Answer:
Explanation:
Convert orbital period into seconds.
21.3 days = 21.3x 24 x 60x60 = 1840320 s
Write the expression for the gravitational force balanced by the linear speed to calculate the distance between the stars.
[tex]\frac{Gm^2}{d^2}=\frac{mv^2}{r}[/tex] [tex]d=2r;v=\frac{2\pi r}{T}[/tex]
[tex]\frac{Gm^2}{(2r)^2}=\frac{m(\frac{2\pi r}{T})^2}{r}\\\\\frac{Gm^2}{4r^2}=\frac{m(\frac{4\pi^2 r^2}{T^2})}{r}\\\\r^3=(\frac{GmT^2}{16\pi^2})[/tex]
[tex]r=(\frac{(6.67\times 10^{-11})(1.99\times 10^{30})(1840320)^2}{16(3.14)^2})^{\frac{1}{3}}\\\\=1.42\times 10^{10}m[/tex]
Calculate the distance between the stars.
[tex]d=2r\\\\=2(1.42\times 10^{10}m)\\\\=2.83\times 10^{10}m[/tex]
