Middle and High School investigations in astronomy

1. Measuring what you can't touch - from the size of the Earth to the structure of the solar system, black holes and the expansion of the Universe Middle and High School investigations in astronomy

2. A little bit about us, and you! • Ian Dell'Antonio • Associate Professor of Physics at Brown (since 1999) • Research astronomer (focus on the distribution of matter in the Universe and gravity) • Instructor of astronomy courses at all level from non-specialist through graduate courses. • New to RITES in 2010 • Laura Woods --Woonsocket High School since 1998 • Cohort 1, year 2 resource team • Biology, Oceanography What drew you to this class?

3. Course logistics—first things first. • First create your student login: go to • http://rites-investigations.org • Directions for signing in are in your registration packet. • For this course, you should register as a student • At the end of the course you can create a teacher account, but for now use a student account (make sure you don’t use your favorite login name, as you’ll want to save that for your teacher account). • Add this course (course word “astro1”)—you should see our names and four investigations—we will only be using the two astronomy investigations.

4. The big picture: ESS GSEs ESS 2 The earth is part of a solar system, made up of distinct parts that have temporal Earth & Space and spatial interrelationships. ESS 3 The origin and evolution of galaxies and the universe demonstrate fundamental principles of physical science across vast distances We have attempted to construct two investigations that address the GSEs—but do not cover all topics in astronomy. One of the central ideas of astronomy is that even in the distant Universe, the same laws of physics apply. Building the connection between measurements on Earth and in space can help make astronomy seem less remote and abstract. The philosophy behind these investigations is to build student understanding starting from ideas that are familiar to them.

5. The Goals of this Investigation: addressing the GSEs • GSEs concerning astronomy are overlooked for a variety of reasons—each investigation has three activities (each broken down into multiple sub-activities) that address different aspects of the ESS GSEs. • Many of the sub-activities can “stand alone” in order to target any holes you have identified • The activities can be combined in many different ways to focus on different topics • We’ll provide you with background knowledge so that you feel comfortable using the activities

6. Two central themes—distances and gravity Distances—important for understanding the scale of the Universe. “Depth” of space is not obvious—you can’t measure distances directly. But you can measure directions. Using angles to measure distances and sizes—connect to measures on Earth and to geometry. We will begin with activity 1 of the investigation (both MS and HS)

7. Background: 1 One of the fundamental issues in astronomy is that space is big. Inconvenient! At the same time, when you look at the night sky, it looks flat—there is (almost) no 3-D information that is apparent in the sky. How do you figure out the scale of the Universe? We don’t have large enough rulers…

8. Distances from angles—triangulation Angles can be thought as measuring the difference between two directions (technically of vectors, but no matter). If you look in two directions, the difference in directions defines an angle. We will use both these ways of defining angles to measure distances and sizes in this investigation. If you move but look at the same object, the two directions you look in also define an angle.

9. A common experience: Imagine you’re driving on a road, and you see a tree with a mountain behind it in the distance. As you drive, the direction to the tree changes quickly—the direction to the mountain does not! This is the secret to measuring distances with angles—for a fixed distance between the two viewpoints, the angle changes more if the object you are viewing is closer.

10. A bit of Math Trigonometry tells you that the relationship between the angle and the distances traveled is: Tangent(angle)= distance traveled/distance to object If the ratio of the distances is small (the distance traveled is less than distance to the object) We can use the “small angle approximation”—to a good approximation, Tan(x) ~ x if x<<1 (good to 20% even when x=1!) This is only true if the angle is measured in radians (these are units in which a circle has 2p radians) . To convert from radians to degrees: If 360 degrees= 2p radians, then 1 radian = 360/2p = 180/p ~ 57.3 degrees. So, in degrees: Tan(x) = x/57.3. For small angles, our relation is: For small angles, our relation is: angle/57.3 = dtraveled/dobject

11. This also can be used for heights and sizes of single objects: The same relation works with the relation between size or height and distance of an object (it’s the same triangle after all). The apparent size of an object—how big it appears to our eyes— is just a measure of the angle between one end of the object and the other. We call this angle the “subtended angle”. Notice, from the formula above, that the subtended angle is proportional to 1/distance. This is just the mathematical statement of something you all know.

