Answer:
M = 9.71 x 10³⁰ Kg
Explanation:
given,
Time period of the planet ,T = 3.31 x 10⁷ s
distance from the star, r = 2.62 x 10¹¹ m
mass of the star = ?
using Kepler third law
[tex]T^2 = \dfrac{4\pi^2}{GM}r^3[/tex]
now,
[tex]M = \dfrac{4\pi^2}{GT^2}r^3[/tex]
where as, G = 6.67 x 10⁻¹¹ m³/kg.s²
[tex]M = \dfrac{4\pi^2}{6.67\times 10^{-11}\times (3.31\times 10^7)^2}\times (2.62\times 10^{11})^3[/tex]
M = 9.71 x 10³⁰ Kg
The mass of the star is equal to M = 9.71 x 10³⁰ Kg.
