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We measure mass using gravity. Direct mass measurements are possible only for stars in binary star systems. P = orbital period a = orbital semimajor axis P2 = a3
4π2 G (M1 + M2)
Measuring stellar masses We measure mass using gravity. Direct mass - - PowerPoint PPT Presentation
Measuring stellar masses We measure mass using gravity. Direct mass - - PowerPoint PPT Presentation
Measuring stellar masses We measure mass using gravity. Direct mass measurements are possible only for stars in binary star systems. 4 2 P 2 = a 3 G ( M 1 + M 2 ) P = orbital period a = orbital semimajor axis Need 2 out of 3 observables to
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Need 2 out of 3 observables to measure mass:
1) Orbital Period (T) 2) Orbital Separation (a or r = radius of circular orbit) 3) Orbital Velocity (v) For circular orbits, v = 2pr / T
r M v
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Visual Binary
We can directly observe the orbital motions of these stars.
α1 α2 = r
2
r
1
= a2 a1 = m1 m2
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Spectroscopic Binary
We determine the orbit by measuring Doppler shifts.
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Spectroscopic Binary: Circular Orbits
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Spectroscopic Binary: Elliptical Orbits
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Most massive stars: ~100 MSun Least massive (hydrogen- burning) stars: 0.08 MSun
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First exoplanet detected around a Sun-like star, discovered independently in 1995 by Mayor & Queloz (Switzerland) and Marcy & Butler (San Francisco State U.)
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Eclipsing Binary
We can measure periodic eclipses.
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Eclipsing Binaries—Light Curves
Total eclipses Partial eclipses
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Credit: P. Zasche, Astronomical Institute, Prague, Czech Republic
Orbit Models Fit to Light Curves of Eclipsing Binaries
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Wright & Gaudi (2012)
Exoplanet Detections as of December 2011
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https://exoplanetarchive.ipac.caltech.edu 3,529 confirmed exoplanets as of October 5, 2017