## Space Math @ NASA

Problem 264: Water on Planetary Surfaces - Students work with watts and Joules to study melting ice. [Grade: 8-10 | Topics: unit conversion, rates]

Problem 263: Ice or Water? - Whether a planetary surface contains ice or liquid water depends on how much heat is available. Students explore the concepts of Specific heat and Latent Heat of Fusion to better understand the and quantify the energy required for liquid water to exist under various conditions. [Grade: 8-10 | Topics: unit conversion, scientific notation]

Problem 254: Solar Insolation Changes and the Sunspot Cycle - Students compare changes in the amount of solar energy reaching Earth with the 11-year sunspot cycle to predict the impact on designing a photovoltaic system for a home. [Grade: 8-10 | Topics: graph analysis, correlations, kilowatt, kilowatt-hours]

Problem 248: Seeing Solar Storms in STEREO - Students work out the details of stereoscopic vision using elementary properties of triangles and the Law of Cosines to determine the distance from Earth of a solar storm cloud. [Grade: 8-10 | Topics: geometry, Law of Cosines, V = D/T]

Problem 244: Solar Storms - Fractions and Percentages - Students create a Venn Diagram to summarize data on a series of solar storms, and determine how often solar flares occur when a solar plasma eruption happens. [Grade: 4-7 | Topics: precentages; Venn Diagramming]

Problem 212: Finding Mass in the Cosmos - Students derive a simple formula, then use it to determine the masses of objects in the universe from the orbit periods and distances of their satellites. [Grade: 9-12| Topics: Scientific Notation; Algebra II; parametric equations]

Problem 199: Solar Storm Energy and Pie Graphs - Students study two Pie graphs describing solar flares and draw conclusions about percentages and their various forms of energy. [Grade: 6-8| Topics: Interpreting Pie Graphs.]

Problem 198: Solar Storm Timeline - Students read a narrative about the events involved in a solar storm, create a chronology for the sequence of events, and answer some simple time-related questions. [Grade: 6-8| Topics: Time calculations.]

Problem 176: Solar Storms: Sequences and Probabilities I - Students continue their study of a stormy week on the Sun by working out the probabilities for joint events. [Grade: 4-7| Topics: probability; numerating possible outcomes]

Problem 175: Solar Storms: Sequences and Probabilities II - Students work out the probabilities for various combinations of solar storms during a given week. [Grade: 4-7| Topics: probability; numerating possible outcomes]

Problem 160: The Relative Sizes of the and Stars - Students work through a series of comparisons of the relative sizes of the Sun compablack to other stars, to create a scale model of stellar sizes using simple fractional relationships. ( e.g if Star A is 6 times larger than Star B, and Star C is 1/2 the size of Star B, how big is Star C in terms of Star A?) [Grade: 4-6 | Topics: working with fractions; scale models]

Problem 134 The Last Total Solar Eclipse--Ever! - Students explore the geometry required for a total solar eclipse, and estimate how many years into the future the last total solar eclipse will occur as the moon slowly recedes from Earth by 3 centimeters/year. [Grade: 7 - 10 | Topics:Simple linear equations]

Problem 118 An Application of the Parallax Effect - The STEREO mission views the Sun from two different locations in space. By combining this data, the parallax effect can be used to determine how far above the solar surface various active regions are located. Students use the Pythagorean Theorem, a bit of geometry, and some actual STEREO data to estimate the height of Active Region AR-978. [Grade: 8-10 | Topics:Pythagorean Theorem; square-root; solving for variables]

Problem 117 CME Kinetic Energy and Mass - Coronal Mass Ejections (CMEs) are giant clouds of plasma released by the Sun at millions of kilometers per hour. In this activity, students calculate the kinetic energy and mass of several CMEs to determine typical mass ranges and speeds. Students will use the formula for kinetic energy to fill-in the missing entries in a table. They will then use the completed table to answer some basic questions about CMEs. [Grade: 8-10 | Topics:time calculation; Evaluating a simple equation; solving for variables]

Problem 116 The Comet Encke Tail Disruption Event - On April 20, 2007 NASA's STEREO satellite captured a rare impact between a comet and the fast-moving gas in a solar Coronal Mass Ejection. In this problem, students analyze a STEREO satellite image to determine the speed of the tail disruption event. [Grade: 8-10 | Topics:time calculation; finding image scale; calculating speed from distance and time]

Problem 115 A Mathematical Model of the - Students will use the formula for a sphere and a shell to calculate the mass of the Sun for various choices of its density. The goal is to reproduce the measured mass and radius of the Sun by a careful selection of its density in a core region and a shell region. Students will manipulate the values for density and shell size to achieve the correct total mass. This can be done by hand, or by programming an Excel spreadsheet. [Grade: 8-10 | Topics: scientific notation; volume of a sphere and a spherical shell; density, mass and volume.]

