What is the magnitude of acceleration of the Earth in the perspective of a falling object? I am currently confused about one concept:
Suppose there is an apple falling to the ground. By Newton's Gravitational Force formula, I can come up with the forces between them. Therefore I can have the accelerations, which are different due to different mass.
However, in the perspective of the apple, or the perspective of the Earth, the acceleration should be the same for the other object, right? But how comes the different acceleration from a=F/m ?
I think I misunderstand something. Could please someone help me clarify? A concrete example is needed if you think it helps better.
 A: Yes, from the perspective of the apple, the ground appears to be coming towards the apple at an increasing speed. However, that is just perspective. If I get in my car and accelerate toward a bridge, the bridge appears to be moving towards me at an increasing speed, but the bridge is not accelerating in any real sense. Newton's laws apply in inertial reference frames only. The falling apple is viewing the movement of the ground from an accelerating frame of reference.
A: 
the acceleration should be the same for the other object, right?

No. I agree that the force of gravity between 2 objects is the same on the 2 objects i.e. each experiences the same amount of  force as the other.
But, both of them do not have same mass. If a same amount of force acts on 2 different masses, then the lighter mass accelerates more than the heavier mass due to the formula a = F/m
Hence, the apple which has a much lower mass will accelerate much more than the earth which has a HUGE mass ( about 25 orders of magnitude more than the apple ) and therefore will experience negligible acceleration
A simple example. Suppose there is an apple with mass 1 kg.
The force of gravity exerted by earth on apple is 9.8 N.
Now, force of gravity exerted by apple on earth IS ALSO 9.8 N
So, acceleration experienced by apple = 9.8 / 1 = 9.8 m/s^2
Acceleration experienced by earth = 9.8 / 6E24 = approximately 10^(-24) m/sec^2
This is the reason magnitude of acceleration of earth is negligible.
A: Acceleration is a relative term. There's no absolute acceleration. In the earth-apple example, acceleration of the apple with respect to the earth is same as acceleration of the earth with respect to the apple. But if you consider the independent observer such as the sun (I'm ignoring the earth-sun gravity for time being), the earth has negligible acceleration but the apple has acceleration g towards the earth.
For the earth-apple system, gravity is just an internal force. The centre of mass of the earth-apple system will not change as gravitational force acting between them is an internal force. Because of the heavy mass of the earth, it doesn't seem moving with respect to the sun.
I can explain further, if you are still confused.
