1. Space Math @ NASA The 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

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

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

10. Students: Textbooks: 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)… million
HS Students taking Algebra II (ACT: ca 2000) – 90%
Textbooks:
‘Algebra II’ by …….
Total Applied Problems……..
Earth Science applications…………

11. A Resource for Teachers, 1972
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

12. 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.

13. PUMAS (1998 – 2008) Archive of 71 math problems
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)

14. 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

15. Space Math @ NASA (2004-2009+) Began with IMAGE Supported by Hinode
Supplemented by NASA grants
One-page math problems posted weekly
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

17. Space Math @ NASA Math Guides

18. 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

19. 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!

20. 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?

21. 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

22. Scientific Notation (Grade 7-9)
Mass of Sun ,989,000,000,000,000,000,000,000,000,000,000 grams
= x 1033 grams
Radius of hydrogen atom centimeters
= x centimeters

23. Unit Conversions (Grade 8-12)

24. The Mass of the Earth – use Moon’s orbit!
R = 384,000 km
= 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 (2.4 x 106)2
M = 5.9 x 1024 kg
The Mass of the Earth – use Moon’s orbit!

25. Total solar power in Watts - Photometry.
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.

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

28. 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

29. 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?

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

31. 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

32. 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?

33. 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 = 47 years
so the average linear increase
was gigatons/47 years = 11 gigatons/year.

34. 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

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

36. 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.

37. 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

38. 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
= – – – 2.2
So: =

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

40. Integrate the equation:dC = 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!

41. 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

42. If you want more insight to how simple mathematics
helps astrophysicists understand the universe,
visit
Space NASA
Hundreds of problems for grades 3-12
New ones added every few months