Can someone explain a Geostationary Orbit in a simpler way?

@Hobbes put the formula:

$V={2pi aover T}$

If you substitute on it $T$ for 1 sidereal day you'll have a one-to-one relation between $V$ and $a$. This seems to imply that you can choose any $a$ and use the corresponding $V$, but this is not true since it does not take into account which force are you using.

The formula above is valid of any object in a circular motion, like a stone on a sling, or a car in a loop. It is also valid for satellites around planets.

But there is another formula stating a relation among $a$ and $T$ when the force is that of Gravity, so you are not free to chose $a$ anymore.

It happens that centripetal acceleration (that of the sling, the Normal force on the loop, or gravity for the satellite) is the Universal Gravity in our case:

$a_c={GMover r^2}$

but it being the centripetal acceleration means

$a_c=omega^2 r$

so we have

$omega^2 r={GMover r^2}$

$omega^2 r^3=GM$

$omega$ is $vover r$ so

$v^2 r=GM$

which gives you a fixed relation between $v$ and $r$ for any planet with mass $M$.