National Aeronautics and Space Administration Space Math VI Math Space i This collection of activities is based on a weekly series of space science problems distributed to thousands of teachers during the 2009- 2010 school year. They were intended for students looking for additional challenges in the math and physical science curriculum in grades 5 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. For more weekly classroom activities about astronomy and space visit the NASA website, http://spacemath.gsfc.nasa.gov Add your email address to our mailing list by contacting Dr. Sten Odenwald at [email protected] Front and back cover credits: Lagrange points (WMAP/NASA); Saturn hexagon clouds (Cassini/NASA); Gravity waves from binary black hole system (LISA); Eta Carina Nebula (Hubble/NASA) Interior Illustrations:6) Chandra/NASA; 7)JPL/NASA; 8)SOHO/ESA/NASA; 9)Author; Fermilab; 11)Aqua/NASA; 12)Deep Impact/NASA; 13)GeoEye; 16)Chandra/NASA; 17)HST/NASA; 18)SOHO/ESA/NASA; 21)Chandra/NASA; 22)NASA Orbital Debris Program Office; NASA Photo 125e006995; 24)HST/NASA; 25)HST/NASA; 27)NASA; 31)Palomar Digital Sky Survey; Carnegie Institution; 34)Digital Globe Inc; 39) NASA/JPL-Caltech; 40)ESO/L.Calcada; 41) Robert Rhodr-Global Warming Art; 48) LHC-Peter Limon; 53) Webb Space Telescope; NASA; 55) NIAID/RML; 71)USDoI/USGS; 83) BP Image from Public Domain Video; 89-91) NASA/Ares; 93) NASA/Sonoma State/Aurore Simonnet; 94-95)NASA/Chandra; 110) LRO/NASA This booklet was created through an education grant NNH06ZDA001N- EPO from NASA's Science Mission Directorate. Space Math http://spacemath.gsfc.nasa.gov Table of Contents ii Grade Page Acknowledgments i Table of Contents ii Mathematics Topic Matrix v How to use this Book ix Alignment with Standards x Teacher Comments x Counting Atoms in Molecules 3-5 1 Planetary Conjunctions 3-5 2 Parts Per Hundred 3-5 3 Star Cluster Math 3-5 4 Atoms – How sweet they are! 3-5 5 The Hand of Chandra 6-8 6 The Martian Dust Devils 6-8 7 Solar Storms – Fractions and Percentages 6-8 8 Energy at Home 6-8 9 Carbon Dioxide Increases 6-8 10 NASA Sees Carbon Dioxide 6-8 11 Tempel-1 : Close-up of a Comet 6-8 12 Exploring a High-Resolution Satellite Photo 6-8 13 Some Famous Unit Conversion Errors 6-8 14 Identifying Materials by their Reflectivity 6-8 15 Chandra Spies the Longest Sound Wave in the Universe 6-8 16 Details from an Exploding Star 6-8 17 Changing Perspectives on the Sun’s Diameter 6-8 18 Earth’s Changing Rotation Rate and Length of the Day 6-8 19 Planetary Alignments 6-8 20 Chandra Studies an Expanding Supernova Shell 6-8 21 Counting Craters on the Hubble Space Telescope 6-8 22 Satellite Drag and the Hubble Space Telescope 9-11 23 Counting Galaxies with the Hubble Space Telescope 9-11 24 The Eagle Nebula Close-up 9-11 25 Angular Size and Similar Triangles 9-11 26 ISS Orbit Altitude Changes 9-11 27 Solid Rocket Boosters 9-11 28 Evaluating Secondary Physical Constants 9-11 29 Space Mobile Puzzle 9-11 30 Spotting an Approaching Asteroid or Comet 9-11 31 The Most Important Equation in Astronomy 9-11 32 Solar Insolation Changes and the Sunspot Cycle 9-11 33 Mare Nubium and Las Vegas 9-11 34 Ice or Water? 9-11 35 Space Math http://spacemath.gsfc.nasa.gov Table of Contents (contd) iii Grade Page Water on Planetary Surfaces 9-11 36 Modeling the Keeling Curve with Excel 9-11 37 The Deep Impact Comet Encounter 9-11 38 Spitzer Studies the Distant Planet Osiris 9-11 39 How Hot is That Planet 9-11 40 Scientists Track the Rising Tide 9-11 41 Getting an Angle on the Sun and Moon 9-11 42 Seeing Solar Storms in STEREO 9-11 43 How to Build a Planet from the Inside Out 9-11 44 Unit Conversions: Energy, Power and Flux 9-11 45 The Elementary Particle Masses 9-11 46 Energy and Mass – Same things but different. 9-11 47 Exploring the Large Hadron Collider 9-11 48 Exploring the Big Bang with the LHC 9-11 49 The Global Warming Debate and the Arctic Ice Cap 9-11 50 Star Light…Star Bright 9-11 51 Fermi Detects Gamma-rays from the Galaxy Messier-82 9-11 52 Webb Space Telescope: Detecting dwarf planets 9-11 53 Computing the Orbit of a Comet 9-11 54 Estimating Maximum Cell Sizes 12 55 A Simple Model for Atmospheric Carbon Dioxide 12 56 From Dust Grains to Dust Balls 12 57 From Dust Balls to Asteroids 12 58 From Asteroids to Planets 12 59 The Higgs Boson and the Mystery of Mass 12 60 The Energy of Empty Space 12 61 The Volume of a Hypersphere 12 62 The Internal Density and Mass of the Sun 12 63 How Many Stars are in the Sky 12 64 Lunar Crater Frequency Distribution 12 65 The Rotation Velocity of a Galaxy 12 66 How Many Quasars are There? 