Charles Hakes Fort Lewis College1

Charles Hakes Fort Lewis College2 Prologue Parallax

Charles Hakes Fort Lewis College3 Logistics Homework If you are not signed up - SIGN UP! #2 due Friday do #1 too! “late fee” is only 3.3%/day Tutor (Wednesday 4:30-6:30, BH640)***

Charles Hakes Fort Lewis College4 Logistics 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 Remove “fringe”

Charles Hakes Fort Lewis College5 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.

Charles Hakes Fort Lewis College6 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

Charles Hakes Fort Lewis College7 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

Charles Hakes Fort Lewis College8 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

Charles Hakes Fort Lewis College9 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

Charles Hakes Fort Lewis College10 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

Charles Hakes Fort Lewis College11 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

Charles Hakes Fort Lewis College12 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.

Charles Hakes Fort Lewis College13 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.

Charles Hakes Fort Lewis College14 Measuring Distances Question for discussion - How can you find the distance to an object? Come up with three methods.

Charles Hakes Fort Lewis College15 Measuring Distances Question for discussion - How can you find the distance to a distant object without traveling to it?

Charles Hakes Fort Lewis College16 Measuring Distances Measuring angles Parallax

Charles Hakes Fort Lewis College17 More Precisely P-1 Angular Measure

Charles Hakes Fort Lewis College18 Trigonometry

Charles Hakes Fort Lewis College19 Trigonometry sin(  ) = opposite/hypotenuse cos(  ) = adjacent/hypotenuse tan(  ) = opposite/adjacent

Charles Hakes Fort Lewis College20 Figure P.10 Triangulation

Charles Hakes Fort Lewis College21 Figure P.11 Parallax

Charles Hakes Fort Lewis College22 Figure P.12 Parallax Geometry

Charles Hakes Fort Lewis College23 Star A has a parallax shift of 0.2 arc second Star 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

Charles Hakes Fort Lewis College24 More Precisely P-2a Measuring Distances with Geometry  x distance

Charles Hakes Fort Lewis College25 Radians Not just an extra button on your calculator 2  radians in a circle Conversion formula 2  rad = 360°

Charles Hakes Fort Lewis College26 Small Angle Approximation Angle must be in radians Angle must be small (opposite << adjacent) Then:   sin(  )  tan(  )

Charles Hakes Fort Lewis College27 Small Angle Approximation For small angles in radians: angle = baseline/distance

Charles Hakes Fort Lewis College28 Small Angle Approximation For small angles in radians: angle = baseline/distance or distance = baseline/angle or baseline = angle*distance

Charles Hakes Fort Lewis College29 Distance of your thumb Group exercise - use parallax to calculate the distance to your thumb.

Charles Hakes Fort Lewis College30 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.

Charles Hakes Fort Lewis College31 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

Charles Hakes Fort Lewis College32 More Precisely P-2b Measuring Distances with Geometry

Charles Hakes Fort Lewis College33 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.

Charles Hakes Fort Lewis College34 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.

Charles Hakes Fort Lewis College35 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?

Charles Hakes Fort Lewis College36 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.

Charles Hakes Fort Lewis College37 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.

Charles Hakes Fort Lewis College38 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.

Charles Hakes Fort Lewis College39 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?