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Question 16 10 p Exoplanets A and B are observed to orbit Star X in circular orbits at distances 1.1 AU and 10.2 AU from Star
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\!\!\!\!\!\!\!\!\!$Centripetal force for moving in circular path is provided by the gravitational force.$\\\\ \frac{m_Av^2}{R} = \frac{Gm_Am_X}{R^2}\;\;\;\Rightarrow \;\;\; v = \sqrt{\frac{Gm_X}{R}}\\\\ $Time period of exoplanet A is given by, $\\\\ T = \frac{2\pi R}{v} = 2\pi R\sqrt{\frac{R}{Gm_X}}\\\\ $Mass of Star X is given by, $\\\\ m_X = \frac{4\pi ^2R^3}{GT^2}= \frac{4\pi^2\times (1.1\times 1.5\times 10^{11})^3}{6.67\times 10^{-11}\times (244\times 86400)^2}= 5.98\times 10^{30}$kg$

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