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Punology 5

Punology 5

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Punology 5

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  1. Punology 5 A woman has twins and gives them up for adoption. One of them goes to a family in Egypt and is named "Ahmal." The other goes to a family in Spain; they name him "Juan." Years later, Juan sends a picture of himself to his birth mother. Upon receiving the picture, she tells her husband that she wishes she also had a picture of Ahmal. Her husband responds, "They're twins! If you've seen Juan, you've seen Ahmal." A good pun is its own reword. ...Author Unknown

  2. Notes 66 - Optional Topic F - Astrophysics* ------------------------------------------------------------------------------- E.3.2 and E.3.3 Stellar Distances using Trigonometric Parallax Stellar Motion A. Radial Motion - the motion of a star directly toward or away from the Earth; determined by the Doppler Shift of the star's light into the blue (moving toward) or red (moving away) end of the spectrum of light; B. Proper Motion (also called transverse motion) - the actual annual movement of a star across the sky as seen from earth; measured in arcseconds per year: Barnard's Star has greatest proper motion of 10.3" per year; only 100 stars have a motion of 1" or greater;

  3. C. Trigonometric Parallax - the apparent changing of a star's position relative to a fixed background of "unmoving stars" due to the earth’s revolution; the motion is cyclic and reverses every year; - Can only be used for "close" stars (ie., 100. pc [326 ly] or closer for earth- based telescopes due to atmospheric interference...the Hubble Space Telescope has measured distances out to 114 pc [372 ly]); - Measured in arc seconds, or (1/3600)'s of a degree of arc; eg., 1" ; - 1o of arc = 60’ (minutes of arc) = 3600” (seconds of arc); (for reference...width of full moon seen from earth = 30’ of arc = 1800”) - For stars, the baseline for observation is the orbit of the earth, ie., 2.0 AU’s = 3.0 x 108 km;

  4. - For a star to have a parallactic angle p = 1", it must be 206,265 AU or 3.1 x 1016 m away from earth; this distance is called 1 parsec and equals 3.26 light years ; (parsec = parallax in arcseconds); d (distance in parsecs) = 1 / parallactic angle (in arcseconds); d = 1/p, where p is always less than 1” ; E.3.1 The Parsec • Distances - in space, measured by astronomical units (AU’s), light years (ly’s), parsecs (pc’s), megaparsecs (Mpc), 1.000 AU (distance to Sol) = 1.496 x 1011 m 1.000 ly = 9.460 x 1015 m = 6.324 x 104 AU 1.000 pc = 3.086 x 1016 m = 2.060 x 105 AU = 3.260 ly; 1.000 Mpc = 3.086 x 1022 m = 2.060 x 1011 AU = 3.260 x 106 ly;

  5. E.3.4 Solve problems involving stellar parallax The parallactic (parallax) angle of the closest star to Sol, Alpha Centauri, is 0.758”. Determine the distance to our nearest stellar neighbor in pc, ly, AU, and meters (put solutions in NB): Given: Unknown: Equation:

  6. E.3.5 Apparent Magnitude Scale •Apparent Magnitude (m) - the brightness of a star as it appears in the night sky without regard to distance;

  7. - The scale used today survives from ancient Greece and Hipparchus (160 BC), who assigned values of 1-6 for visible stars 2000 years ago, with 1 as the brightest visible star and 6 as the faintest star still visible; - It has been determined that a magnitude 1 star is 100x the brightness of a magnitude 6 star; that is, a difference of 5 levels (6 -1 = 5) produces a brightness that is 100 times greater between those levels; So...if r5 = 100, then r = 2.512; - Thus, the difference in brightness between a magnitude 1 and a magnitude 2 star is 2.5121, or 2.512times; - The difference in brightness between a magnitude 1 and a magnitude 3 star is 2.5122, or 6.31 times; - The difference in brightness between a magnitude 1 and a magnitude 4 star is 2.5123, or 15.85 times; - The difference in brightness between a magnitude 1 and a magnitude 5 star is 2.5124, or 39.82 times; - The difference in brightness between a magnitude 1 and a magnitude 6 star is 2.5125, or 100. times; If the difference in apparent magnitudes = ∆m = m2 - m1, then R (theratio of apparent brightnesses between stars) is defined as: R = b1/b2 = (2.512)∆m

  8. E.3.6and E.3.7 Absolute Magnitude Absolute Magnitude (M) - the apparent magnitude of a star that is placed 10. pc from the observer; gives relative brightnesses of all stars and is defined as: m - M = 5 logd - 5 M = m - 5 logd +5, where dis distance in pc; ABSOLUTE MAGNITUDES http://casswww.ucsd.edu/public/bright.html Example 1: What is the absolute magnitude of Sol? (show solution in NB) Given: Unknown: Equation: Example 2: The nearest star to Sol is 1.3 pc distant and has an apparent magnitude of 0.1. Determine the absolute magnitude of Alpha Centauri. Which star is brighter and by how much? (show solution in NB) Given: Unknown: Equation:

  9. E.3.8 Problem involving Apparent Brightness and Apparent Magnitude Example: The apparent magnitude of Sol is -26.7 and that of Betelgeuse is +0.50. How many times brighter is Sol than Betelgeuse? (show solution in NB) Given: Unknown: Equation:

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