In 1922, a Canadian astronomer John Stanly Plaskett discovered a binary star sys
ID: 1514364 • Letter: I
Question
In 1922, a Canadian astronomer John Stanly Plaskett discovered a binary star system in the constellation of Monoceros that is still one of the most massive ever found. The binary has two star of equal mass in a circular orbit about their centerof mass. The mass of each star is 1.26x10^32kg. Find the orbital speed of each star, if the orbital period of each is 14.4 days. Use G=6.67x10^11 Nm^2/kg^2.
The answer is V = 2.22 * 10^(5) m/s according to my professor, I need the work explained though. I don't understand how she got that answer.
Explanation / Answer
we know that orbital speed is V = sqrt(GM/R) = 2 pi R /T
given orbital period T = 2 pi R/ V = 14.4 days
so R = cube root of (GMT^2 *4pi^2) sunstituting the data
R = 1.0134*10613
now V = sqrt(GM/R) = sqrt(6.67*10^-11*2.52*10^32/1.013*10^12) = 1.28812 *10^5 m/s
universal gravitaional constant is 6.67*10^-11 Nm2/kg2 not 6.67*10^11 Nm2/kg2