A planet of mass $m$ is orbiting around a non-rotating star of mass am $(\alpha \gg 1)$ with an orbital radius $r$. The star ejects mass $\lambda m(\lambda \ll 1)$ radially outwards in a spherically symmetric fashion. Neglecting any impact of ejected mass on the planet, the radius of new circular orbit of the planet is

• A

  $\left(1+\frac{\lambda}{\alpha}\right)^{-1} r$
• B

  $(1-\lambda \alpha)^{-1} r$
• C

  $(1+\lambda \alpha) r$
• Correct answer
  D

  $\left(1-\frac{\lambda}{\alpha}\right)^{-1} r$

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