate away from you.