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### Stars

1. 1. stars Parallax and Magnitude
2. 2. 2p 1AU 1AU 61Cygni To distant star p p
3. 3. <ul><li>A Star with a parallax of 1 arc-second is </li></ul><ul><li>1 parsec from the Earth </li></ul><ul><li>1 par ( allax) sec ( ond ) </li></ul>
4. 4. <ul><li>Distance ( pc ) = 1 . </li></ul><ul><li>Parallax ( s ) </li></ul>
5. 5. 61 Cygni is 0.3 seconds of arc <ul><li>Distance = 1 </li></ul><ul><li>0.3 </li></ul><ul><li>= 3.33 pc from Earth. </li></ul>
6. 6. Consider a star 1 parsec from Earth
7. 7. 1AU CIRCUMFERENCE=60 X 60 X 360 AU
8. 8. 1 PARSEC CIRCUMFERENCE = 2 π parsec
9. 9. <ul><li>So 2 π parsecs = 60 x 60 x 360 AU </li></ul><ul><li>1 parsec = 5 x 10 AU </li></ul>
10. 10. <ul><li>= 3.26 LIGHT YEARS </li></ul><ul><li>61 Cygni is 3.33 x 3.26 Light Years </li></ul>
11. 11. About 11 Light Years away
12. 12. Looking At Brightness <ul><li>Using the inverse square law </li></ul>
13. 13. <ul><li>Observed Brightness 1 . </li></ul><ul><li>Area </li></ul><ul><li>1 . </li></ul><ul><li>distance ² </li></ul>
14. 14. <ul><li>Magnitude </li></ul>
15. 15. Ancient Greeks <ul><li>Brightest stars = Magnitude 1 </li></ul><ul><li>Dimmest stars = Magnitude 6 </li></ul>
16. 16. 19 th CENTURY LIGHT from a magnitude 1 star was 100 times brighter than from a magnitude 6 star.
17. 17. <ul><li>A Difference of 5 magnitudes </li></ul><ul><li>Corresponds to a ratio of 100 </li></ul>
18. 18. <ul><li>Since </li></ul><ul><li>2.5 x 2.5 x2.5 x 2.5 x 2.5 = 100 </li></ul><ul><li>A Difference of 1 magnitude </li></ul><ul><li>Corresponds to a ratio of 2.5 in the measured intensity of light </li></ul>
19. 19. <ul><li>The Sun has a magnitude of -26.7 </li></ul><ul><li>The dimmest star using a giant telescope + 25 </li></ul><ul><li>Naked eye +6 </li></ul>
20. 20. PROBLEMS <ul><li>How bright a star is ( apparent magnitude) </li></ul><ul><li>Doesn’t tell us how bright a star really is. </li></ul><ul><li>Why not ? </li></ul>
21. 21. <ul><li>It may be brighter, but distant </li></ul><ul><li>It may be dimmer ,but closer. </li></ul><ul><li>Stars are not all the same! </li></ul>
22. 22. ABSOLUTE MAGNITUDE <ul><li>Defined as equal to the apparent magnitude the star would have at a distance of 10 parsecs from Earth. </li></ul>
23. 23. <ul><li>The absolute magnitude of stars ranges from – 10 to +15 </li></ul>
24. 24. <ul><li>Absolute Magnitude = M </li></ul><ul><li>Apparent magnitude = m </li></ul><ul><li>Distance = d </li></ul><ul><li>M = m – 5 log d </li></ul><ul><li>10 </li></ul>
25. 25. Sirius <ul><li>Apparent magnitude – 1.46 </li></ul><ul><li>distance = 2.65 parsecs from Earth. </li></ul><ul><li>Absolute Magnitude M = - 1.46 -5 log(0.265) </li></ul><ul><li>= - 1.46 – 5( -0.58) </li></ul><ul><li>= - 1.46 + 2.9 </li></ul><ul><li>= 1.44 </li></ul>
26. 27. <ul><li>Period = 5.75 days </li></ul><ul><li>Magnitude increases at twice the rate it falls. </li></ul><ul><li>Magnitude changes by 0.7 </li></ul><ul><li>Hence intensity ratio = </li></ul><ul><li>= 1.9 </li></ul>
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