If a planet of mass ‘m’ is revolving around the sun in a circular orbit of radius ‘r’ with time period T, then the mass of the sun is

The gravitational force at attraction provides the necessary centripetal

force for revolution of planet around the sun

$\frac{\text{GMm}}{{\text{r}}^{\text{2}}}=\text{mr}{\omega }^{\text{2}}=\text{mr}\frac{4{\pi }^2}{{\text{T}}^2}\Rightarrow \text{M}=\frac{4{\pi }^2{\text{r}}^3}{{\text{GT}}^2}$

Second method:

${\text{F}}_{\text{c}}={\text{F}}_{\text{g}}$

$\frac{{\text{mv}}^{\text{2}}}{\text{R}}=\frac{\text{GMm}}{{\text{R}}^{\text{2}}}$

$\frac{{\text{v}}^{\text{2}}}{\text{R}}=\frac{\text{GM}}{{\text{R}}^{\text{2}}}\Rightarrow \frac{{\left(\frac{2\pi \text{R}}{\text{T}}\right)}^2}{\text{R}}=\frac{\text{M}}{{\text{R}}^{\text{2}}}$

$\therefore \text{M}=\frac{\text{G}{\pi }^2{\text{R}}^3}{4{\text{T}}^2}$