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3241004551 [841]
3 years ago
14

Two stars M1 and M2 of equal mass make up a binary star system. They move in a circular orbit that has its center at the midpoin

t of the line that separates them. If M1-M2-6.95 sm (solar mass), and the orbital period of each star is 2.20 days, find their orbital speed. (The mass of the sun is 1.99x 1030 kg.) km/s M2
Physics
1 answer:
ozzi3 years ago
3 0

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) = \sqrt{\frac{G(M1+M2)}{r} }

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, T^{2} = r^{3} x k

where

  • T = orbital period
  • r = orbital radius
  • k = \frac{4n^{2} }{G(M1+M2)}  (take note that π is shown as n)

making r the subject of the formula we now have

r = (\frac{G(M1+M2).T^{2}}{4n^{2} } )^{\frac{1}{3} }    (take note that π is shown as n)

r = (\frac{ 6.67 x 10^{-11} ( 13.8305x 10^{30}+ 13.8305x 10^{30} )x190080^{2}}{4x3.142^{2} } )^{\frac{1}{3} }

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) = \sqrt{\frac{G(M1+M2)}{r} }

V = \sqrt{\frac{6.67 x 10^{-11} ( 13.8305x 10^{30}+ 13.8305x 10^{30}}{1.38 x 10^{10} } }\\

V = 365643.04 m/s

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