Find equation for mass in gravityA satellite is moving in circular motion round a planet.From...

Find equation for mass in gravity
A satellite is moving in circular motion round a planet.
From the physics we know that
$\mathrm{\Sigma }{F}_r=m{a}_r=\frac{GMm}{r^2}$
So I wanted to find the equation for $M$ knowing also that
$v=\omega r=\frac{2\pi r}{T}$
and
$a_r=\frac{v^2}{r}$
Thus,
$m{a}_r=\frac{GMm}{r^2}$
$a_r=\frac{GM}{r^2}$
$\frac{v^2}{r}=\frac{GM}{r^2}$
$\frac{{\left(\frac{2\pi r}{T}\right)}^2}{r}=\frac{GM}{r^2}$
$\frac{\frac{4{\pi }^2{r}^2}{T^2}}{r}=\frac{GM}{r^2}$
$\frac{4{\pi }^2{r}^3}{T^2}=\frac{GM}{r^2}$
$\frac{4{\pi }^2{r}^5}{T^2}=GM$
$\frac{4{\pi }^2{r}^{5}G}{T^2}=M$
However, this is wrong! It should be:
$M=\frac{4{\pi }^2{r}^3}{G{T}^2}$
What was my mistake in Mathematics? Please don't migrate it to physics because my misunderstanding is on math.
Note: I would be very happy if you show my mistake, instead of showing me another way to get to the equation.