Suppose that a binary star system consists of two stars of equal mass. They are observed to be separated by 370 million kilometers and take 6.0 Earth years to orbit about a point midway between them. What is the mass of each?
answer is in kg
2007-12-25 06:38:48 · 2 answers · asked by hermionegranger 2 in Science & Mathematics ➔ Physics
The faux centrifugal force C = mv^2/R; where m is the mass of one star revolving around the center of mass (CM) which is R = r/2 = 370/2 km away. The gravitational force F = Gm^2/r^2 = mv^2/R = C. In other words, the gravitational force over a distance r is the centripetal force that is offset by the centrifugal force C at a radius R.
So Gm/(2R)^2 = v^2/R and Gm/4R = v^2 = w^2 R^2. Then m = 4 w^2 R^3/G; where w = 1 cycle/6 years = 2 pi/6 years angular velocity around the CM at radius R = r/2. Look up G, which is a constant anywhere in the universe, make sure all the units are consistent, and you can do the math.
2007-12-25 06:59:02 · answer #1 · answered by oldprof 7 · 2⤊ 1⤋
well i think each star have to be 185 kilometers
2007-12-25 06:41:58 · answer #2 · answered by kidmohamedhi 1 · 0⤊ 6⤋