National Aeronautics and Space Administration

Transcription

1 I National Aeronautics and Space Administration

2 i This collection of activities is based on a weekly series of space science problems distributed to thousands of teachers during the 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, Add your address to our mailing list by contacting Dr. Sten Odenwald at Sten.F.Odenwald@nasa.gov 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.

3 Table of Contents ii Acknowledgments Table of Contents Mathematics Topic Matrix How to use this Book Alignment with Standards Teacher Comments Grade Page i ii iv vi vii viii Fun with Gears and Fractions RBSP - A New Belt for the Van Allen Belts! Hinode Observes a Solar Eclipse From Space Curiosity -Telling Time on Mars SDO-Solar Flares and the Stormy Sun Landsat - Exploring Water Use in Kansas RBSP Spacecraft Hears Dawn Chorus in Space - I RBSP Spacecraft Hears Dawn Chorus in Space - II RBSP Spacecraft Hears Dawn Chorus in Space - III SDO Sees Coronal Rain - Estimating Plasma Speed A Mathematical Model of Magnetic Field Lines - I A Mathematical Model of Magnetic Field Lines - II InSight The Seismographic Station - Wave Arrival Times Planck Mission Sees Ancient Universe Clearly Curiosity Discovers an Ancient Mars River - Elementary Hubble Extreme Deep Field - Counting Galaxies Grail Spacecraft Create New Craters on the Moon Space- Exploring the Launch of the Falcon Fermi Observatory and the Origin of Cosmic Rays The Frequency of Large Meteorite Impacts Kepler - Alpha Centauri Bb - A Nearby Extrasolar Planet Curiosity Rover on the Move! Curiosity - Exploring Gale Crater Hubble - The Expanding Gas Shell of U Camelopardalis Exploring Density, Mass and Volume Across the Universe Hubble - A Distant Supernova Remnant Discovered Landsat - NASA Satellite Takes Pictures of the Salton Sea Chandra - Giant Gas Cloud in System NGC Fermi - The Remarkable Gamma Ray Burst GRB A Hubble - Exploring the Most Distant Galaxies Grail Satellites Create a Gravity Map of the Moon Curiosity Uses -Ray Diffraction to Identify Minerals Hubble - An Enormous Stellar Spiral Pattern in Space

4 UTable of Contents (contd) iii Curiosity Discovers an Ancient Martian River - Advanced Hubble - Pluto's Fifth Moon The Radioactive Dating of a Star in the Milky Way Calculus: The Close Encounter to te Sun of Barnards Star The Volume of a Lunar Impact Crater How to Grow a Planet or a Raindrop! A Mathematical Model of a Magnetic Field Line - III Special NASA Mission Section - InSight Scheduling Events in Time for Launch Exploring a Possible InSight Landing Area on Mars Comparing the InSight Landing Area to a City Block! Exploring Temperature Change in Earth's Outer Crust Exploring the InSight Lander Telemetry Data Flow Seeing the Martian Surface with IDC Telling Time on Mars - Earth Days and Mars Sols The InSight Seismographic Station Solar Power System The Work Area In Front of the Lander Marsquake Energy and the Moment Magnitude Scale Exploring Logarithms and the Richter Magnitude Scale The Distance to the Martian Horizon Exploring the Interior of Mars with Spheres and Shells Exploring the Mass of Mars Exploring Impacts and Quakes on Mars Comparing the Heat Output of Mars and Earth Exploring Heat Flow and Insulation Radio Communications with Earth -The Earth-Sun Angle Estimating the Mass of a Martian Dust Devil! The InSight Seismographic Station - Wave arrival times Special NASA Mission Section - Juno Solar Electricity for a New Spacecraft Investigating Juno's Elliptical Transfer Orbit The Launch of the Juno Spacecraft The Launch of the Juno Spacecraft - Ascent to Orbit Solar Energy and the Distance of Juno from the Sun The Speed of the Juno Spacecraft Investigating the Elliptical orbit of Juno Around Jupiter Investigating the Radiation Belts Around Jupiter Special NASA Mission Section - MMS The MMS Satellites and Solar Power Some Facts About the MMS Atlas Rocket Launching the MMS Satellite Constellation into Orbit

5 Table of Contents (contd) iv The MMS Launchpad at Cape Canaveral Stacking Four MMS Satellites Inside the Atlas Nosecone Volume and Surface Area of an Octagonal MMS Satellite The MMS Payload Up Close The Acceleration Curve for the MMS Launch The Orbit of the MMS Satellite Constellation The Orbit of the MMS Satellite Constellation - Advanced Radiation Belts Storm Probes - RBSP Working with Areas of Rectangles and Circles The RBSP Satellite - Working with Octagons Radiation Belts Storm Probes - Telemetry Math Exploring Gas Density in Space Electricity from Sunlight Exploring the Outer Atmosphere - Gas Density Measuring the Mass of Earth with the RBSP Satellites Exploring the Donut-Shaped van Allen Belts Estimating the Total Mass of the van Allen Belts Measuring Earth's Magnetic Field in Space Exploring the Density of Gas in the Atmosphere The Science of Clouds- S'COOL Using Proportions to Estimate the Height of a Cloud Using Proportions to Estimate the Size of a Cloud Estimating the Mass of a Cloud Working with Rainfall Rates and Water Volume Cloud Droplets and Rain Drops How Clouds Form - Working with Rates of Change Cloud Cover and Solar Radiation Cloud Cover, Albedo, Transmission and Opacity 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 Snow to Water Ratios Snow Density and Volume Snow Density, mass and Roof Failure Exploring Energy and Temperature Exploring Temperature and States of Matter What is a Snowball's Chance on Mars? Useful Links 107 Author Comments 108

