# National Aeronautics and Space Administration

## Year 3: Problems 65 to 101

Problem 101 Super-Fast Solar Flares!! - Students will analyze consecutive images taken of an erupting solar flare, and use the information provided to calculate the speed of the flare. [Grade level: 6-9 | Topics:image scales; time calculations; speed calculations]

Problem 100 The Sunspot Cycle - endings and beginnings - Students will examine a plot of the sunspot cycle and extract information from the plotted data about the previous sunspot cycle, and make predictions about the next one about to start in 2007. [Grade level: 6-9 | Topics:graph reading; extrapolation; time calculations]

Problem 99 The Hinode Satellite Views the Sun - Students will use a full-sun image from the new Hinode satellite to sketch the locations of magnetic fields on the sun's surface using information in the introductory article as a guide. [Grade level: 6-8 | Topics:image interpretation; eye-hand coordination; reading to be informed]

Problem 98 Solar Flare Reconstruction - Students will use data from a solar flare to reconstruct its maximum emission using graphical estimation (pre-algebra), power-law function fitting (Algebra 2), and will determine the area under the profile (Calculus). [Grade level: 9-11 | Topics:plotting tabular date; fitting functions; integration]

Problem 97 Hinode - Closeup of a Sunspot - Students will determine the sizes of sunspots and solar granulation cells from a recent image taken by the Hinode solar observatory. [Grade level: 6-8 | Topics:image scales, metric units, unit conversion]

Problem 96 Hinode Satellite Power - Students will study the design of the Hinode solar satellite and calculate how much power it can generate from its solar panels. [Grade level: 6-8 | Topics:area of rectangle,area of cylinder, unit conversion]

Problem 95 A Study on Astronaut Radiation Dosages in SPace - Students will examine a graph of the astronaut radiation dosages for Space Shuttle flights, and estimate the total dosages for astronauts working on the International Space Station. [Grade level: 9-11 | Topics:Graph analysis, interpolation, unit conversion]

Problem 94 Solar Storms: Odds, Fractions and Percentages - Students will use actual data on solar storms to learn about the different kinds of storms and how common they are. This is a basic science activity that professionals do in order to look for relationships between different kinds of events that might lead to clues about what causes them. Can your students come up with something new that noone has thought about before? The Venn Diagramming activity is a key element of the activity and is reasonably challenging! [Grade level: 6-8 | Topics: Averaging; fractions; percentages; odds; Arithmetic Operations; Venn Diagrams]

Problem 93 An Introduction to Radiation Shielding - Students calculate how much shielding a new satellite needs to replace the ISO research satellite. Students use a graph of the wall thickness versus dosage, and determine how thick the walls of a hollow cubical satellite have to be to blackuce the radiation exposure of its electronics. Students calculate the mass of the satellite and the cost savings by using different shielding. [Grade level: 9-11 | Topics: Algebra; Volume of a hollow cube; unit conversion]

Problem 92 A Lunar Transit of the Sun from Space - One of the STEREO satellites observed the disk of the moon pass across the sun. Students will use simple geometry to determine how far the satellite was from the moon and Earth at the time the photograph was taken. [Grade level: 9-11 | Topics: Geometry; parallax; arithmetic]

Problem 91 Compound Interest - Students use the 'compound interest' formula to examine rates of growth for space mission costs, and the salaries of astronomers, with allowance for inflation. [Grade level: 8-10 | Topics: Algebra II]

Problem 90 A Career in Astronomy - This problem looks at some of the statistics of working in a field like astronomy. Students will read graphs and answer questions about the number of astronomers in this job area, and the rate of increase in the population size and number of advanced degrees. [Grade level: 6-8 | Topics: graph reading; percentages; interpolation]

Problem 89 Atmospheric Shielding from Radiation- III - This is Part III of a 3-part problem on atmospheric shielding. Students use exponential functions to model the density of a planetary atmosphere, then evaluate a definite integral to calculate the total radiation shielding in the zenith (straight overhead) direction for Earth and Mars. [Grade level: 11-12 | Topics: Evaluating an integral, working with exponential functions]

Problem 88 Atmospheric Shielding from Radiation- II - This is the second of a three-part problem dealing with atmospheric shielding. Students use the formula they derived in Part I, to calculate the radiation dosage for radiation arriving from straight overhead, and from the horizon. Students also calculate the 'zenith' shielding from the surface of Mars. [Grade level: 9-11 | Topics: Algebra I; evaluating a function for specific values]

