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Understanding Celestial Measurements: Parallax and Distance Calculation Techniques

maia-benjamin avatar
maia-benjamin
39 diapositives · 542 Views · Nov 21, 2014

Dive into the fascinating world of celestial measurements, focusing on parallax and geometry principles. This guide covers essential logistics, homework requirements, and the significance of measuring celestial objects like the Sun and Polaris from different locations. Explore key questions regarding the Earth's wobble, the rising positions of celestial bodies, and practical exercises to calculate distances using parallax. Transform your understanding of the universe and enhance your observational skills in astrophysics.

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  1. 1

  2. Prologue Parallax 2

  3. Logistics • Homework • If you are not signed up - SIGN UP! • Tutor (TBD - drop in time? - one on one?) • Clicker • If you do not have one - GET ONE! • register • Folder • If you do not have one - GET ONE! • Use the correct box • Re-use pages 3

  4. Review • What was the most important thing you learned? • Elliptical orbit does not create our seasons. • The Earth is on a wobble, but it takes 26,000 years. • You cannot “prove” something, but you can disprove it. 4

  5. Lab Notes • Binocular lab Monday, Thursday (?) • http://faculty.fortlewis.edu/hakes_c 5

  6. Where along the horizon does the Sun rise on June 21 in Durango, Colorado? A) North of east B) Due east C) South of east D) Can’t tell with information given 6

  7. Where along the horizon does the Sun rise on June 21 in Durango, Colorado? A) North of east B) Due east C) South of east D) Can’t tell with information given 7

  8. Where along the horizon does the Sun rise on June 21 in Sydney, Australia? A) North of east B) Due east C) South of east D) Can’t tell with information given 8

  9. Where along the horizon does the Sun rise on June 21 in Sydney, Australia? A) North of east B) Due east C) South of east D) Can’t tell with information given 9

  10. You carefully measure the height of Polaris from Durango and from Grand Junction to the north. A) Polaris appears higher in Durango B) Polaris appears higher in Grand Junction C) Polaris is the same height in both places D) not enough information 10

  11. You carefully measure the height of Polaris from Durango and from Grand Junction to the north. A) Polaris appears higher in Durango B) Polaris appears higher in Grand Junction C) Polaris is the same height in both places D) not enough information 11

  12. You carefully measure the height of the noon Sun from Durango and from Grand Junction. A) The Sun is higher in Durango B) The Sun is higher in Grand Junction C) Which is higher depends on the season. D) Not enough information. 12

  13. You carefully measure the height of the noon Sun from Durango and from Grand Junction. A) The Sun is higher in Durango B) The Sun is higher in Grand Junction C) Which is higher depends on the season. D) Not enough information. 13

  14. Measuring Distances • Question for discussion - How can you find the distance to an object? Come up with three methods. 14

  15. Measuring Distances • Question for discussion - How can you find the distance to a distant object without traveling to it? 15

  16. Measuring Distances • Measuring angles • Parallax 16

  17. More Precisely P-1Angular Measure 17

  18. Trigonometry 18

  19. Trigonometry • sin(q) = opposite/hypotenuse • cos(q) = adjacent/hypotenuse • tan(q) = opposite/adjacent 19

  20. Figure P.10Triangulation 20

  21. Figure P.11Parallax 21

  22. Figure P.12Parallax Geometry 22

  23. Star A has a parallax shift of 0.2 arc secondStar B has a parallax shift of 0.5 arc seconds A) Star B is more than twice as far as star A B) Star B is a little farther than star A C) Star A is more than twice as far as star B D) Star A is a little farther than star B E) Not enough information 23

  24. More Precisely P-2aMeasuring Distances with Geometry x distance 24

  25. Radians • Not just an extra button on your calculator • 2p radians in a circle • Conversion formula 2p rad = 360° 25

  26. Small Angle Approximation • Angle must be in radians • Angle must be small • (opposite << adjacent) • Then: q sin(q)  tan(q) 26

  27. Small Angle Approximation • For small angles in radians: angle = baseline/distance 27

  28. Small Angle Approximation • For small angles in radians: angle = baseline/distance or distance = baseline/angle or baseline = angle*distance 28

  29. Distance of your thumb • Group exercise - use parallax to calculate the distance to your thumb. 29

  30. Distance of your thumb • If your baseline is 5cm, (about the width of your eyes) and • You observe a parallax shift of 0.1 radian (about 5.7 degrees) then • Use distance = baseline/angle • Your thumb is about 50cm away. 30

  31. If your baseline is 25cm, and you observe a parallax shift of 0.01 rad. • The distance to the object is: 1: 2.5cm 2: 2500cm 3: 25000cm 31

  32. More Precisely P-2bMeasuring Distances with Geometry 32

  33. Small Angle Approximation • If you know the size of an object, you can determine it’s distance using the same triangle formulas distance = baseline/angle • This time the “baseline” is the known diameter of the object and the angle is the observed apparent “size” of the object. 33

  34. Observing from a latitude of 25° North A) The star Polaris appears about 65° above the horizon. B) The celestial equator has a maximum height of 65° above the horizon. C)The star Polaris appears about 25° north of the zenith point. D) The celestial equator has a maximum height of 25° above the horizon. 34

  35. Discussion • Where does Polaris appear when standing on the equator? • Where does Polaris appear when standing on the pole? • How high does the celestial equator appear when standing on the equator? • How high does the celestial equator appear when standing on the pole? 35

  36. Observing from a latitude of 25° North A) The star Polaris appears about 65° above the horizon. B) The celestial equator has a maximum height of 65° above the horizon. C)The star Polaris appears about 25° north of the zenith point. D) The celestial equator has a maximum height of 25° above the horizon. 36

  37. Observing from a latitude of 55° North A) The star Polaris appears about 35° above the horizon. B) The celestial equator has a maximum height of 55° above the horizon. C)The star Polaris appears about 35° north of the zenith point. D) The celestial equator appears about 35° south of the zenith point. 37

  38. Observing from a latitude of 55° North A) The star Polaris appears about 35° above the horizon. B) The celestial equator has a maximum height of 55° above the horizon. C)The star Polaris appears about 35° north of the zenith point. D) The celestial equator appears about 35° south of the zenith point. 38

  39. Three Minute Paper • Write 1-3 sentences. • What was the most important thing you learned today? • What questions do you still have about today’s topics? 39