1. ASTROID [1][2] [1] Gravitational Lens, HST observation of Abell 2218 [2] Rotation curve (observed and theoretical), SuW 1/2005 S.32ff. Lesson Plan Guided Research Model Dr. Christian Reimers reimers@astro.univie.ac.at http://www.virtuelleschule.at/cosmos/

2. General Information The scenario aims to illustrate one of the evidences for dark matter. This includes the study of the rotational curves of spiral galaxies. –Duration: 3 x 50 min. –Vocabulary: dark matter, galaxies, rotation curve –Tools and Materials: PC with Internet connection, Paper, work sheets (excel, diagram), Pencil –Aims and Objectives: Students should... -... be able to plot data -... learn basics on the structure and detection of matter –Students‘ Misconception: - confusing types of matter - visible parts of galaxies are dominant

3. Educational Phase 1: Stimulation –Presentation/Discussion: motivation by emotion (pictures of galaxies) [1] HST observation of M51 „Whirlpool Galaxy“[2] HST observation of M104 „Sombrero Galaxy“

4. Educational Phase 2: Scientific Prediction –Discuss list of possible dark matter candidates and their interactions with measurable quantities / indirect detection –Draw up a list on the blackboard with various proposed methods and missions to detect dark matter –Finding pictures of galaxies and their rotation curves (internet research) [2] Interactive Applet on the Doppler effect [3] Doppler image of M33 [1] Illustration of the galaxies rotation (Sextans A)

5. Educational Phase 3: Experimental Activities –Kepler rotation in the Solar System (central point mass) –Applet with M(r) => v(r) [in development] [2] „rotcurve“-Applet of real galaxies http://burro.cwru.edu/JavaLab/RotcurveWeb/main.html [1] Work sheet: Kepler rotation in the Solar System

6. Educational Phase 4: Abstraction of the finding –Prediction Compared to Results: v 2 (r) = G * (M visible (r) + M dark (r)) / r If existing matter is only the observed (visible) matter, the rotation curves of spiral galaxies could not be described. M tot > M visible => M dark thus M tot = M visible + M dark With assistance of Tutorials and Links. –Discussion: Short discussion on detection methods and theoretical issues.

7. Educational Phase 5: Consolidation –Quiz/Multiple-Choice-Test with Feedback –Exercises/Tasks: Comparing simple calculations and self-composed diagrams with obtained data Talk: Thoeretical background ist provided to find information on the internet to start a talk about types of dark matter Discussion: Change of paradigm of matter over the centuries [1] Multiple-Choice-Test (ASTROID)

8. Ressources: –Worksheet (solar system; xls) –Worksheet (diagram; pdf) –Simulation (rotation curve; Applet) –Glossary (of related terms; pdf) –Examples with solutions and diagrams (for teachers; pdf) –Informationsheet (types of matter; pdf) –Informationsheet (posibilities of types of DM; pdf) –Informationsheet (internetlinks and further infos; pdf)