1. NASA’s Mysteries of the Universe: Dark Matter Janet Moore NASA Educator Ambassador Janet Moore NASA Educator Ambassador

2. Merry-Go-Round

4. Solar System

8. In Summary - Solar System F Orbital speed depends on force of gravity F Force of gravity depends on mass within the radius F Therefore, orbital speed depends on mass within the radius

9. What About Galaxies? F How would you expect stars to move around in a spiral galaxy? F What would you expect the mass distribution in a spiral galaxy to be?

10. The Activity - NGC 2742 F You will be given: F Rotation Curve (velocity vs. radius) F Luminosity Curve (luminosity vs. radius) F Use the Data Chart to analyze the mass in the galaxy F G = 4.31 x 10 -6

11. Sample Data Chart RadiusRot. Vel. Grav. Mass Lum.Lum. Mass Lum/ Grav 1801.5 e93 e86 e80.4 31006.9 e91 e92 e90.29 51201.7 e102 e94 e90.24 81403.6 e103.5 e97 e90.19

12. Evidence for Dark Matter F Light (visible matter) drops off as you go farther out in a galaxy F BUT... Velocities do not drop off F Result: Dark Matter mass is about 10x Luminous Matter mass F Light (visible matter) drops off as you go farther out in a galaxy F BUT... Velocities do not drop off F Result: Dark Matter mass is about 10x Luminous Matter mass

13. What is Dark Matter? F Baryonic (Normal) Matter: F Low mass stars, brown dwarfs (likely), large planets, meteoroids, black holes, neutron stars, white dwarfs, hydrogen snowballs, clouds in halo. F Non-Baryonic (Exotic) Matter: F Hot Dark Matter: fast-moving at time of galaxy formation, eg massive neutrinos F Cold Dark Matter: slow-moving at times of galaxy formation, eg WIMPs -- particle detector experiments looking for them F Baryonic (Normal) Matter: F Low mass stars, brown dwarfs (likely), large planets, meteoroids, black holes, neutron stars, white dwarfs, hydrogen snowballs, clouds in halo. F Non-Baryonic (Exotic) Matter: F Hot Dark Matter: fast-moving at time of galaxy formation, eg massive neutrinos F Cold Dark Matter: slow-moving at times of galaxy formation, eg WIMPs -- particle detector experiments looking for them

14. NASA’s Fermi Mission

15. Common Core Mathematical Practices F Make sense of problems and persevere in solving them. F Reason abstractly and quantitatively. F Construct viable arguments and critique the reasoning of others. F Model with mathematics. F Use appropriate tools strategically. F Attend to precision. F Look for and make use of structure. F Look for and express regularity in repeated reasoning. F Make sense of problems and persevere in solving them. F Reason abstractly and quantitatively. F Construct viable arguments and critique the reasoning of others. F Model with mathematics. F Use appropriate tools strategically. F Attend to precision. F Look for and make use of structure. F Look for and express regularity in repeated reasoning.

16. Mathematical modeling F 1. Observing a phenomenon, delineating the problem situation inherent in the phenomenon, and discerning the important factors that affect the problem. F 2. Conjecturing the relationships among factors and interpreting them mathematically to obtain a model for the phenomenon. F 3. Applying appropriate mathematical analysis to the model. F 4. Obtaining results and reinterpreting them in the context of the phenomenon under study and drawing conclusions. Swetz, F., & Hartzler, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. (pp. 2-3). Reston, VA: National Council of Teachers of Mathematics. F 1. Observing a phenomenon, delineating the problem situation inherent in the phenomenon, and discerning the important factors that affect the problem. F 2. Conjecturing the relationships among factors and interpreting them mathematically to obtain a model for the phenomenon. F 3. Applying appropriate mathematical analysis to the model. F 4. Obtaining results and reinterpreting them in the context of the phenomenon under study and drawing conclusions. Swetz, F., & Hartzler, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. (pp. 2-3). Reston, VA: National Council of Teachers of Mathematics.

17. Questions? Janet Moore www.NASAJanet.com JanetMoore@gmail.com epo.sonoma.edu Janet Moore www.NASAJanet.com JanetMoore@gmail.com epo.sonoma.edu