# I Why Earth has constant acceleration?

1. Jul 8, 2017

### 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?

2. Jul 8, 2017

### Staff: Mentor

Yes, it varies slightly as $r$ changes.
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).

3. Jul 8, 2017

### Staff: Mentor

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.