Answer:
Mass of star is [tex]1.31\times10^{35}[/tex] kg.
Explanation:
The cube of orbital radius is equal to the square of its orbital time period is known as Kepler's law.
[tex]T^{2} = (\frac{4\pi^{2} }{GM})r^{3}[/tex] .....(1)
Here T is time period, r is orbital radius, G is universal gravitational constant and M is the mass of the star.
According to the problem,
Time period, T = 109 days = 109 x 24 x 60 x 60 s = 9.41 x 10⁶ s
Orbital radius, r = 18 AU = 18 x 1.496 x 10¹¹ m = 2.70 x 10¹² m
Gravitational constant, G = 6.67 x 10⁻¹¹ m³ kg⁻¹ s⁻²
Substitute these values in equation (1).
[tex](9.41\times10^{6}) ^{2} = (\frac{4\pi^{2} }{6.67\times10^{-11}\times M})(2.70\times10^{12}) ^{3}[/tex]
M = [tex]1.31\times10^{35}[/tex] kg
