Final answer:
The acceleration of the earth towards the apple is negligible due to the earth's significantly larger mass. Both the apple and the earth exert equal and opposite forces on each other, according to Newton's third law, but only the apple's acceleration is noticeable.
Step-by-step explanation:
The correct answer to why an apple falls towards the earth but the earth does not move noticeably towards the apple is because acceleration is inversely proportional to mass, so the acceleration of earth is negligible. This can be understood through Newton's second law of motion, which states that the force acting on an object causes acceleration (F=ma). Although both the earth and the apple exert forces on each other that are equal in magnitude and opposite in direction, the mass of the earth is so much greater than that of the apple that the earth's acceleration towards the apple is incredibly small and thus imperceptible.
Newton's third law explains that for every action there is an equal and opposite reaction, which means that the force the apple exerts on the earth is equal to the force the earth exerts on the apple. However, since the earth has a much larger mass, we only observe the acceleration of the apple but not of the earth. This is analogous to the interaction between the Earth and the Moon, where both bodies exert equal and opposite gravitational forces on each other, but only the Moon's orbit is noticeably affected due to its smaller mass compared to Earth.