Question

A binary star system has a period of 520 days, and a semi-major axis of 4 AU. The ratio of the star's mass is as follows: Star Mass 1/ Star Mass 2 = 0.45. What is the total mass of the system? Find the mass of each individual star.

Answer 1

The orbital period is 520 days i.e 1.42 years.

Now we can use the Kepler's law to calculate the total mass of the system of two stars as ;

total mass = where D is the separation between the two stars and T is the period.

hence M= 31.73 solar mass

now the ratio of star 1 to star 2 is = 0.45

mass of star 2 = M/(1+0.45) = 31.73/(1.45) = 21.88 solar mass

mass of star 1= mass of star 2 x 0.45 = 9.85 solar mass

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