Answer to Question #127540 in Physics for kumera

Question

An extra solar planet is found orbiting a star in the Orion nebula. Determine the mass of the star if the planet has an orbital period of 420.0 Earth Days and has an orbital radius of 1.29x1011m.

Answer 1

According to the Kepler's Third Law:

$$\dfrac{a^3}{T^2} = \dfrac{GM}{4\pi^2},$$

the mass of the star will be:

$$M = \dfrac{4a^3\pi^2}{GT^2},$$

where $a = 1.29\times10^{11} m$ is the orbital radius, $T = 420 days = 420\cdot 86400s = 36288000s$ is the orbital period and $G = 6.6\times10^{-11} m^3kg^{-1}s^2$.

Thus, obtain:

$$M = \dfrac{4(1.29\times10^{11})^3\pi^2}{6.6\times10^{-11} (36288000)^2} = 9.75\times10^{29}kg$$

Answer. 9.75*10^29 kg.