How Are the Masses of Binary Stars Calculated?

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SUMMARY

The discussion focuses on calculating the masses of binary stars using their orbital characteristics. Specifically, it examines a binary star system where one star orbits with a radius of 7 x 1011 m and the other with a radius of 10 x 1011 m, completing a revolution every 49 years. The gravitational equation G*m1*m2/(r1+r2)=m1r1(2pi/T)2 is utilized for mass calculations. Participants highlight the importance of correctly applying the formula, particularly ensuring that (r1 + r2) is squared in the calculations.

PREREQUISITES
  • Understanding of binary star systems and their orbital mechanics.
  • Familiarity with gravitational equations, specifically Newton's law of gravitation.
  • Basic knowledge of circular motion and period calculations.
  • Proficiency in algebraic manipulation and unit conversions.
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  • Study the application of Newton's law of gravitation in astrophysics.
  • Learn about orbital mechanics and the calculation of center of mass in binary systems.
  • Explore the significance of mass in determining stellar properties.
  • Investigate common errors in gravitational calculations and how to avoid them.
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Astrophysics students, educators, and amateur astronomers interested in understanding binary star systems and the methods used to calculate stellar masses.

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Homework Statement



(a) About half of the visible "stars" are actually binary star systems, two stars that orbit each other with no other objects nearby. Consider the motion of the center of mass of a binary star system. For a particular binary star system, telescopic observations repeated over many years show that one of the stars (whose unknown mass we'll call M1) has a circular orbit with radius R1 = 7 ee11 m, while the other star (whose unknown mass we'll call M2) has a circular orbit of radius R2 = 10e11 m about the same point. Make a sketch of the orbits, and show the positions of the two stars on these orbits at some instant. Label the two stars as to which is which, and label their orbital radii. Indicate on your sketch the location of the center of mass of the system. (Do this on paper; you will not be asked to turn it in. )
(c) This double star system is observed to complete one revolution in 49 years. What are the masses of the two stars? (For comparison, the distance from Sun to Earth is about 1.5 1011 m, and the mass of the Sun is about 2 1030 kg.) This method is often used to determine the masses of stars. The mass of a star largely determines many of the other properties of a star, which is why astrophysicists need a method for measuring the mass.

Homework Equations



G*m1*m2/(r1+r2)=m1r1(2pi/T)^2


The Attempt at a Solution



m2=(r1+r2)^2(r1)(2pi/t)^2

I plugged all the numbers in but got the wrong answer is there something I am doing wrong?

Thank you
 
Physics news on Phys.org
Could it be that you just forgot to square (r1 + r2) ?
Perhaps a calculation error? If you show your calc, someone will check it for you.
 

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