## College Physics (4th Edition)

Since the units for $T^2$ should be $s^2$, we can see that the equation is dimensionally correct.
We can analyze the dimensions of the equation $T^2 = \frac{4\pi^2~r^3}{GM}$: $\frac{m^3}{(m^3/kg\cdot s^2)\cdot kg} = \frac{m^3\cdot kg\cdot s^2}{m^3\cdot kg} = s^2$ Since the units for $T^2$ should be $s^2$, we can see that the equation is dimensionally correct.