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Chapter 2: The Sky

0. Chapter 2: The Sky. Common Units we will use. Common Conversions. Standard Prefixes. Review Notation. 1,000,000,000 = 10 9 1,000,000 = 10 6 1,000 = 10 3 1 = 10 0 .001 = 10 -3 .000001 = 10 -6 .000000001 = 10 -9. Celestial Sphere.

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Chapter 2: The Sky

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  1. 0 Chapter 2:The Sky

  2. Common Units we will use

  3. Common Conversions

  4. Standard Prefixes

  5. Review Notation • 1,000,000,000 = 109 • 1,000,000 = 106 • 1,000 = 103 • 1 = 100 • .001 = 10-3 • .000001 = 10-6 • .000000001 = 10-9

  6. Celestial Sphere • When we look at the sky, we see stars but have no actual clue as to how far away they are. Therefore it is as if they were all on a sphere out a long distance from us. This conceptual device is known as the celestial sphere. • Distances between objects then are measured in angles since all objects appear to be at the same distance. • This is an example of the use of a model.

  7. Celestial Sphere Attributes • North and South Celestial Poles. • Zenith (point directly overhead. • Nadir (point directly below – through earth) • Celestial equator (extension of plane through the earth at equator and extended to sphere.

  8. 0 The Celestial Sphere • Zenith = Point on the celestial sphere directly overhead • Nadir = Point on the c. s. directly underneath (not visible!) • Celestial equator = projection of the Earth’s equator onto the c. s. • North celestial pole = projection of the Earth’s north pole onto the c.s.

  9. Discussion • If the Earth did not rotate about its axis, could we define a celestial sphere as we do now? • Could we even define a set of poles and equator? • What is the difference between a constellation and an asterism? Examples? • What does the word apparent mean in the context of “apparent visual magnitude”?

  10. More discussion • Where on Earth can you see both the North and South Celestial poles simultaneously?

  11. Constellations 0 Orion Betelgeuse Rigel Stars are named by a Greek letter (a, b, g) according to their relative brightness within a given constellation + the possessive form of the name of the constellation: Betelgeuse = a Orionis, Rigel = b Orionis

  12. 0 The Magnitude Scale First introduced by Hipparchus (160 - 127 B.C.) • Brightest stars: ~1st magnitude • Faintest stars (unaided eye): 6th magnitude More quantitative: Now that we have instrumentation: • 1st mag. stars appear 100 times brighter than 6th mag. stars • 1 mag. difference gives a factor of 2.512 in apparent brightness (larger magnitude => fainter object!)

  13. Where did 2.512 come from? • There are 5 magnitudes difference between magnitude 1 and magnitude 6 stars. • The magnitude 1 star is defined to be 100 times as bright as a magnitude 6 star. • The steps are equal brightness factor. • Therefore each one of the steps is equal to (100) 1/5 = 2.512 (fifth root of 100)

  14. 0 Example: Betelgeuse Magnitude = 0.41 mag Rigel For a magnitude difference of 0.41 – 0.14 = 0.27, we find an intensity ratio of (2.512)0.27 = 1.28 Magnitude = 0.14 mag

  15. 0 The Magnitude Scale The magnitude scale system can be extended towards negative numbers (very bright) and numbers > 6 (faint objects): Sirius (brightest star in the sky): mv = -1.42 Full moon: mv = -12.5 Sun: mv = -26.5

  16. More standard values

  17. 0 The Celestial Sphere On the sky, we measure distances between objects as angles: The full circle has 360o (degrees) 1o has 60’ (arc minutes) 1’ has 60” (arc seconds).

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