Problem 87 Atmospheric Shielding from Radiation- I - This is the first part of a three-part problem series that has students calculate how much radiation shielding Earth's atmosphere provides. In this problem, students have to use the relevant geometry in the diagram to determine the algebraic formula for the path length through the atmosphere from a given location and altitude above Earth's surface. [Grade level: 9-11 | Topics: Algebra II, trigonometry]

Problem 86 Do Fast CMEs Produce SPEs? - Recent data on solar proton storms (SPEs) and coronal mass ejections (CMEs) are compa black using Venn Diagrams to see if the speed of a CME makes solar proton storms more likely or not. [Grade level: 5-8 | Topics: Venn Diagrams; counting; calculating percentages and odds]

Problem 85 The Solar Tsunami! - Recent data from the Hinode satellite is used to measure the speed of a solar explosion on the surface of the sun using a series of images taken by the satellite at three different times. Students calculate the speed of the blast between the first pair and last pair of images, and determine if the blast wave was accelerating or decellerating in time. [Grade level: 5-8 | Topics: Finding image scale; calculating time differences; calculating speed from distance and time]

Problem 84 Beyond the Blue Horizon - How far is it to the horizon? Students use geometry, and the Pythagorean Theorem, to determine the formula for the distance to the horizon on any planet with a radius, R, from a height, h, above its surface. Additional problems added that involve calculus to determine the rate-of-change of the horizon distance as you change your height. [Grade level: 9-11 | Topics: Algebra, Pythagorean Theorem; Experts: DIfferential calculus) ]

Problem 83 Luner Meteorite Impact Risks - In 2006, scientists identified 12 flashes of light on the moon that were probably meteorite impacts. They estimated that these meteorites were probably about the size of a grapefruit. How long would lunar colonists have to wait before seeing such a flash within their horizon? Students will use an area and probability calculation to discover the average waiting time. [Grade level: 8-10 | Topics: arithmetic; unit conversions; surface area of a sphere) ]

Problem 82 Are U nuts? - Students will use a number of obscure English units measures to convert from metric to English units and back, and answer some unusual questions! [Grade level: 6-8 | Topics: arithmetic; unit conversions involving 1 to 5 steps) ]

Problem 81 The Pressure of a Solar Storm - Students will examine three mathematical models for determining how much pressure a solar storm produces as it affects Earth's magnetic field. They will learn that magnetism produces pressure, and that this accounts for many of the details seen in solar storms. [Grade level: 9-11 | Topics: Substituting numbers into equations; filling out missing table entries; data interpretation; mathematical models ]

Problem 80 Data Corruption by High Energy Particles - Students will see how solar flares can corrupt satellite data, and create a timeline for a spectacular episode of data loss recorded by the SOHO satellite using images obtained by the satellite. Students will also calculate the speed of the event as particles are ejected from the sun and streak towards earth. [Grade level: 6-8 | Topics: Time and speed calculations; interpreting scientific data ]

Problem 79 Correcting Bad Data Using Parity Bits - Students will see how computer data is protected from damage by radiation 'glitches' using a simple error-detection method involving the parity bit. They will reconstruct an uncorrupted sequence of data by checking the '8th bit' to see if the transmitted data word has been corrupted. By comparing copies of the data sent at different times, they will reconstruct the uncorrupted data. [Grade level: 4-6 | Topics: addition, subtraction, comparing the numbers 1 and 0 ]

Problem 78 Moving Magnetic Filaments Near Sunspots - Students will use two images from the new, Hinode (Solar-B) solar observatory to calculate the speed of magnetic filaments near a sunspot. The images show the locations of magnetic features at two different times. Students calculate the image scales in kilometers/mm and determine the time difference to estimate the speeds of the selected features. [Grade level: 6-8 | Topics: scaling, estimation, speed calculations, time arithmetic ]

Problem 77 Some Puzzling Thoughts about Radiation! - Students fill-in the blanks in an essay on radiation risks using a word bank tied to solving quadratic equations to find the right words from a pair of possible 'solutions'. [Grade level: 8-10 | Topics: Finding the roots of a quadratic equation; solving for X ]

Problem 76 Radon Gas in the Basement - This problem introduces students to a common radiation problem in our homes. From a map of the United States provided by the US EPA, students convert radon gas risks into annual dosages. [Grade level: 6-8 | Topics: Unit conversion, arithmetic operations]