Problem 114 The Heliopause...a question of balance - Students will learn about the concept of pressure equilibrium by studying a simple mathematical model for the Sun's heliopause located beyond the orbit of Pluto. They will calculate the distance to the heliopause by solving for 'R' and then using an Excel spreadsheet to examine how changes in solar wind density, speed and interstellar gas density relate to the values for R. [Grade: 8-10 | Topics: Formulas with two variables; scientific notation; spreadsheet programming]

Problem 112 How fast does the Sun spin? - Students will use two x-ray images of the Sun taken by the Hinode satellite to determine how fast the Sun rotates. [Grade: 5-9 | Topics:calculating map scales; time calculations; unit conversion]

Problem 111 Scientific Notation III - In this continuation of the review of Scientific Notation, students will perform simple multiplication and division problems with an astronomy and space science focus. [Grade: 5-9 | Topics:Scientific notation - multiplication and division]

Problem 107 Monster Sunspots! - Some sunspots are so big that they can be seen from Earth without a telescope. In this problem, students will use images of three super-spots and calculate their sizes from the image scaling information. They will then order the images from the smallest super-spot to the largest super-spot. [Grade: 5-9 | Topics:multiplication; calculating length from image scale]

Problem 104 Loopy Sunspots! - Students will analyze data from the Hinode satellite to determine the volume and mass of a magnetic loop above a sunspot. From the calculated volume, based on the formula for the volume of a cylinder, they will use the density of the plasma determined by the Hinode satellite to determine the mass in tons of the magnetically trapped material. [Grade: 9-11 | Topics:image scales; cylinder volume calculation; scientific notation; unit conversions]

Problem 103 The Mysterious Solar Micro-Flares! - Students will analyze an image taken by the Hinode solar satellite to determine the scale of the image in kilometers per millimeter, then use this to determine the sizes of solar micro-flares. From the number of micro-flares that they count in the image, the area of the image in square kilometers, and the surface area of a spherical Sun, they will calculate the total number of micro-flares on the solar surface. [Grade: 6-9 | Topics:image scales; area calculation; unit conversions]

Problem 102 How fast does the Sun rotate? - Students will analyze consecutive images taken by the Hinode satellite to determine the Sun's speed of rotation, and the approximate length of its 'day'. [Grade: 6-9 | Topics:image scales; time calculations; speed calculations, unit conversions]

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 - 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 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 92 A Lunar Transit of the 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 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 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 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 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 64 Solar Activity and Satellite Mathematics - When solar storms cause satellite problems, they can also cause satellites to lose money. The biggest source of revenue from communications satellites comes from transponders that relay television programs, ATM transactions and many other vital forms of information. They are rented to many different customers and can cost nearly $2 million a year for each transponder. This activity examines what happens to a single satellite when space weather turns bad! [Grade level: 4-6 | Topics: Decimals; money; percents]

Problem 63 Solar Activity and Tree Rings - What's the connection? - Trees require sunlight to grow, and we know that solar activity varies with the sunspot cycle. Can an average tree sense solar activity cycles and change the way it grows from year to year? This activity uses a single tree to compare its growth rings to the sunspot cycle. This is also an interesting suggestion for science fair projects! Here is the accompanying Excell Spreadsheet Data File. [Grade level: 4-6 | Topics: Spreadsheets and technology; decimal math]

Problem 53 Astronomy: A Moving Experience! - Objects in space move. To figure out how fast they move, astronomers use many different techniques depending on what they are investigating. In this activity, you will measure the speed of astronomical phenomena using the scaling clues and the time intervals between photographs of three phenomena: A supernova explosion, a Coronal Mass Ejection, and a solar flare shock wave. [Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; distance = speed x time; scientific notation]

Problem 51 Sunspots Close-up and Personal - Students will analyze a picture of a sunspot to learn more about its size, and examine the sizes of various other features on the surface of the Sun that astronomers study. [Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; decimal math]

Problem 43 An Interplanetary Shock Wave - On November 8, 2000 the Sun released a Coronal Mass Ejection that traveled to Earth, and its effects were detected on Jupiter and Saturn several weeks later. In this problem, students will use data from this storm to track its speed and acceleration as it traveled across the solar system. [Grade level: 6-10 | Topics: Time calculations; distance = speed x time ]

Problem 42 Solar Storms in the News - Students will use a newspaper archive to explore how reporters have described the causes of aurora since the 1850's. They will see how some explanations were popular for a time, then faded into oblivion, as better scientific explanations were created. [Grade level: 6-10 | Topics: Online research; tallying data]

Problem 41 Solar Energy in Space - Students will calculate the area of a satellite's surface being used for solar cells from an actual photo of the IMAGE satellite. They will calculate the electrical power provided by this one panel. Students will have to calculate the area of an irregular region using nested rectangles. [Grade level: 7-10 | Topics: Area of an irregular polygon; decimal math]

Problem 39 Solar Storm Timeline - How long does a solar storm last? How fast does it travel? Students will examine an event timeline for a space weather event and use time addition and subtraction skills to calculate storm durations and speeds. [Grade level: 7-9 | Topics: time math; decimal math; speed = distance/time]

Problem 38 Solar Eclipses and Satellite Power - From the ground we see total solar eclipses where the New Moon passes directly between Earth and . 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 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 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 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 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 '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]