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Space Math @ NASA The Earth Science Connection

Space Math @ NASA The Earth Science Connection. Dr. Sten Odenwald (ADNET / Catholic University) . National Council of Teachers of Mathematics: "We live in a mathematical world. In such a world, those who understand and can do mathematics will have opportunities that others do not.

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Space Math @ NASA The Earth Science Connection

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  1. Space Math @ NASAThe Earth Science Connection Dr. Sten Odenwald (ADNET / Catholic University)

  2. National Council of Teachers of Mathematics: "We live in a mathematical world. In such a world, those who understand and can do mathematics will have opportunities that others do not. Mathematical competence opens doors to productive futures. A lack of mathematical competence closes those doors."

  3. NASA Science Mission Directorate Goals: Attract and retain students in STEM disciplines Build on existing programs, institutions, and infrastructure, and by coordinating activities and encouraging partnerships within and external to NASA

  4. The general level of mathematics enrichment is below-grade-level in most earth science curricula.

  5. Grade Math Course ‘Earth’ Science 6 graphing, decimals,metrics. Graphing, decimals, fractions, areas, geometry metric conversions 7 Volumes, rates, plane geom, plane geometry, graphing simple linear equations (1 var) temperature conversion 8 Scientific Notation; geometry; plane geometry, scale, equations with exponents, temperature conversion mean, median, mode averages, graph trends 9 Algebra I, Geometry plane geometry, scale 10 Algebra II temperature conversion averages, graph trends 11-12 Calculus Algebra 1

  6. Example: Algebra II “The vast majority (84 percent) of those who hold highly paid professional jobs have taken Algebra II or higher. (Educational Testing Service: “Ready for the Real World?”, October 2005) Students: Number of 10th Grade Students…(US Census 2008)…..... 4.1 million HS Students taking Algebra II (ACT: ca 2000) ................. 88 – 90% Textbooks: ‘Algebra II’ by ……. Total Applied Problems…….. Earth Science applications…………

  7. Space Mathematics, A Resource for Teachers, 1972 Quickly became one of the most popular and oft-requested mathematics resources at NASA. Converted to an interactive format in 1989 Internet version debut 1996 http://er.jsc.nasa.gov/seh/math.html

  8. NASA-CONNECT (1998 – 2005) NASA CONNECT series of integrated math, science, and technology programs for students in grades 6–8. 35 programs for NASA-TV 130,000 teachers and 20 million students Numerous awards.

  9. PUMAS (1998 – 2008) Practical Uses of Math And Science Archive of 71 math problems “ …collection of brief examples showing how math and science topics taught in K-12 classes can be used in interesting settings, including every day life. …The examples are written primarily by scientists, engineers, and other content experts having practical experience with the material. “ Ralph Khan (Editor)

  10. These NASA math E&PO efforts tended to provide book-length guides covering a single theme in science, physics or astronomy. Advantages: In-depth treatment of science topic Multiple math skills reinforced in a thematic setting Students get to see how ideas progress as data is analyzed Disadvantages Lack of teacher time to cover a full math guide Perceived as a curriculum replacement Not friendly to teacher scheduling of topics during year

  11. Space Math @ NASA (2004-2009+) Began with IMAGE Supported by Hinode Supplemented by NASA grants One-page math problems posted weekly http://spacemath.gsfc.nasa.gov 69,000 problems downloaded each month 5,700 visitors 85% of traffic domestic 15% of traffic international NASA - WEBEX teacher training sessions bi-weekly to 160 participants 22 NASA missions and programs provide data and problem suggestions 1-page format is non-threatening and does not require curriculum change

  12. Space Math @ NASA Math Guides

  13. 3-5 Math Topics Numbers and Operations Planets, Fractions and Scales Fractions in Space Time Zone Math Algebra Number Sentence Puzzles Equations with One variable Geometry, Areas, Volumes Solar power and satellite design Getting a round in the solar system Measurement Image scales – lunar craters Image scales – Sunspots up close Data Analysis and Probability The sunspot cycle Lunar cratering – probability and odds Problem Solving A solar storm timeline Classifying stellar spectra using patterns

  14. 6 - 8 Math Topics Numbers and Operations Are U Nuts? Scientific Notation I, II, III Themis – A problem in satellite synchrony Algebra Measuring Star Temperatures Black Holes - I Geometry, Areas, Volumes Is there a lunar meteorite impact hazard? An introduction to radiation shielding Measurement XZ Tauri’s super-CME viewed from Hubble Closeup of a sunspot - Hinode Data Analysis and Probability The Hubble Law Astronaut radiation dosages in space Problem Solving The last total solar eclipse – ever. A hot time on mars!

  15. 9 - 12 Math Topics Numbers and Operations Extracting oxygen from moon rocks Unit conversion exercises Scientific Notation – an astronomical perspective Algebra A model of the solar interior Black hole – Fadeout! Geometry, Areas, Volumes A Model of the Solar Interior Beyond the blue horizon Measurement A star sheds a comet tail! The transit of mercury Data Analysis and Probability How fast does the sun rotate? The space station orbit decay Calculus, Limits Calculating arc lengths - spiral motion Why are hot things red?

