How to Determine the Period and Separation of an Eclipsing Binary Star System?

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SUMMARY

This discussion focuses on determining the period (P) and separation (a) of an eclipsing binary star system consisting of two main sequence stars. The brighter star has an absolute magnitude of -1, a temperature of 17,000 K, a radius of 1.74 solar radii, and a mass of 3.17 solar masses, while the smaller star has an absolute magnitude of 3 and a mass of 1.4 solar masses. The eclipse duration of the smaller star is given as P/7. The user references Kepler's laws and seeks additional formulas to solve the problem, indicating a need for deeper understanding of binary star dynamics.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Familiarity with absolute magnitude and luminosity concepts
  • Knowledge of stellar masses and radii
  • Basic grasp of orbital mechanics and time-period calculations
NEXT STEPS
  • Study the application of Kepler's Third Law in binary star systems
  • Learn how to calculate the semi-major axis (a) using mass and period
  • Research the methods for determining stellar luminosity and temperature
  • Explore additional formulas related to eclipsing binaries and their dynamics
USEFUL FOR

Astronomy students, astrophysicists, and educators preparing for science competitions, particularly those focused on binary star systems and their characteristics.

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This problem deals with two main sequence stars in an eclipsing binary star system. I need to determine the system's peiod and separation (P and a).
Right now i know that the brightest star has an absolute magnitude of -1 (219 solar luminosity), is 17,000 degrees kelvin, has a radius of 1.74 solar radii (1,280,000 km) and is 3.17 solar masses. The smaller star has an absolute magnitude of 3 (6 solar luminosity), and is 1.4 solar masses.
the time it takes for the eclipse of the small star (the smaller dip) is P/7.

Go to this site (#24 +#25) to see the illustration of the problem...

h ttp://www.tufts.edu/as/wright_center/fellows/sci_olympiad/astro_ohio_questions_2003.pdfthis site has the answers... i just don't know how to get them!

h ttp://www.tufts.edu/as/wright_center/fellows/sci_olympiad/astro_ohio_answers2003.pdf

i know kepler's law: m1 +m2 = a^3/p^2
2(pi)R= (velocity) x p
m/M=x1/x2
There must be other formulas i don't know about...i am going nowhere. i have asked my teachers and they don't know what to do either. This is practice for a science olympiad competion and it will likely be on the test. Help please! i don't have much time!
 
Last edited:
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Those links don't work.
 
now they do.. just delete the space between the "h" and the "t" in http
 

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