A certain quaternary star system consists of a central star of mass $M$ and three smaller stars, each of mass $m$. The three smaller stars orbit the central star in the same circular orbit of radius $r$ and have the same sense of revolution. They are positioned one-third of a revolution apart from one another in the orbit. The period of revolution of each smaller star is

• A

  $2 \pi \sqrt{\frac{r^3}{G(m+M)}}$
• B

  $2 \pi \sqrt{\frac{r^3}{G\left(m+\frac{M}{\sqrt{3}}\right)}}$
• C

  $2 \pi \sqrt{\frac{r^3}{G(M-m)}}$
• Correct answer
  D

  $2 \pi \sqrt{\frac{r^3}{G\left(M+\frac{m}{\sqrt{3}}\right)}}$

Hence, the correct answer is option: 'D'.