If a graph is plotted between T² and r³ for a planet then, its slope will be

Time period of the planet,

$\mathrm{T}=\frac{2\mathrm{\pi r}}{\mathrm{v}}=\frac{2\mathrm{\pi r}}{\sqrt{{\displaystyle \frac{\mathrm{GM}}{\mathrm{r}}}}}=\frac{2\mathrm{\pi r}\sqrt{\mathrm{r}}}{\sqrt{\mathrm{GM}}}$

$\Rightarrow {\mathrm{T}}^2=\frac{4{\mathrm{\pi }}^2{\mathrm{r}}^3}{\mathrm{GM}}=\left(\frac{4{\mathrm{\pi }}^2}{\mathrm{GM}}\right){\mathrm{r}}^3$

$\mathrm{Slope} \mathrm{of} {\mathrm{T}}^2 \mathrm{vs} {\mathrm{r}}^3 \mathrm{graph}:$

$\mathrm{m}=\frac{{\mathrm{T}}^2}{{\mathrm{r}}^3}=\frac{4{\mathrm{\pi }}^2}{\mathrm{GM}}$