1. Journal 9/9/14 Imagine you’re standing at the base of a tall flagpole. Explain how you might measure the height of this flagpole without getting closer than 50 feet to it. To learn how we measure the distances to the nearest stars Read section 1.6. Do review q’s 17-19 on pp 28 Objective Tonight’s Homework

2. x x 2 Let’s take 5 minutes to share how we’d do the warmup. Let’s come up with a real, workable plan. Calculating Distance

3. 3 Hold a finger at arm’s length and close one eye. Focus where your eye is in relation to something in the background. Now switch which eye is open. You’ll notice that your finger has moved relative to the background. This phenomenon is called parallax. Notes on Distance and Position

4. 4 We can do the same thing with the Earth and close stars. The difference in position between Earth in winter and summer is like the distance between your eyes. How the star moves compared to the background is like how your finger moves compared to a distant object. Notes on Distance and Position

5. 5 150,000,000 km distance to star P - parallax rangle d visible angle change seen

6. 6 Notes on Distance and Position Using simple trigonometry, we can calculate the distance to the nearby star. d(km) = r (km) / tan(P) 150,000,000 km distance to star P - parallax rangle d visible angle change seen

7. 7 Notes on Distance and Position If you don’t know what “tan” is or haven’t taken trigonometry, don’t worry. You can still use this equation pretty easily without having to understand. Let’s do an example: Let’s say we see a star shift by 0.8 degrees between summer and winter. How far is it?

8. 8 Notes on Distance and Position If you don’t know what “tan” is or haven’t taken trigonometry, don’t worry. You can still use this equation pretty easily without having to understand. Let’s do an example: Let’s say we see a star shift by 0.8 degrees between summer and winter. How far is it? 0.8 degrees is the “visible angle”, so parallax angle is 0.4 degrees. d(km) = r (km) / tan(P) r = 150,000,000 km / tan(0.4) r = 150,000,000 km / 0.00698 r = 2.15x10 10 km. Really far away!

9. 9 Notes on Distance and Position So we can calculate distances to the nearest stars in kilometers. But even the nearest star is 4.11x10 13 kilometers away! 41,100,000,000,000 km is really awkward to write.

10. 10 Notes on Distance and Position So we can calculate distances to the nearest stars in kilometers. But even the nearest star is 4.11x10 13 kilometers away! 41,100,000,000,000 km is really awkward to write. We use the speed of light to get distances in space instead. Light travels at 3x10 8 m/s. At this speed, it can travel from the sun to the Earth in just 8 minutes. We say that the sun is 8 light minutes away from Earth.

11. 11 Notes on Distance and Position The distance light can travel in one year is called a “light-year”. This is equal to 9.46x10 15 meters, or 9.46x10 12 km The nearest star is 4.3 light years away.

12. 12 Notes on Distance and Position So lastly, we can use our parallax equation in reverse to see just how much real stars shift between summer and winter. Nearest star = 4.3 ly 4.3 ly * (9.46x10 12 km/ly) = 4.068x10 13 km d = r / tan(p) 4.068x10 13 km = 150,000,000 km / tan (p) tan (p) = 150,000,000 km / 4.068x10 13 km p = tan -1 (150,000,000 km / 4.068x10 13 km) p = 2.11x10-4 x2 for visible shift, so… We see the star shift by 0.00042 degrees. That’s not very much!

13. 13 Practicing Parallax Find the distance in light years to a star if it has an angle shift of… 1) 0.000 002 1 degrees 2) 0.000 000 33 degrees 3) 0.000 000 066 degrees

14. Exit Question #9 What does an increased baseline do for calculating parallax? a) Increase the minimum distance we can measure to b) Decrease the accuracy of the measurement c) Increase the distance to the measured object d) Increase the precision of the measurement e) Increasing the baseline does nothing for us f) None of the above