In a certain binary-star system, each star has the same mass which is 9.8 times
ID: 2195617 • Letter: I
Question
In a certain binary-star system, each star has the same mass which is 9.8 times of that of the Sun, and they revolve about their center of mass. The distance between them is the 3.6 times the distance between Earth and the Sun. What is their period of revolution in years?
Chapter 13, Problem 57 In a certain binary-star system, each star has the same mass which is 9.8 times of that of the Sun, and they revolve about their center of mass. The distance between them is the 3.6 times the distance between Earth and the Sun. What is their period of revolution in years?Explanation / Answer
Mass of each star = 9*Ms
Distance between them = 3.6*d
Time period of revolution of earth around the sun = 1 year
T = 2**d/v
where v is the velocity of earth in orbit around the sun
m*v2/d = G*Ms*m/d2
v = (G*Ms/d)
T = 2**d/(v*(G*Ms/d)) = 2**(d3/(G*Ms)) =1 year
Time period of revolution of the twin star system = 2**1.8*d/(G*9*Ms/(4*1.8*d))
= 1.8*(9/7.2)*1 year = 2.01 years