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exc2 - Introduction to Astrophysics 0321.3108 Exercise 2 1...

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Introduction to Astrophysics 0321.3108 Exercise 2 1. The maximal radial velocities measured for the two components of a spectroscopic binary are 100 km s - 1 and 200 km s - 1 , with an orbital period of 2 days. The orbits are circular. a. Find the mass ratio of the two stars. b. Use Keplers Law to calculate the value of M sin 3 i for each star, where M is the mass and i is the inclination to the observers line of sight of the perpendicular to the orbital plane. c. Calculate the mean expectation value of the factor sin 3 i , i.e., the mean value it would have among an ensemble of binaries with random inclinations. Find the masses of the two stars, if sin 3 i has its mean value. Hint: In spherical coordinates, ( θ, φ ), integrate over the solid angle of a sphere where the observer is in the direction of the z axis, with each solid angle element weighted by sin 3 θ . 2. In an eclipsing spectroscopic binary, the maximal radial velocities measured for the two com- ponents are 20 km s - 1 and 5 km s - 1 . The orbit is circular, and the orbital period is
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