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National Aeronautics andSpace Administration Aeronautics National Astrobiology Math This collection of activities is based on a weekly series of space science problems intended for students looking for additional challenges in the math and physical science curriculum in grades 6 through 12. The problems were created to be authentic glimpses of modern science and engineering issues, often involving actual research data. The problems were designed to be one-pagers with a Teacher’s Guide and Answer Key as a second page. This compact form was deemed very popular by participating teachers. Astrobiology Math Mathematical Problems Featuring Astrobiology Applications Dr. Sten Odenwald NASA / ADNET Corp. [email protected] Astrobiology Math i http://spacemath.gsfc.nasa.gov Acknowledgments: We would like to thank Ms. Daniella Scalice for her boundless enthusiasm in the review and editing of this resource. Ms. Scalice is the Education and Public Outreach Coordinator for the NASA Astrobiology Institute (NAI) at the Ames Research Center in Moffett Field, California. We would also like to thank the team of educators and scientists at NAI who graciously read through the first draft of this book and made numerous suggestions for improving it and making it more generally useful to the astrobiology education community: Dr. Harold Geller (George Mason University), Dr. James Kratzer (Georgia Institute of Technology; Doyle Laboratory) and Ms. Suzi Taylor (Montana State University), For more weekly classroom activities about astronomy and space visit the Space Math@ NASA website, http://spacemath.gsfc.nasa.gov Image Credits: Front Cover: Collage created by Julie Fletcher (NAI), molecule image created by Jenny Mottar, NASA HQ. Back Cover: The Milky Way showing Kepler search field (Photo courtesy NASA Kepler Mission/ Carter Roberts and Jon Lomberg); Transiting planet (Artist Lynette Cook’s depiction of a planetary eclipse in the HD 209458 system. Copyright 1999, Lynette Cook, all rights reserved). Interior: 6) Murchison meteorite (Chip Clark, Smithsonian Institution); 9) Bacterium (NASA/Jodi Blum); 11) S. Aureus (NIAID/RML); 12) Methanosarcinae acetavorans (Anon. Internet); 13) Brain (Anon. Internet); 19) Mioon atmosphere (T.A. Rector NOAO/AURA/ NSF); 20) CoRot 7b (ESO/ L. Calcada); 29) Exoplanets (Anon Internet); 456) HD209458b (NASA/ JPL-Caltech/T. Pyle (SSC)); 60) Stellar spectra (Helmut Abt/NOAA); 63) Sunset (Anon Internet); 65) Milky Way (R. Hurt, SSC/JLP/NASA); 72) Asteroid impact (David A. Hardy/AstroArt.com); 74) E.T. (Anon Internet). All other images are courtesy of NASA, NASA missions, or NASA facilities (e.g. STScI, JPL, etc) as indicated in text. Created under an Education and Public Outreach grant, NNH08CD59C administered through the NASA Science Mission Directorate. Astrobiology Math ii http://spacemath.gsfc.nasa.gov Table of Contents Acknowledgments ..................................................................................................................................... ii Table of Contents .....................................................................................................................................iii Alignment With Standards .....................................................................................................................vi Mathematics Topic Matrix .....................................................................................................................vii Additional Titles in this Series ................................................................................................................ x Introduction to Astrobiology ................................................................................................................xi What is Life? The Tree of Life and the Most Primitive Ancestor (6-8) .................................................................1 The Origin of Life (6-8) ..............................................................................................................................3 How Rapidly are New Species Formed in Nature? (6-8) ...............................................................5 The Smallest Terrestrial Life Forms (9-12) ..........................................................................................7 Atoms – How Sweet They Are! (6-8) .....................................................................................................9 The Largest Known Extraterrestrial Molecules (9-12) .................................................................11 The Miller-Urey Experiment: Complex Organic Molecules (9-12) ...........................................13 DNA and the Genome (6-8) ..................................................................................................................15 An Organism Based upon Arsenic not Phosphorus (9-12) .......................................................17 The Evolution of Nucleotides and Genes (9-12) ............................................................................19 Estimating Maximum Cell Sizes (9-12) ..............................................................................................21 Exploring Archaen Life Forms (9-12) .................................................................................................23 The Evolution of Intelligence (9-12) ..................................................................................................25 Genetic Determinants of Species Intelligence (6-8) ....................................................................27 Natural Cataclysms and Species Evolution (9-12).........................................................................29 What Makes a World Habitable? Kelvin Temperatures and Very Cold Things (6-8) ..........................................................................31 How to Build a Planet from the Inside Out! (9-12) ........................................................................33 A Basic Planetary Atmosphere Model (9-12) ..................................................................................35 The Moon's Atmosphere! (9-12) ..........................................................................................................37 How Hot is That Planet? (9-12) .............................................................................................................39 The Greenhouse Effect and Planetary Temperature (9-12) .......................................................41 Albedo and Heat Balance (9-12) .........................................................................................................43 Another Look at Solar Energy (9-12) .................................................................................................45 Heat Flow Balance and Melting Ice (9-12) .......................................................................................47 Ice or Water? (9-12) ..................................................................................................................................49 Ice to Water...and the Power of a Little Warmth! (9-12) ...............................................................51 Lakes of Methane on Titan (6-8) ..........................................................................................................53 A Mathematical Model of Water Loss from Comet Tempel-1 (9-12) ......................................55 Habitable Zones and Stellar Luminosity (9-12) .............................................................................57 Death Stars (9-12) .....................................................................................................................................59 Astrobiology Math iii http://spacemath.gsfc.nasa.gov The Search for Earth-Like Planets Areas Under Curves: An Astronomical Perspective (9-12) .........................................................61 Kepler-The hunt for Earth-like planets (6-8) ...................................................................................63 Kepler Spies Five New Planets (6-8) ...................................................................................................65 Kepler’s First Look at Transiting Planets (6-8) .................................................................................67 Earth-like Planets by the Score! (6-8).................................................................................................69 Earth-like Planets by the Score – 2 (6-8) ...........................................................................................71 The Goldilocks Planets – Not too Hot or Cold! (6-8) ....................................................................73 Exoplanets and their Properties? The Webb Space Telescope: Detecting Dwarf Planets (9-12) ...................................................77 Dwarf Planets and Kepler’s Third Law (9-12) ..................................................................................79 Seeing a Dwarf Planet Clearly: Pluto (9-12) ....................................................................................81 The Changing Atmosphere of Pluto (9-12) .....................................................................................83 The Earth-like Planet Gliese 581g (6-8) .............................................................................................85 The Cometary Planet: HD209458b (9-12) ........................................................................................87 Hubble Sees a Distant Planet (6-8) .....................................................................................................89
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