National Aeronautics and Space Administration S pacM e aIX th i This collection of activities is based on a weekly series of space science problems distributed to thousands of teachers during the 2012- 2013 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: Front) Grail Gravity Map of the Moon -Grail NASA/ARC/MIT; Dawn Chorus - RBSP/APL/NASA; Erupting Prominence - SDO/NASA; Location of Curiosity - Curiosity/JPL./NASA; Chelyabinsk Meteor - WWW; LL Pegasi Spiral - NASA/ESA Hubble Space Telescope. Back) U Camalopardalis (Courtesy ESA/Hubble, NASA and H. Olofsson (Onsala Space Observatory) Interior Illustrations: All images are courtesy NASA and specific missions as stated on each page, except for the following: 20) Chelyabinsk Meteor and classroom (chelyabinsk.ru); 32) diffraction figure (Wikipedia); 39) Planet accretion (Alan Brandon, Nature magazine, May 2011); 44) Beatrix Mine (J.D. Myers, University of Wyoming); 53) Mars interior (Uncredited ,TopNews.in); 89) Earth Atmosphere (NOAA); 90, 91) Lonely Cloud (Henriette, The Cloud Appreciation Society, 2005); 101, 103) House covered in snow (The Author); 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 iv How to use this Book vi Alignment with Standards vii Teacher Comments viii Fun with Gears and Fractions 3-5 1 RBSP - A New Belt for the Van Allen Belts! 3-5 2 Hinode Observes a Solar Eclipse From Space 3-5 3 Curiosity -Telling Time on Mars 3-5 4 SDO-Solar Flares and the Stormy Sun 3-5 5 Landsat - Exploring Water Use in Kansas 6-8 6 RBSP Spacecraft Hears Dawn Chorus in Space - I 6-8 7 RBSP Spacecraft Hears Dawn Chorus in Space - II 6-8 8 RBSP Spacecraft Hears Dawn Chorus in Space - III 6-8 9 SDO Sees Coronal Rain - Estimating Plasma Speed 6-8 10 A Mathematical Model of Magnetic Field Lines - I 6-8 11 A Mathematical Model of Magnetic Field Lines - II 6-8 12 InSight – The Seismographic Station - Wave Arrival Times 6-8 13 Planck Mission Sees Ancient Universe Clearly 6-8 14 Curiosity Discovers an Ancient Mars River - Elementary 6-8 15 Hubble Extreme Deep Field - Counting Galaxies 6-8 16 Grail Spacecraft Create New Craters on the Moon 6-8 17 Space-X Exploring the Launch of the Falcon 9 6-8 18 Fermi Observatory and the Origin of Cosmic Rays 6-8 19 The Frequency of Large Meteorite Impacts 6-8 20 Kepler - Alpha Centauri Bb - A Nearby Extrasolar Planet 6-8 21 Curiosity Rover on the Move! 6-8 22 Curiosity - Exploring Gale Crater 6-8 23 Hubble - The Expanding Gas Shell of U Camelopardalis 6-8 24 Exploring Density, Mass and Volume Across the Universe 6-8 25 Hubble - A Distant Supernova Remnant Discovered 6-8 26 Landsat - NASA Satellite Takes Pictures of the Salton Sea 6-8 27 Chandra - Giant Gas Cloud in System NGC 6240 8-10 28 Fermi - The Remarkable Gamma Ray Burst GRB 130427A 8-10 29 Hubble - Exploring the Most Distant Galaxies 9-12 30 Grail Satellites Create a Gravity Map of the Moon 9-12 31 Curiosity Uses X-Ray Diffraction to Identify Minerals 9-12 32 Hubble - An Enormous Stellar Spiral Pattern in Space 9-12 33 Space Math http://spacemath.gsfc.nasa.gov TableU of Contents (contd) iii Curiosity Discovers an Ancient Martian River - Advanced 9-12 34 Hubble - Pluto's Fifth Moon 9-12 35 The Radioactive Dating of a Star in the Milky Way 9-12 36 Calculus: The Close Encounter to te Sun of Barnards Star 12 37 The Volume of a Lunar Impact Crater 12 38 How to Grow a Planet or a Raindrop! 12 39 A Mathematical Model of a Magnetic Field Line - III 12 40 Special NASA Mission Section - InSight Scheduling Events in Time for Launch 5-7 41 Exploring a Possible InSight Landing Area on Mars 6-8 42 Comparing the InSight Landing Area to a City Block! 6-8 43 Exploring Temperature Change in Earth's Outer Crust 6-8 44 Exploring the InSight Lander Telemetry Data Flow 6-8 45 Seeing the Martian Surface with IDC 6-8 46 Telling Time on Mars - Earth Days and Mars Sols 6-8 47 The InSight Seismographic Station Solar Power System 6-8 48 The Work Area In Front of the Lander 6-8 49 Marsquake Energy and the Moment Magnitude Scale 8-10 50 Exploring Logarithms and the Richter Magnitude Scale 8-10 51 The Distance to the Martian Horizon 8-10 52 Exploring the Interior of Mars with Spheres and Shells 8-10 53 Exploring the Mass of Mars 8-10 54 Exploring Impacts and Quakes on Mars 8-10 55 Comparing the Heat Output of Mars and Earth 8-10 56 Exploring Heat Flow and Insulation 8-10 57 Radio Communications with Earth -The Earth-Sun Angle 8-10 58 Estimating the Mass of a Martian Dust Devil! 