# National Aeronautics and Space Administration

## Year 1: Problems 1 to 38

Problem 38 Solar Eclipses and Satellite Power From the ground we see total solar eclipses where the New Moon passes directly between Earth and Sun. Satellites use solar cells to generate electricity, but this is only possible when the Earth is not 'eclipsing' the sun. Students will create a scaled drawing of the orbits of three satellites around Earth, and calculate how long each satellite will be in the shadow of Earth. They will be asked to figure out how to keep the satellites operating even without sunlight to power their solar panels. [Grade: 5 - 8 | Topics: Geometry; decimal math]

Problem 37 Time Zone Mathematics. Students will learn about the time zones around the world, and why it is important to keep track of where you are when you see an astronomical phenomenon. A series of simple time calculations teaches students about converting from one time zone to another. [Grade: 5 - 7 | Topics: Time zone math]

Problem 36 The Space Station Orbit Decay and Space Weather Students will learn about the continued decay of the orbit of the International Space Station by studying a graph of the Station's altitude versus time. They will calculate the orbit decay rates, and investigate why this might be happening. [Grade: 5 - 8 | Topics: Interpreting graphical data; decimal math]

Problem 35 Exploring the Plasmasphere Students use an image of the plasmasphere obtained by the IMAGE satellite to calculate how fast it orbits the Earth. They will use this to determine whether gravity or Earth's magnetic field provides the forces responsible for its movement through space. [Grade: 7 - 9 | Topics: Geometry; ratios; decimal math; time arithmetic]

Problem 34 Using the TV Program CSI to Explore Matter Students will read about how a mass spectrometer works - the kind used in the TV Series CSI, and learn how to interpret a simple spectrum to find out which elements are present in a mystery sample. [Grade: 7 - 9 | Topics: Geometry; ratios; decimal math]

Problem 33 Magnetic Energy From B to V Students will use formulas for the volume of a sphere and cylinder, and magnetic energy, to calculate the total magnetic energy of two important 'batteries' for space weather phenomena- solar prominences and the Earth's magnetotail. This requires scientific notation, a calculator, and experience with algebraic equations with integer powers of 2 and 3. [Grade: 8 - 10 | Topics: Algebra I; volumes; decimal math; scientific notation]

Problem 32 Solar Proton Events and Satellite Damage Students will examine the statistics for Solar Proton Events since 1996 and estimate their damage to satellite solar power systems. [Grade: 7 - 9 | Topics: Interpreting tabular data; histogramming]

Problem 31 Airline Travel and Space Weather Students will read an excerpt from the space weather book 'The 23rd Cycle' by Dr. Sten Odenwald, and answer questions about airline travel during solar storms. They will learn about the natural background radiation they are exposed to every day, and compare this to radiation dosages during jet travel. [Grade: 6 - 8 | Topics: Reading to be informed; decimal math]

Problem 30 Exploring Earth's Magnetosphere [DOC] Students will examine a NASA website that discusses Earth's magnetosphere, and identify the definitions for key phenomena and parts to this physical system. They will write a short essay that describes, in their own words, how aurora are produced based on what they have read at the NASA site. [Grade: 6 - 8 | Topics: non-mathematical; reading to be informed; online research]

Problem 29 The Wandering Magnetic North Pole Mapmakers have known for centuries that Earth's magnetic North Pole does not stay put. This activity will have students read a map and calculate the speed of the 'polar wander' from 300 AD to 2000 AD. They will use the map scale and a string to measure the distance traveled by the pole in a set period of time and calculate the wander speed in km/year. They will answer questions about this changing speed. [Grade: 6 - 8 | Topics: Interpreting graphical data; speed = distance/time]

Problem 28 Satellite Power and Cosmic Rays Most satellites operate by using solar cells to generate electricity. But after years in orbit, these solar cells produce less electricity because of the steady impact of cosmic rays. In this activity, students read a graph that shows the electricity produced by a satellite's solar panels, and learn a valuable lesson about how to design satellites for long-term operation in space. Basic math ideas: Area calculation, unit conversions, extrapolation and interpolation of graph trends. [Grade: 6 - 8 | Topics: Interpreting graphical data; decimal math]

Problem 27 Satellite Failures and the Sunspot Cycle There are over 1500 working satellites orbiting Earth, representing an investment of 160 billion dollars. Every year, between 10 and 30 of these re-enter the atmosphere. In this problem, students compare the sunspot cycle with the record of satellites re-entering the atmosphere and determine if there is a correlation. They also investigate how pervasive satellite technology has become in their daily lives. [Grade: 6 - 8 | Topics: Graphing tabular data; decimal math]

Problem 26 Super-sized Sunspots and the Solar Cycle. Students compare the dates of the largest sunspots since 1900 with the year of the peak sunspot cycle. They check to see if superspots are more common after sunspot maximum or before. They also compare superspot sizes with the area of earth. [Grade: 6 - 8 | Topics: Interpreting tabular data; decimal math]

Problem 25 The Distance to Earth's Magnetopause Students use an algebraic formula and some real data, to calculate the distance from Earth to the magnetopause, where solar wind and magnetosphere pressure are in balance. [Grade: 8 - 10 | Topics: Evaluating a function with two variables; completing tabular entries]

Problem 24 Reading Between the Lines Students solve simple equations for x, (like 2x + 3 = 5) to discover which words complete an essay on the causes of aurora, and answer questions after reading the completed essay. [Grade: 5 - 7 | Topics: solving for X; distributive law; associative law]

Problem 23 Solar Flares and Sunspot Sizes Students compare sunspot sizes to the frequency of solar flares and discover that there is no hard and fast rule that relates sunspot size to its ability to produce very large flares. [Grade: 6 - 8 | Topics: Interpreting tabular data; percentages; decimal math ]

