Binaries_all - Binary Stars Key Characteristics About half...

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Unformatted text preview: Binary Stars Key Characteristics About half of all stars are binary or multiple star systems Key Fundamentals Binary Stars Used to determine stellar masses Used to determine stellar diameters Major Types of Binary Stars Visual Binaries Spectroscopic Binaries Eclipsing Binaries Visual Binaries Visual Binaries Visual Binaries are Resolved Skinny Triangle Approximation D = d tan Resolution = 2.5 x 105 / D Example: GT 16-inch telescope = 2.5 x 105 (500 x 10-9 m) / (0.4 m) = 0.3 arcsec The atmosphere limits all telescopes to a resolution of ~1.0 arcseconds. Shapes of Orbits First Kepler tried circles, equants, ovals, etc. Finally, after years, he tried an ellipse. Found that the orbit of Mars is an ellipse with the Sun at a focus. The sum of the distances to the two foci is always constant for all points on the ellipse. Ellipses are described by their semi-major axis and by their eccentricity. e = ( foci / major axis) Kepler’s Three Laws 1. All planets have elliptical orbits with the Sun at a focus (conic sections). 2. Law of Equal Areas: Equal areas are swept out in equal time intervals. Kepler’s Second Law Interactive Kepler’s Three Laws 3. Harmonic Law (published in The Harmony of the Worlds): P2 = k a3, where k = 1 if P is in earth years and a is in AUs. Modification of Kepler’s Laws All orbiting bodies have a conic-section orbit, with the massive body (i.e., the Sun) at a focus. Modification of Kepler’s Laws Law of Equal Areas: Equal areas are swept out in equal time intervals. This is explained by Conservation of Angular Momentum. r1 v1 = r2 v2 Modification of Kepler’s Laws The Third Law needs to have the sum of the masses included. (M + m) P2 = k a3, where k = 1 if P is in earth years, a is in AUs, and (M + m) is in solar masses. For objects orbiting the Sun, (M + m) = 1. Visual Binaries Kepler’s 3rd Law (M1 + M2) P2 = a3 M is in solar masses P is in years, and a is in Astronomical Units (1 AU = mean Earth-Sun distance) Kepler's Third Law Interactive PRS Question 1. If two stars with the mass of the Sun had a circular orbit (radius = 5 AU), the orbital period would be about a. 4.0 years d. 12.0 years b. 5.5 years e. 16.0 years c. 8.0 years Resolution Improvements Speckle Techniques Resolutions to 0.02 arcsec Interferometric Techniques Resolutions to 0.001 arcsec Spectrum Binaries Spectroscopic Binaries Spectroscopic Binaries Conservation of Angular Momentum M1 / M2 = v2 / v1 = r2 / r1 Doppler Shift = v / c Radial Velocity Interactive PRS Question 2. If the orbital velocity of Star A is 5 times that of Star B, then Star A is how many times as massive as Star B? a. The same d. 1/5 times b. 5 times e. 1/25 times c. 25 times Eclipsing Binaries Eclipsing Binaries Unresolved – appear as a single star Orbital plane lies close to our line-of-sight Partial Eclipse Binary Star Interactive Phase Horizontal Axis Observed Time – Reference Time XX . XXXX Orbital Period Phase Textbook Binary Observational HD 71636 Partial P = 5.0 days a = 17.4 R M1 = 1.5 M M2 = 1.3 M R1 = 1.4 R R2 = 1.6 R Diameters of Stars L = 4 R2 T4 L R2 T4 PRS Question 3. Two stars in a binary system have the same temperature but the diameter of Star A is twice that of Star B. How many times brighter is Star A than Star B? a. 1 X d. 16 X b. 2 X e. 32 X c. 4 X Mass-Luminosity Relationship L M 4.0 0.08 solar < M < 50 solar ...
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