12. Exploring the Investigation--1 • To get a practical feel for measuring distances with angles, we will build an instrument to measure angles and explore the measurements. • Open the investigation: Measuring what you can't touch - from the size of the Earth to the structure of the solar system (We will start with the middle-school version—the high school version is very similar but adds one more sub-activity and uses a little more math). • Teacher Guide • Activity 1, sub activity 1

13. Some FYI sources of information/tools to use: • www.xtranormal.com • Make your own movies with any text (examples within teacher introduction and other investigations) • Free for educators, but you must request an account • http://www.forestwatch.sr.unh.edu/ • Tool used to measure heights indirectly (hypsometer clinometer) • Students collect data that is used to assess tree health – white pine trees are “green canaries”

14. Up next: Subactivity 2 • How Far Away is the Moon? It makes sense to start the investigation of space with our nearest neighbor. (familiar to everybody) Even though the distance to the Moon is no longer measured using angles (radar is even more accurate)

15. Triangulation and the distance to the Moon. • The Moon is too far away for the direction to change much if you just move a short distance (have you experienced the “Moon seems to follow you” phenomenon? We are so used to directions changing as we move that the fixed direction to the Moon seems odd!) However, moving a bit further and using a telescope (why a telescope?), it can be done (this is sub-activity 2 of the MS and HS investigations)

16. A little more math. As the distances get bigger, the angles get smaller. Measuring the angles in degrees no longer works. Introduce smaller units: 1 degree = 60 arcminutes 1 arcminute = 60 arcseconds. Look familiar? The sexagesimal system is our inheritance from the babilonians If we measure the angles in arcseconds, the small angle formula becomes: angle/(57.3x60x60) = angle/206,265 = dtraveled/dobject The naked eye can resolve differences in direction of about 1 arcminute. Telescopes can do much better—even a small amateur telescope brings this down to around an arcsecond, where the atmosphere permits it.

17. Measuring the distance to the Moon To see a shift in the direction to the Moon, you have to move a long way – road trip! You also need a reference point to compare to (remember the mountain?) But, there’s a catch. The Moon moves, too. It takes about 27.5 days to orbit the Earth– that’s about ½ an arcsecond every second. If you wait two hours, the Moon wll have moved a degree. How can you measure from two places at once? On October 10, 2006, the Moon passed right in front of the Pleiades—it happened to be Brown’s fall break.

18. Double vision… Robert Horton, Brown astronomy lab manager was on vacation in New Hampshire, about 120 miles north of Providence; the exact distance can be found using the latitude and longitude of the observing sites. Using the same telescopes and cameras, we observed the Moon at the same time (cell phones are useful) The two images were digitized, and we measured the position of a crater on the Moon relative to the stars (The stars are very far away, and their direction doesn’t change in a measurable way—they are our reference)

19. The two images Rhode Island image New Hampshire image Maia Merope Alcyone

20. How to find the coordinates on each image? • Based on the position of three stars, software programs can calculate the position of any object in the image (we will use the aladin java applet developed by the european southern observatory) Measure the coordinates on the sky (like latitude and longitude of the same crater in both images. How to measure angles?

21. The size of the Moon? Once we have the distance to the Moon, we can use the same relation to measure the size of the Moon. Measuring the angular size of the Moon in arcseconds, we use: (angle/206,265) = size/distance The angular size of the Moon is about 2000 arcseconds (it varies, why?) How big is the Moon?

22. Beyond the Moon--Parallax This part of the investigation is only in the high-school investigation. In the previous section, we used the stars as reference—even between here and New Hampshire doesn’t change their direction. Need to move further. But rockets are expensive.

23. Eppursimuove… We are sitting on a moving platform! As the Earth goes around the Sun, we move relative to the stars! If we observe the same star twice, six months apart, we will have moved 300 million kilometers—much more than to NH. In six months, the star’s position changes by 2p (p is the parallax angle, the angle shift when one moves a distance equal to the Earth-Sun distance). All we have to do is measure p, and then D = 206,265 Dsun / p

24. History of parallax measurements The figures are misleading, the angles are really small! (in fact, in ancient times the lack of parallax was cited as proof that the Earth stood still. Now we know the stars are just very far away!) First parallax for a star measured in 1838 (by Bessel)– p=0.38 arcseconds. The biggest parallax is Proxima Centauri: p=0.61 arcseconds. Because the values are small, define a new unit: the parsec: 1 parsec = 206,265 Dsun. Why? Because D = 206,265 Dsun / p = 1 parsec / p Only a few hundred stars measured before 1990 Need to escape the blurring of the atmosphere

25. The Hipparcos satellite and data Named after the greek astronomer who made very early charts of stellar positions. Launched by ESA (European version of NASA) in 1989, made very careful measurements of stars for 5 years—why multiple yeears? Stars move, too….

26. Stellar parallax and the properties of stars. Hipparcos has made available online a catalog of positions of more than 1 million stars—1000x what was known before (but less than 0.001% of the stars in the Milky Way!) Students can search the parallax via the star names. For example, Maia: Brightness (smaller is brighter) Parallax, in milli-arcseconds Angular motion of the star itself.