Any Ideas?

Question

Plaskett’s binary system consists of two stars that revolve in a circular orbit around a center of mass, midway between them. This means that the masses of the two stars are equal. If the orbital velocity of each star is 220 km/s and the orbital period of each is 1404 days, find the mass of each star and compare the mass of the stars to the Sun of the earth.

Answer 1

If you can find the orbital radius, then then you can find the centrifugal force. The centrifugal force must equal the gravitaional attraction. First, find orbital radius. This you get from the angular velocity w = 2π/1404 day^-1, The orbital velocity is v = w*r, or r = v/w; this comes out 4.25*10^9km. The centrifugal force is m*r*w^2. The gravitational force is G*m^2/(2r)^2 (the masses are the same; the distance between the stars is 2*r). Equating these gives G*m^2/4*r^2 = m*r*w^2, so
G*m/4*r^2 = r*w^2

m= 4*r^3*w^2/G. since r = v/w, m = 4*v^3/w*G

G = universal gravitational constant = 6.67*10^-11 N m^2 kg^-1

Plugging the numbers in gives a mass value of 10^35 kg

Mass of earth = 5.97×10^24 kg
Mass of sun = 2*10^30 kg

Answer 2

None at all. Many physics students should be intrigued by your question though.
My math skills are "limited" so I could only make some observations which may have nothing to do with your question.
Are these two stars related. They must have an origin that is similar.
Their solar system would have planets that would have to share orbits. Gosh............way out of my league. Good luck!

Answer 3

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