I don’t distinguish gravity and centripetal acceleration

1. The problem statement, all variables and given/known data
There is a famous thought experiment that Newton put forward: imagine a very tall mountain where there is no air friction. We’ll put a cannon on top of this mountain, and we’ll fire cannon balls put of with greater and greater velocities in the horizontal direction.
Let’s say we don’t shoot practically at all. The ball comes out, and almost inmediately falls into the Earth. The more initial velocity, the later it falls.
At the right speed, the ball will never fall. Better said, it falls at the right rate, and it will describe an orbit around the Earth.
¿Which is the relation between centripetal acceleration and gravity, in each example?

2. Relevant equations
The formula that expresses the acceleration towards the Earth is [itex]a=\frac{v^2}{r}[/itex]. And there is gravity [itex]9,8\;m/s^2[/itex], which is a constant

3. The attempt at a solution
It’s a conceptual doubt, so no idea
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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