8-10 59 The InSight Seismographic Station - Wave arrival times 8-10 60 Special NASA Mission Section - Juno Solar Electricity for a New Spacecraft 5-7 61 Investigating Juno's Elliptical Transfer Orbit 8-10 62 The Launch of the Juno Spacecraft 8-10 63 The Launch of the Juno Spacecraft - Ascent to Orbit 8-10 64 Solar Energy and the Distance of Juno from the Sun 10-12 65 The Speed of the Juno Spacecraft 10-12 66 Investigating the Elliptical orbit of Juno Around Jupiter 10-12 67 Investigating the Radiation Belts Around Jupiter 10-12 68 Special NASA Mission Section - MMS The MMS Satellites and Solar Power 5-7 69 Some Facts About the MMS Atlas Rocket 5-7 70 Launching the MMS Satellite Constellation into Orbit 6-8 71 Space Math http://spacemath.gsfc.nasa.gov Table of Contents (contd) iv The MMS Launchpad at Cape Canaveral 6-8 72 Stacking Four MMS Satellites Inside the Atlas Nosecone 6-8 73 Volume and Surface Area of an Octagonal MMS Satellite 8-10 74 The MMS Payload Up Close 8-10 75 The Acceleration Curve for the MMS Launch 8-10 76 The Orbit of the MMS Satellite Constellation 8-10 77 The Orbit of the MMS Satellite Constellation - Advanced 10-12 78 Radiation Belts Storm Probes - RBSP Working with Areas of Rectangles and Circles 3-5 79 The RBSP Satellite - Working with Octagons 6-8 80 Radiation Belts Storm Probes - Telemetry Math 6-8 81 Exploring Gas Density in Space 6-8 82 Electricity from Sunlight 6-8 83 Exploring the Outer Atmosphere - Gas Density 6-8 84 Measuring the Mass of Earth with the RBSP Satellites 8-10 85 Exploring the Donut-Shaped van Allen Belts 8-10 86 Estimating the Total Mass of the van Allen Belts 8-10 87 Measuring Earth's Magnetic Field in Space 8-10 88 Exploring the Density of Gas in the Atmosphere 8-10 89 The Science of Clouds- S'COOL Using Proportions to Estimate the Height of a Cloud 6-8 90 Using Proportions to Estimate the Size of a Cloud 6-8 91 Estimating the Mass of a Cloud 6-8 92 Working with Rainfall Rates and Water Volume 6-8 93 Cloud Droplets and Rain Drops 6-8 94 How Clouds Form - Working with Rates of Change 8-10 95 Cloud Cover and Solar Radiation 8-10 96 Cloud Cover, Albedo, Transmission and Opacity 8-10 97 The History of Winter Graphing a Snowflake Using Symmetry 6 98 The Surface Area of a Snowflake 6 99 Snowflake Growth Rates and Surface Area 6 100 Snow to Water Ratios 7 101 Snow Density and Volume 7 102 Snow Density, mass and Roof Failure 7 103 Exploring Energy and Temperature 8 104 Exploring Temperature and States of Matter 8 105 What is a Snowball's Chance on Mars? 8 106 Useful Links 107 Author Comments 108 Space Math http://spacemath.gsfc.nasa.gov v MathematicsU Topic Matrix 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, rulers Numbers, patterns, X X X X X X X percentages Averages X Time, distance, speed X X X X X X X X X Density, mass, X X X X volume Areas and volumes X X X X X X Scale Drawings, X X X X X X X X X X X X X X X X X X X proportions Geometry, Pythagorean X X X X X X X X X Theorem Scientific X X X X X X X X Notation Unit Conversions X X X X X Fractions X Graph or Table X X X X X X X Analysis Solving for X X X Evaluating Fns X X X X X X Modeling X X X X Probability X Rates/Slopes X Logarithmic Fns Polynomials X Power Fns Exponential Fns Conics Piecewise Fns Trigonometry 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 Numbers, patterns, X X X X percentages Averages Time, distance, speed X X X X X Density, mass, X X volume Areas and volumes X X X X X Scale drawings X X X X X X X X X Geometry, X X X X X X X X Pythagorean Theorem Scientific Notation X X X X X X X X X X Unit X X X X X X Conversions Fractions Graph or Table Analysis X X X X Solving for X X X X X Evaluating Fns 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 X X X Logarithmic X X Fns Polynomials X Power Fns Exponential Fns X Conics X Piecewise Fns Trigonometry X X X Integration X X Differentiation X X X Limits Space Math http://spacemath.gsfc.nasa.gov