I don't distinguish gravity and centripetal acceleration

[mcastillo356]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

It's a conceptual doubt, so no idea

 

[BvU]

So if v² / r = 9.8 you are in business, right ?
Because then the Earth provides the required centripetal force !

 

[mcastillo356]

So, given the right velocity to a particle, gravity will become centripetal force, isn't it?

 

[BvU]

Correct!

 

[adjacent]

See this also:

 

[BvU]

Note that exactly only one initial speed ("v² / r = 9.8") gives you a circular trajectory, anything above (up to about 10000 m/s) an elliptical trajectory, then a parabola for higher v. See Newton's_cannonball[/PLAIN]