“The Distance to the Stars: How Do Scientists Know?”

1. “The Distance to the Stars: How Do Scientists Know?” Teacher Training Courses in Ohio and Michigan, June 2006

2. Pre-Test • Q. 1 Which of the following best represents your understanding of the distances to the stars that are visible (w/o telescope) in our night sky? • Within a small range, all of the stars are at about the same distance. • All the stars we see vary greatly in distance from the Earth. • Most of the stars vary greatly in distance, however the stars in a constellation like Orion are all at the same distance.

3. Pre-test (con.) • Q. 2 Explain how you believe astronomers can measure the distance to a star. • Q. 3 Distinguish between the Brightness of a star and the Luminosity of a star.

4. Pre-test (con.) • Q. 4 Imagine a square meter in a field near your house at high noon on a bright, sunny day. Approximately how many watts of light would you estimate is falling on that area? a. 10 watts, b. 100 watts, c. 1,000 watts, d. 10,000 watts, e. greater than 10 KW

5. Pre-test (con.) • Q. 5 If the sun were twice as far away from the Earth, how would you answer Q. 4? • Q. 6 Estimate how many toothpicks, laid end-to-end, it would take to reach the planet Mars. Assume Mars is at its closest point to the Earth.

6. Answers?? Let’s answer them together……

7. “The Distance to the Stars” • Workshop inspired by article in February 2005 issue of The Science Teacher, (NSTA, National Science Teachers Assoc.) • Title: “How Far Are the Stars?”

8. Concept: Distance Ladder

9. HOU Curriculum Books • Measuring Distance: Distance Ladder introduction, Inverse Square Law, Standard Candle introduction, using Cepheid Variables to determine distance. • Measuring Brightness: SN Light Curves. • Searching for SNe: How to locate a SN.

10. What to add? • Parallax • Using a Supernova Ia as a standard candle to calculate distance. • Performing a “Distance Ladder” calculation

11. Simple Distance Ladder Activity GOAL: Determine the length of this room in #’s of paperclips. • Begin with one paperclip as the smallest unit. • Create a larger unit with X paperclips. • Create one unit even larger. • Estimate the # of paperclips for this room.

12. Parallax • Concept: thumb in front of your eyes. One eye open, one eye closed. • Switch open and closed eyes. What does your thumb appear to do? • Thumb close…….more parallax. • Thumb far…….less parallax. • An INVERSE relationship.

13. Outdoor Parallax C “Pole” p’ B Distant Background p Baseline (b) A d D p = parallax angle

14. A p B d Basic Geometry The small angle formula gives us: p = (AB/d), with p in RADIANS (pR). A little algebra manipulation gives: d = (AB/pR)

15. Outdoor approximation • It’s impossible to measure p directly. However, if the distance to the background is >>> d, then angle p’ is approximately equal to p. Justification with long string • We can measure p’ directly by measuring the “Angular Size” of segment CD.

16. Measuring Angular Size C p’ B Distant Background EYE x A Y Hold ruler in front of your eye. Match up “x” with C and D. Measure x. Partner measures y. Angular size of CD = p’ = (X/Y) radians D

17. Example • Measure AB = 8.4 meters • Measure angle p’ (angular size of CD) using ruler and meter stick. x = 5 cm, y = 60 cm. • Calculate p’ = x/y = 0.083 radians • Calculate d = AB/pR = 8.4/0.083 ~ 100 m. • Alternate: d = AB * (Y/X)

18. Setting up a baseline

19. Measuring the angle

20. Do it INSIDE with Eye-Eye as baseline • Baseline = Eye to Eye • “Pole” = your thumb held at arm’s length • Switch eyes to locate C and D on the wall • Measure p’ using X and Y (approx.) • Measure Eye-Eye distance (approx.) • Calculate d (to your thumb) = AB/p’ = (Eye to Eye distance) x (Y/X)

21. Parallax of an Asteroid • Use HOU-IP: Display two images taken of an asteroid from two different telescopes • OR at two different times from the same telescope. (difficult to determine baseline) • Can view and measure the parallax angle directly from subtracted images. Shift in pixels x plate scale = p” (in arcsecs) • Calculate distance: d = (AB/p”)*206,265

22. Next steps on Distance Ladder • Investigate Inverse Square Law with Light probes. • Clarify distinction between Brightness (B) and Luminosity (L) for stars in the formula B = L/4pd2. • Use HOU Unit on Cepheid Variables to get distance measurement in our galaxy. • Use SN Ia to get d for distant galaxies.

23. Supernova Light Curve Unit

24. Light Curve Data taken from SN1994i in M51

25. Results from Measurements and Calculations in activity • Light Curve peaks at 1.46 x Reference Star on ~day 11 and drops quickly • Most likely a SN type I (assume Ia although probably a Ic from spectroscopic data) • SN at max ~ same as galaxy core • Core ~ one billion “Suns” in luminosity • SN ~ 200 million “Suns” using Aperture tool

26. New Activity: Distance to M51 GOAL: Determine the distance to M51, using a simple distance ladder. Already known: • Max B of SN compared to Ref Star • L of SN in terms of “Suns” • Relationship between L, B and d

27. Distance to M51 (con.) To measure or find on internet: • B of the Sun on the Earth (“Solar constant” from internet shows ~1370 w/m2. Light probe in Michigan measured ~1000 w/m2) • Distance from the Sun to the Earth (1 AU = 150 million km) **originally w/ parallax! • B of the Ref Star (8 E-14 w/m2 from http://simbad.u-strasbg.fr/sim-fid/pl )

28. Measuring the “solar constant”

29. Calculations: • L (Sun): ~1000 w/m = L/4pd2. Inserting d = 1.5 E11 m. gives L ~ 2.8 E26 watts. • L (SN) ~ 200 million Suns = 2 E8 x 2.8 E26 = 5.6 E34 watts. • B (SN) = 1.46 x Ref Star = 1.46 x 8 E-14 ~ 1.2 E-13 w/m2. • Finally: d (SN) = sqrt(L/4pB) ~ 1.9 E23 m ~ 20 Mly ~ 6.2 Mpc

30. Using Standard Candle value • L of SN Ia thought to be a “standard candle” at ~ 9 E34 watts. • The B of the SN in 1994i is still ~ 1.46 x Ref Star = 1.2 E-13 w/m2. • Applying the inverse square law gives d ~ 8 Mpc. The published value of the distance to M51 is ~10 Mpc!

31. M 51 L (M 51) = ? d = ? L (sun) = ? Sun 1 AU B (sun) = ? B (M 51) = ? Earth