Answer:
V = 365643.04 m/s
Explanation:
mass of the sun = 1.99 x 10^{30} kg
mass of M1 = mass of M2 = 6.95 solar mass = 6.95 x 1.99 x 10^{30} = 13.8305x 10^{30} kg
orbital period of each star (T) = 2.20 days = 2.20 x 24 x 60 x 60 =190,080 s
gravitational constant (G) = 6.67 x 10^{-11} N m2/kg2
orbital speed (V) = [tex]\sqrt{\frac{G(M1+M2)}{r} }[/tex]
we need to find the orbital radius (r) before we can apply the formula above and we can get it from Kepler's third law, [tex]T^{2} = r^{3}[/tex] x k
where
making r the subject of the formula we now have
[tex]r = (\frac{G(M1+M2).T^{2}}{4n^{2} } )^{\frac{1}{3} }[/tex] (take note that π is shown as [tex]n[/tex])
[tex]r = (\frac{ 6.67 x 10^{-11} ( 13.8305x 10^{30}+ 13.8305x 10^{30} )x190080^{2}}{4x3.142^{2} } )^{\frac{1}{3} }[/tex]
r = 1.38 x 10^{10} m
Now that we have the orbital radius (r) we can substitute all required values into the formula for orbital speed
orbital speed (V) = [tex]\sqrt{\frac{G(M1+M2)}{r} }[/tex]
[tex]V = \sqrt{\frac{6.67 x 10^{-11} ( 13.8305x 10^{30}+ 13.8305x 10^{30}}{1.38 x 10^{10} } }\\[/tex]
V = 365643.04 m/s
