Question

A planet or butting a distant star has been observed to have an orbital period of 0.76 earth years at a distance of 1.2 au. What is the mass of the star the planet is orbiting

Answer 1

Answer:

The mass of the star is, M = 5.9567x10³⁰ Kg

Explanation:

Given

The orbital period of the planet, T = 0.76 year

                                                        = 2.3967x10⁷ seconds

The distance between planet and sun, R+h = 1.2 a.u

                                                                        = 1.795 x 10¹¹ meters

The orbital period of the planet is given by the formula

                                 $T={2\pi\sqrt{\frac{(R+h)^{2}}{GM}}}$

Squaring and solving for M

                                   $M=\frac{4\pi ^{2} (R+h)^{3}}{GT^{2} }$

Substituting the given values in the above equation

                          $M=\frac{4\pi ^{2}(1.795X10^{11} )^{3} }{6.673X10^{-11}X(2.3967X10^{7})^{2}}$    

                                     M = 5.9567 x 10³⁰ Kg

Hence, the mass of the star the planet is orbiting, M = 5.9567 x 10³⁰ Kg