6 UMathematics Topic Matrix v Topic Problem Numbers Inquiry Technology, rulers Numbers, patterns, percentages Averages Time, distance, speed Density, mass, volume Areas and volumes Scale Drawings, proportions Geometry, Pythagorean Theorem Scientific Notation Unit Conversions Fractions Graph or Table Analysis Solving for Evaluating Modeling Probability Rates/Slopes Logarithmic Polynomials Power Exponential Conics Piecewise Trigonometry Integration Differentiation Limits

7 Mathematics Topic Matrix (cont'd) vi Topic Problem Numbers Inquiry Technology, rulers Numbers, patterns, percentages Averages Time, distance, speed Density, mass, volume Areas and volumes Scale drawings Geometry, Pythagorean Theorem Scientific Notation Unit Conversions Fractions Graph or Table Analysis Solving for Evaluating Modeling Probability Rates/Slopes Logarithmic Polynomials Power Exponential Conics Piecewise Trigonometry Integration Differentiation Limits

8 Mathematics Topic Matrix (cont'd) vii Topic Problem Numbers Inquiry Technology, rulers Numbers, patterns, percentages Averages Time, distance, speed Density, mass, volume Areas and volumes Scale drawings Geometry, Pythagorean Theorem Scientific Notation Unit Conversions Fractions Graph or Table Analysis Solving for Evaluating Modeling Probability Rates/Slopes Logarithmic Polynomials Power Exponential Conics Piecewise Trigonometry Integration Differentiation Limits

9 Mathematics Topic Matrix (cont'd) viii Topic Problem Numbers Inquiry Technology, rulers Numbers, patterns, percentages Averages Time, distance, speed Density, mass, volume Areas and volumes Scale drawings Geometry, Pythagorean Theorem Scientific Notation Unit Conversions Fractions Graph or Table Analysis Solving for Evaluating Modeling Probability Rates/Slopes Logarithmic Polynomials Power Exponential Conics Piecewise Trigonometry Integration Differentiation Limits

10 Useful Internet NASA A Math Refresher Developers Guide to Excelets Interactive Science Simulations My Physics Lab NASA Press Releases NCTM - Principles and Standards for School Mathematics Practical Uses of Math and Science (PUMAS) Teach Space Science

11 June, 2013 A note from the Author: Hi again! Here is another collection of 'fun' problems based on NASA space missions across the solar system and the universe! The 106 problems in this collection of SpaceMath@NASA problems from span the gamut from fractions and percentages, to the challenges of algebraic manipulation. This has certainly been an exciting year. We opened the year with the exciting landing of the Curiosity Rover on Mars and the steady stream of surface imagery from this car-sized super rover. A powerful gamma-ray burst lit up the sky and was captured by Fermi; the Planck mission resolved the cosmic background radiation to milky way-sized blobs of matter existing 700,000 years after the Big Bang. We also discovered a long-awaited planet orbiting the nearby star Alpha Centauri. And of course, as we entered sunspot maximum conditions in 2013, the sun popped off plenty of solar storms to keep us busy. And of course, then there was the spectacular Russian Meteor of February that was captured on hundreds of dashboard cameras in Russia. Sadly over 1000 people were injured by flying glass as the shock wave shattered thousands of windows in the town of Chelyabinsk. This meteor was a near-twin to the famous 1909 Tunguska Meteor, and one shudders to think what would have happened had it entered over New York City an hour or two earlier! This year also marked the beginning of a disturbing discussion about the future of STEM education funding across the federal government. Several years ago, a presidential Committee on STEM education (costem) was set up to see what could be done to tightenup all of the hundreds of STEM programs funded outside the Department of Education and the National Science Foundation. In April, over 2 months before the panel submitted its final recommendations, the Office of Management and Budget (OMB) moved ahead with its own ideas for consolidating STEM education in the Presidential FY14 budget. This budget ELIMINATED all of NASA s science mission education programs and gave this money to DoED and NSF. Gone would be all the classroom and teacher professional training support by NASA s science missions (Hubble, Curiosity, etc). There has now been a major protest filed by dozens of educational institutions, museums, and professional societies (NSTA, NCTM, AAAS, AAS etc) to stop this implementation. At the present time, we do not know what the future of NASA s science education programs will be, but many of its STEM teachers and scientists are making plans to look for other jobs, or retire early, as missions move ahead with losing their education funding for FY14 and beyond. As for SpaceMath@NASA, we are supported through education grants at NASA, and from individual missions that have stepped forward to support math enrichment. By Spring, 2014 as for the many NASA missions, we may well no longer exist to provide new resources to teachers and students. This will indeed be a very tense summer for all NASA STEM professionals as the FY14 budget moves through Congress and we learn more about our fates during the school year and beyond. Sincerely, Dr. Sten Odenwald NASA Astronomer sten.f.odenwald@nasa.gov

12 National Aeronautics and Space NASA Goddard Spaceflight Center Greenbelt, Maryland spacemath.gsfc.nasa.gov