12 67 Deep Impact Comet Fly-by 12 68 In the News… Kepler Spies Five New Planets 3-5 69 LRO Sees Apollo 11 on the Moon 6-8 70 LRO and the Apollo-11 Landing Site 6-8 71 LRO’s First Image of Mare Nubium 6-8 72 LRO- Searching for Lunar boulders 6-8 73 LRO Explores Lunar Surface Cratering 6-8 74 IBEX Creates an Unusual Image of the Sky 6-8 75 The Mysterious Hexagon on Saturn 6-8 76 Scientific Data – The gift that keeps on giving! 6-8 77 Space Math http://spacemath.gsfc.nasa.gov Table of Contents (contd) iv Grade Page Methane Lakes on Titan 6-8 78 SDO: Measuring the Speed of an Eruptive Prominence 6-8 79 SDO Reveals Details on the Surface of the Sun 6-8 80 The Terra Satellite Spies the Gulf Oil Catastrophe of 2010 6-8 81 Recent Events: A Perspective on Carbon Dioxide 6-8 82 The Rate of Oil Leakage in the Gulf Oil Spill of 2010 6-8 83 LRO-The Apollo-11 Landing Area at High Resolution 9-11 84 Spitzer Telescope Discovers New Ring of Saturn 9-11 85 IBEX Uses Fast-moving Particles to Map the Sky 9-11 86 Chandra Sees the Most Distant Cluster in the Universe 9-11 87 Solid Rocket Boosters and Thrust 9-11 88 Exploring the Ares-1X Launch: Downrange Distance 9-11 89 Exploring the Ares-1X Launch: Parametrics 9-11 90 Exploring the Ares-1X Launch: Energy Changes 9-11 91 Exploring the Ares-1X Launch: The Hard Climb to Orbit 9-11 92 Fermi Observatory Measures the Lumps in Space 9-11 93 Calculating the Thickness of a Neutron Star Atmosphere 9-11 94 Chandra Sees the Atmosphere of a Neutron Star 9-11 95 Water on the Moon! 9-11 96 LCROSS Sees Water on the Moon 9-11 97 Seeing Solar Storms in STEREO 9-11 98 STEREO Watches the Sun Kick Up a Storm 9-11 99 Calculating Black Hole Power 9-11 100 WISE, Hubble, Power Functions: A question of magnitude 9-11 101 Hubble: Seeing a dwarf planet clearly 9-11 102 SDO: Working with Giga, Tera and Peta 9-11 103 Asteroids and Ice 9-11 104 Hubble: The Changing Atmosphere of Pluto 9-11 105 WISE; F(x)G(x) – A tale of two functions 12 106 Exploring Power-law Functions using WISE Data 12 107 The Ares-V Cargo Rocket 12 108 Hubble Spies Colliding Asteroids 12 109 LRO Spots A Rolling Boulder on the Moon 12 110 Useful Links 111 Author Comments 112 Space Math http://spacemath.gsfc.nasa.gov Mathematics Topic Matrix v Topic Problem Numbers 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 Inquiry Technology, X X X X X X X X X rulers Numbers, patterns, X X X X X X X X X X X X X percentages Averages X X Time, distance,speed X X X X X Areas and X X volumes Scale drawings X X X X X X X X X X Geometry X X X X X Scientific Notation X X X Unit X X Conversions Fractions X Graph or Table Analysis X X X X Solving for X X X Evaluating Fns X Modeling X X X X Probability X X Rates/Slopes X Logarithmic X Fns Polynomials Power Fns Conics Piecewise Fns Trigonometry X Integration Differentiation Limits Space Math http://spacemath.gsfc.nasa.gov Mathematics Topic Matrix (cont'd) vi Topic Problem Numbers 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 Inquiry Technology, rulers X X Numbers, patterns, percentages Averages Time, distance,speed Areas and volumes X X X X X X X X X Scale X X drawings Geometry X X X X X X X X X X X X X Scientific X X X X X X X X X X X X X Notation Unit Conversions X X X X X X X X X X X Fractions Graph or Table X X X X Analysis Solving for X X X X X X X X X X X X X Evaluating Fns X X X X X X X X X X X X X Modeling X X X X X X X X X X Probability Rates/Slopes X X Logarithmic Fns Polynomials X X X X Power Fns X Exponential Fns Conics X Piecewise Fns Trigonometry X X Integration X X X Differentiation Limits Space Math http://spacemath.gsfc.nasa.gov Mathematics Topic Matrix (cont'd) vii Topic Problem Numbers 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 Inquiry Technology, X X X X X X X X X X X X X rulers Numbers, patterns, X X percentages Averages Time, distance,speed X X X X X X Areas and X X X X X X X X X volumes Scale drawings X X X X X X X X X X X X X X X Geometry X X X X X X X X X X X X Scientific Notation X X X X X X X X X Unit X X X X X X X X X X X X X X X X Conversions Fractions Graph or Table Analysis X Solving for X X X X X X X X X X X X Evaluating Fns X X X X X X X X X X X Modeling X X X X X X X X X X X X X X X X Probability Rates/Slopes Logarithmic X Fns Polynomials X Power Fns X Exponential Fns Conics Piecewise Fns Trigonometry X Integration X X Differentiation X X X Limits X Space Math http://spacemath.gsfc.nasa.gov Mathematics Topic Matrix (cont'd) viii Topic Problem Numbers 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 4 5 6 7 8