Answer :
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
[tex]T={2\pi\sqrt{\frac{(R+h)^{2}}{GM}}}[/tex]
Squaring and solving for M
[tex]M=\frac{4\pi ^{2} (R+h)^{3}}{GT^{2} }[/tex]
Substituting the given values in the above equation
[tex]M=\frac{4\pi ^{2}(1.795X10^{11} )^{3} }{6.673X10^{-11}X(2.3967X10^{7})^{2}}[/tex]
M = 5.9567 x 10³⁰ Kg
Hence, the mass of the star the planet is orbiting, M = 5.9567 x 10³⁰ Kg
