Why Earth has constant acceleration?

[Akshaydave14]

according to f=GMm/r^2 if force changes based on a distance between 2 objects, so during free fall object is constantly changing its distance, so does that mean the Earth is exerting a non-constant force on that object? if that was right, why's that object accelerate at a constant rate of a=9.81?
does changing force in F=ma also change acceleration? and why the Earth has a constant acceleration rather than changing?

 

[Nugatory]

so does that mean the Earth is exerting a non-constant force on that object?

Yes, it varies slightly as $r$ changes.

if that was right, why's that object accelerate at a constant rate of a=9.81?

They don't. 9.81 is not exact. It is a very good approximation near the surface of the earth, so we use it when we're solving problems near the surface of the earth. To get a sense of just how good an approximation it is, try calculating the difference between the the force when $r$ is equal to 6371 km (the average radius of the earth) and when $r$ is equal to 6371.1 km (100 meters higher up).

 

[Dale]

so during free fall object is constantly changing its distance, so does that mean the Earth is exerting a non-constant force on that object? if that was right, why's that object accelerate at a constant rate of a=9.81?

You are completely correct, the force varies with r, so the "constant" acceleration is just an approximation.

To see why that approximation works consider what it would take to get a 1% error in the force. Since the force is proportional to 1/r^2 you would need about a 0.5% change in r of about 20 miles. So for throwing a baseball or shooting a gun it is approximately constant, but for launching a rocket you need to account for the changing force.