Answer:
Their period of revolution is 1.408 years
Explanation:
Given data:
G = gravitational constant = 6.67x10⁻¹¹Nm²/kg²
M = mass of star = 1.2x10³⁰kg
D = distance between stars = 2x10⁸km = 2x10¹¹m
The radius of each star is:
[tex]r=\frac{D}{2} =\frac{2x10^{11} }{2} =1x10^{11} m[/tex]
The gravitational force between stars is equal to:
[tex]\frac{V^{2} }{r} =\frac{GM}{D^{2} } \\V=\sqrt{\frac{GMr}{D^{2} } } =\sqrt{\frac{6.67x10^{-11}*1.2x10^{30}*1x10^{11} }{(2x10^{11})^{2} } } =14145.671m/s[/tex]
The period is:
[tex]T=\frac{2\pi r}{V} =\frac{2\pi 1x10^{11} }{14145.671} =44417725.445s=1.408years[/tex]