  16. Image Scaling problems: (Grade 4-8) Image scale = 350 km/150 mm = 2.3 km/mm Diameter of Tycho 35 mm = 2.3 x 35 = 80.5 km. Smallest feature = 0.5 mm = 2.3 x 0.5 = 1,250 m

  17. Scientific Notation (Grade 7-9) Mass of Sun 1,989,000,000,000,000,000,000,000,000,000,000 grams = 1.989 x 1033 grams Radius of hydrogen atom 0.00000000529 centimeters = 5.29 x 10-9 centimeters

  18. Unit Conversions (Grade 8-12)

  19. R = 384,000 km = 3.84 x 108 meters T = 28 days = 2.4 x 106 seconds 4 p2 R3 M = ------------------ G T2 M = 4 (3.14)2 (3.84 x 108)3 ------------------------------ 6.6 x 10-11 (2.4 x 106)2 M = 5.9 x 1024 kg The Mass of the Earth – use Moon’s orbit!

  20. Solar flux at Earth’s surface: 1,366 watts/meter2 Distance from Sun = 149 million km Surface area = 4 p R2 = 4 (3.14) (149 x 109 meters)2 = 2.8 x 1023 meters2 Luminosity = 1,366 x 2.8 x 1023 = 3.8 x 1026 watts Total solar power in Watts - Photometry.

  21. 2897 Temperature = -------------- K Wavelength Peak wavelength = 0.55 micrometers Temperature = 2897 / 0.55 = 5250 K (Space Math IV) Measuring the solar temperature.

  22. Problem 1 - 350 watts x 5 hours = 1,750 watt hours/1000 = 1.75 kWh. Problem 2 – E = 6 x 75 watts x 5 hrs/day x 30 days/mo = 67,500 watt hrs = 67.5 kWh

  23. Problem 1 – What was the total electrical energy consumption by this house in 2008? Problem 2 - if 1 kWh equals 700 grams of carbon, how many tons of carbon does this house generate?

  24. Problem – What was the total electrical energy consumption by this house in 2008? Answer: 11,140 kWh.

  25. Problem 2 - if 1 kWh equals 700 grams of carbon, how many tons of carbon does this house generate? Answer: 11,140 kWh x (700 grams/kWh) = 7,798,000grams = 7,798 kilograms = 7.80 metric tons

  26. Problem 1 – If 127 ppm = 1000 gigaton of carbon, what was the average annual increase in atmospheric carbon between 1958 and 2005 in gigatons/year? Problem 2 – What is a linear equation that models the carbon increase in gigatons?

  27. From the y-axis, the change in carbon dioxide concentration was from 315 ppm to 379 ppm which is a difference of 379 – 315 = 64 ppm of carbon dioxide. Since 127 ppm = 1000 gigatons of carbon, 64 ppm x (1000 gigaton/127 ppm) = 500 gigatons This increase happened over 2005-1958 = 47 years so the average linear increase was 500 gigatons/47 years = 11 gigatons/year.

  28. Problem 2 – What is a linear equation that models the carbon increase in gigatons? From the graph, in 1958 the concentration was 315 ppm This is equal to 315 ppm x 1000 gigatons/127 ppm = 2,500 gigatons of carbon Carbon (gigatons) = 11 (Year – 1958) + 2,500

  29. What is the total volume of fresh water lost in this glacier between 1973 and 1991 in cubic kilometers?

  30. The scale of the image, based on the 1-mile legend, is 115 meters/mm The glacier retreated 1,150 meters. Assume the glacier is a rectangular wall with dimensions 1300m x 1000m x 16,000 m = 21 cubic kilometers.

  31. Problem 1 - Create a simple differential equation for the carbon dioxide in the atmosphere, given the rates and reservoir sizes defined in this figure for 2005. Problem 2 – Use integral calculus to estimate the total atmospheric mass in 2050, if C(2009) = 775 gigatons

  32. Vegitation a1 = 60.0 gigatons/yr a2 = 61.3 gigatons/yr Ocean b1 = 90 gigatons/yr b2 = 92 gigatons/yr O1 = 2.2 gigatons/yr Land c1 = 1.4 gigatons/yr c2 = 1.7 gigatons/yr Humans h1 = 6.0 gigatons/yr dC ----- = a1 - a2 + b1 – b2 + c1 – c2 + h1 – O1 dt = 60.0 -61.3 + 90.0 – 92.0 +1.4 – 1.7 + 6.0 – 2.2 So: dC ---- = 0.2 dt

  33. Integrate the equation: dC ---- = 0.2 dt to get C(t) = 0.2t + a Since C(2009) = 775 gigatons we have: 775 = 0.2 (2009-2005) + a and so the integration constant has the value: a = 774.2 So the equation is C(t) = 0.2 t + 774.2 where t is the elapsed time since 2005. For 2050, t = 2050-2005 = 45 so C(45) = 0.2 (45) + 774.2 = 783.2 gigatons of carbon

  34. Integrate the equation: dC ---- = 0.2 dt to get C(t) = 0.2t + a This is a simple ‘linear’ example, but it is unrealistic. We know that many of the constants we used, a1, a2, b1, b2, c1, c2 etc are themselves actually changing with time. Some are even dependent on the previous rates of change or the reservoir size at a previous time. On-grade-level high school calculus students will be able to handle more complicated differential equations with polynomial terms or exponential / logarithmic terms….trust me!

  35. Current collaborative projects : GLOBE – Advanced problems in statistics and algebra Landsat– Resource assessment; irregular areas. Terra - Wind velocity; vector math; calculus EOS – Data analysis; mathematical modeling MMS – Measuring and modeling electric fields in space RBSP - Van Allen belts and radiation in space

  36. If you want more insight to how simple mathematics helps astrophysicists understand the universe, visit Space math @ NASA http://spacemath.gsfc.nasa.gov Hundreds of problems for grades 3-12 New ones added every few months

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