What Are the Radii of the Two Stars in This Binary System?

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SUMMARY

The discussion focuses on calculating the radii of two stars in a binary system based on their orbital characteristics. Given an orbital period of 3.15 years and maximum radial velocities of 5.2 km/s for star A and 21.6 km/s for star B, participants derive the mass ratio (mA/mB) and individual masses (mA and mB) using the equations v1=(2πa1)/p and m1=(4V1^2*r1)/G. The hint suggests utilizing eclipse timings to determine the radii, specifically using the formula r=a(1-e^2)/(1+ecos@), although participants initially consider alternative methods.

PREREQUISITES
  • Understanding of binary star systems and their dynamics
  • Familiarity with Kepler's laws of planetary motion
  • Knowledge of basic astrophysical equations related to mass and radius
  • Proficiency in using the gravitational constant (G) in calculations
NEXT STEPS
  • Study the application of Kepler's laws in binary star systems
  • Learn how to calculate stellar masses using radial velocity data
  • Research the methods for determining stellar radii from eclipse timings
  • Explore the implications of orbital inclination on mass calculations
USEFUL FOR

Astronomy students, astrophysicists, and anyone involved in stellar dynamics and binary star research will benefit from this discussion.

leonne
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Homework Statement


From the light and velocity curves of an eclipsing, double-lined spectroscopic binary
star system, it is determined that the orbital period is 3.15 yr, and the maximum radial
velocities of stars A and B are 5.2 km s^-1 and 21.6 km s^-1, respectively. Furthermore,
the time between first contact and minimum light is tb-ta = 0.45 days, while the length
of the primary minimum is tc -tb = 0.52 days. Relative to the maximum brightness,
the primary minimum is only 54.8% as bright, while the secondary minimum is 88.1%
as bright
You may assume the orbits are circular and seen perfectly edge on.

Find the ratio of the stellar masses (mA/mB), the sum of the masses (M =
mA + mB), and the individual masses (mA and mB).
(b) Find the radii of the two stars. Hint: Use the speed of one star relative to the
other and the eclipse timings given.


Homework Equations


v1=(2pie a1)/p r=a(1-e^2)/(1+ecos@) m1=(4V1^2*r1)/G


[c]3. The Attempt at a Solution [/b]
so becasue its edge on that means inclination angle is 90degrees so that's the real velocity and e = 0 too so just use these formula to find masses right?
now for part B would i just the formula r=a(1-e^2)/(1+ecos@) to find the radii? checked in book showed this as radii but hint says to use something different i think
 
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nvm i think i figured it out
 

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