Problem 75 Parametric Functions and Substitution - The relationship between the strength of a solar storm and the resulting magnetic disturbance on Earth is given as a series of equations. Students are asked to create new formulae based on these parametric these equations using the method of substitution. [Grade level: 11-12 | Topics: Algebraic manipulation, integer exponents, scientific notation, significant figures and rounding ]

Problem 74 A Hot Time on Mars - The NASA Mars Radiation Environment (MARIE) experiment has created a map of the surface of mars, and measu black the ground-level radiation background that astronauts would be exposed to. This math problem lets students examine the total radiation dosage that these explorers would receive on a series of 1000 km journeys across the martian surface. The students will compare this dosage to typical background conditions on earth and in the International Space Station to get a sense of perspective [Grade level: 6-8 | Topics: decimals, unit conversion, graphing and analysis ]

Problem 73 Monster Functions in Space Science I. - This problem has students employ a pair of complicated algebraic equations to evaluate the strength of the sun's magnetic field near Earth's orbit. The equations are a model of the sun's magnetic field in space based on actual research by a solar physicist. This introduces students to a real-world application of mathematical modeling, and extracting p blackictions from theoretical models that can be tested. Students are provided the values for the relevant variables, and through substitution, calculate the numerical values for two 'vector' components of the sun's magnetic field near Earth's orbit. [Grade level: 9-11 | Topics: decimals, scientific notation, significant figures ]

Problem 72 Systems of Equations in Space Science - This problem has students solve two problems involving three equations in three unknowns to learn about solar flares, and communication satellite operating power. [Grade level: 8-10 | Topics: decimals, solving systems of equations, matrix math, algebraic substitution ]

Problem 71 Are the Van Allen Belts Really Deadly? - This problem explores the radiation dosages that astronauts would receive as they travel through the van Allen Belts enroute to the Moon. Students will use data to calculate the duration of the trip through the belts, and the total received dosage, and compare this to a lethal dosage to confront a misconception that Apollo astronauts would have instantly died on their trip to the Moon. [Grade level: 8-10 | Topics: decimals, area of rectangle, graph analysis]

Problem 70 Calculating Total Radiation Dosages at Mars - This problem uses data from the Mars Radiation Environment Experiment (MARIE) which is orbiting Mars, and measures the daily radiation dosage that an astronaut would experience in orbit around Mars. Students will use actual plotted data to calculate the total dosage by adding up the areas under the data curve. This requires knowledge of the area of a rectangle, and an appreciation of the fact that the product of a rate (rems per day) times the time duration (days) gives a total dose (Rems), much like the product of speed times time gives distance. Both represent the areas under their appropriate curves. Students will calculate the dosages for cosmic radiation and solar proton flares, and decide which component produces the most severe radiation problem. [Grade level: 6-8 | Topics: decimals, area of rectangle, graph analysis]

Problem 69 Single Event Upsets in Aircraft Avionics - Radiation is problem for high-altitude commercial and research aircraft. Showers of high-energy neutrons cause glitches in computer electronics and other aircraft systems. This problem investigates the neutron background radiation at 30,000 to 100,000 feet based on actual flight data, and has students calculate how many computer memory glitches will happen over a set amount of flight time. [Grade level: 8-10 | Topics: decimals, unit conversions, graph analysis]

Problem 68 An Introduction to Space Radiation - Read about your natural background radiation dosages, learn about Rems and Rads, and the difference between low-level dosages and high-level dosages. Students use basic math operations to calculate total dosages from dosage rates, and calculating cancer risks. [Grade level: 6-8 | Topics: Reading to be Informed; decimals, fractions, square-roots]

Problem 67 Unit Conversion Exercises - Radiation dosages and exposure calculations allow students to compare several different ways that scientists use to compare how radiation exposure is delive black and accumulated over time.Like converting 'centimeters per sec' to 'kilometers per year' ,this activity reinforces student Topics in converting from one set of units to another. [Grade level: 6-8 | Topics: fractions, decimals, units]

Problem 66 Background Radiation and Lifestyles - Living on Earth, you will be subjected to many different radiation environments. This problem follows one person through four different possible futures, and compares the cumulative lifetime dosages. [Grade level: 6-8 | Topics: fractions, decimals, unit conversions]

Problem 65 A Perspective on Radiation Dosages - Depending on the kind of career you chose, you will experience different lifetime radiation dosages. This problem compares the cumulative dosages for someone living on Earth, an astronaut career involving travel to the Space Station, and the lifetime dosage of someone traveling to Mars and back. [Grade level: 6-8 | Topics: decimals, unit conversions, graphing a timeline, finding areas under curves using rectangles]