Problem 22 The Auroral Oval Students learn that the aurora are observed as two 'halos' of light encircling the North and South Poles. Students use measurements made from two satellite images of the 'auroral ovals' to determine the diameter of the rings, and their approximate geographic centers - which are not at the geographic poles! [Grade: 5 - 7 | Topics: Finding the scale of an image; measurement; decimal math]

Problem 21 Exploring the Plasmasphere Students learn that the Pythagorean Theorem is more than a geometric concept. Scientists use a photograph taklen by the IMAGE satellite to measure the size of Earth's plasmasphere region using a ruler and protractor. [Grade: 7 - 9 | Topics: Finding the scale of an image; decimal math; measurement]

Problem 20 A Space Science Crossword Puzzle Students work with positive and negative numbers to solve a crossword puzzle. The theme is 'Scientists use math to explore Nature'. Good exercise for pre-algebra review of adding and subtracting positive and negative numbers. [Grade: 4 - 6 | Topics: Integer arithmetic; associative and distributive laws]

Problem 19 An Application of the Pythagorean Theorem Students learn that the Pythagorean Theorem is more than a geometric concept. Scientists use it all the time when calculating lengths, speeds or other quantities. This problem is an introduction to magnetism, which is a '3-dimensional vector', and how to calculate magnetic strengths using the Pythagorean Theorem. [Grade: 8 - 10 | Topics: Squares and square-roots; Pythagorean Theorem in 3-D]

Problem 18 Magnetic Forces and Particle Motion Students learn about the spiral-shaped trajectories of charged particles moving in magnetic fields, and calculate some basic properties of this 'cyclotron' motion. [Grade: 9 - 11 | Topics: Algebra I; evaluating a function; scientific notation]

Problem 17 Magnetic Forces and Kinetic Energy Students use the formula for the Kinetic Energy of a charged particle to calculate particle speeds for different voltages, and answer simple questions about lightning, aurora and Earth's radiation belts. [Grade: 6 - 8 | Topics: Square root; time=speed x distance; decimal math; significant figures]

Problem 16 Solar Power and Satellite Design Students perform simple surface area calculations to determine how much solar power a satellite can generate, compared to the satellite's needs. [Grade: 6 - 8 | Topics: Area of irregular polygons]

Problem 15 Radio Plasma Imaging with IMAGE Students use the Distance=VelocityxTime relationship to determine the distances to plasma clouds seen by the IMAGE satellite. [Grade: 6 - 8 | Topics: Polar graphs; time = distance x speed; decimal math]

Problem 14 Kinetic Energy and Particle Motion Students learn about kinetic energy and how this concept applies to charged particles. They calculate the speed of a particle for various particle energies. [Grade: 7 - 9 | Topics: Evaluating a function; square-roots; scientific notation]

Problem 13 Plasma Clouds Students use a simple 'square-root' relationship to learn how scientists with the IMAGE satellite measure the density of clouds of plasma in space. [Grade: 7 - 9 | Topics: Square-root; solving for X; evaluating a function]

Problem 12 The Ring Current Students use the formula for a disk to calculate the mass of the ring current surrounding Earth. [Grade: 7 - 9 | Topics: Volume of a disk; scientific notation; mass = density x volume]

Problem 11 How high is an aurora Students use the properties of a triangle to determine how high up aurora are. They also learn about the parallax method for finding distances to remote objects. [Grade: 5 - 8 | Topics: Geometery; angle measure]

Problem 10 The Life Cycle of an Aurora Students examine two eye-witness descriptions of an aurora and identify the common elements so that they can extract a common pattern of changes. [Grade: 4 - 6 | Topics: Creating a timeline from narrative; ordering events by date and time]

Problem 9 Aurora Power! Students use data to estimate the power of an aurora, and compare it to common things such as the electrical consumption of a house, a city and a country. [Grade: 5 - 7 | Topics: Interpreting tabular data]

Problem 8 Making a Model Planet Students use the formula for a sphere, and the concept of density, to make a mathematical model of a planet based on its mass, radius and the density of several possible materials (ice, silicate rock, iron, basalt). [Grade: 7 - 9 | Topics: Volume of sphere; mass = density x volume; decimal math; scientific notation]

Problem 7 Solar Flares, CME's and Aurora Some articles about the Northern Lights imply that solar flares cause them. Students will use data to construct a simple Venn Diagram, and answer an important question about whether solar flares cause CME's and Aurora. [Grade: 5 - 7 | Topics: Venn Diagramming]

Problem 6 Observing the Sun's rotation Students use a Sunspotter to track sunspots during the week of November 7, 2004, and calculate the rotation period of the sun. [Grade: 6 - 8 | Topics: Lab exercise using a 'Sunspotter' to measure sun's rotation]

Problem 5 The November 8, 2004 solar storm Students calculate the speed of a CME, and describe their aurora observations through writing and drawing. [Grade: 6 - 8 | Topics: Time calculations; distance = speed x time]

Problem 4 Sketching the Northern Lights Students read an account of an aurora seen by an observer, and create a drawing or painting based on the description. [Grade: 5 - 7 | Topics: non-mathematical art problem]

Problem 3 Magnetic Storms II Students learn about the Kp index using a bar graph. They use the graph to answer simple questions about maxima and time. [Grade: 6 - 8 | Topics: Interpreting bar graphs; time calculations]

Problem 2 Satellite Surface Area Students calculate the surface area of an octagonal cylinder and calculate the power it would yield from solar cells covering its surface. [Grade: 7 - 9 | Topics: surface areas; hexagone; decimal math]

Problem 1 Magnetic Storms I Students learn about magnetic storms using real data in the form of a line graph. They answer simple questions about data range, maximum, and minimum. [Grade: 7 - 9 | Topics: Interpreting a graph; time calculations]