 | This web page contains problem sets in PDF format. The goal of these problems is to teach students about astronomy and space science by using mathematics and real-world problems. The current batch is for January-March. New batches will be posted in April. For email announcements about Space Math, join the E-Teachers Listserve. |
This Quarter's Problems:
Problem 189: Stellar Temperature, Size and Power- Students work with a basic equation to explore the relationship between temperature, surface area and power for a selection of stars. [Grade: 8-10| Skills: Algebra]
Problem 188: Cross Sections and Collision Times - Students explore the relationship between density, speed and size in determining how quickly particles collide in a gas. [Grade: 9-11| Skills: Algebra; Area]
Problem 187: Differentiation- Students explore partial derivatives by calculating rates of change in simple equations taken from astrophysics. [Grade: 11-12| Skills: differentiation; algebra]
Problem 186: Collapsing Gas Clouds and Stability- Students use the derivative to find an extremum of an equation governing the pressure balance of an interstellar cloud. [Grade: 11-12| Skills: differentiation; finding extrema; partial derivitives]
Problem 185: The International Space Station: Follow that graph!- Students use a plot of the orbit altitude of the ISS to predict its re-entry year after the peak of the next solar activity cycle. [Grade: 6-8| Skills: extrapolating a simple graph; estimation; forecasting]
Problem 184: The Ant and the Turntable: Frames of reference - Students predict the motion of an ant crawling from the center of a spinning CDrom to the edge. They also use calculus to estimate the length of the spiral path seen by a stationary observer. [Grade: 11-12| Skills: integration; parametric equations; polar coordinates]
Problem 183: Calculating Arc Lengths of Simple Functions- Students determine the basic equation for arclength and its integral, and evaluate it for simple polar functions. [Grade: 11-12| Skills: calculus; integration; parametric equations]
Problem 182: Our Neighborhood in the Milky Way- Students create a scale model of the local Milky Way and estimate distances and travel times for a series of voyages. [Grade: 6-8| Skills: scale models; speed-distance-time]
Problem 181: Extracting Oxygen from Moon Rocks- Students use a chemical equation to estimate how much oxygen can be liberated rom a sample of lunar soil. [Grade: 9-11| Skills: ratios; scientific notation; unit conversions]
Problem 180: Planets, Fractions and Scales- Students work with relative planet comparisons to determine the actual sizes of the planets given the diameter of Earth. [Grade: 4-6| Skills: scale models; decimals; fractions]
Problem 179: Is There a Lunar Meteorite Impact Hazard? - Students work with areas, probability and impact rates to estimate whether lunar colonists are in danger of meteorite hazards. [Grade: 5-7| Skills: Area; unit conversions; rates]
Problem 178: The Mass of the Moon - Students use the period and altitude of a NASA lunar spacecraft to determine the mass of the moon. [Grade: 8-11| Skills: Algebra]
Problem 177: Lunar Cratering: Probability and Odds- Students work with crater counting to estimate the area covered by craters and how to convert this into impact probabilities. [Grade: 4-7| Skills: Area; probability]
Problem 176: Solar Storms: Sequences and Probabilities II - Students continue their study of a stormy week on the sun by working out the probabilities for joint events. [Grade: 4-7| Skills: probability; numerating possible outcomes]
Problem 175: Solar Storms: Sequences and Probabilities I - Students work out the probabilities for various combinations of solar storms during a given week. [Grade: 4-7| Skills: probability; numerating possible outcomes]
Problem 174: A Matter of Timing - Students study satellites of Saturn to work out graphically how often they will line up. [Grade: 3-6| Skills: scale model; time calculation; fractions; working with rulers and compasses]
Problem 173: Groups, Clusters and Individuals- Students determine the number of individual objects given the number of groups and the number of individuals in an average group for clusters of stars and galaxies. [Grade: 3-5 | Skills: multiplication]
Problem 172: The Stellar Magnitude Scale- Students learn about positive and negative numbers using a popular brightness scale used by astronomers. [Grade: 3-6| Skills: number relationships; decimals; negative and positive numbers]
Previous Problems:
Problem 171: Are U Really Nuts?- Students work with four unit conversion problems that are a bit tricky! [Grade: 6-8 | Skills: unit conversions]
Problem 170: Measuring Star Temperatures- Students use a simple formula to determine the temperatures of stars, and to use a template curve to analyze data for a specific star to estimate its temperature. [Grade: 6-8 | Skills: algebra, graph analysis]
Problem 169: The Limiting Behavior of Functions- Students work with two complex formulae to determine their limiting behavior as the independent variables approach infinity and zero. [Grade: 9-12 | Skills: Algebra II, pre-calculus]
Problem 168: Fitting Periodic Functions - Distant Planets- Students work with data from a newly-discovered extra-solar planet to determine its orbit period and other parameters of a mathematical model. [Grade: 9-12 | Skills: trigonometry; functions; algebra]
Problem 167: Areas and Probabilities- Students work with various means of estimating probabilities using a comparison of areas. [Grade: 4-6 | Skills: percentages,calculating areas; probability]
Problem 166: The Dollars and Cents of Research - Students work with dollar amounts, hourly salary rates, percentages to explore various models of the cost of scientific research as seen by the individual scientist. [Grade: 4-6 | Skills: percentages, decimal math, simple rates (e.g dollars/hour)]
Problem 165: Fractionsw in Space - Students explore the many ways that simple fractions come up in the study of planetary motion. [Grade: 3-5 | Skills: working with fractions; time calculations]
Problem 164: Equations with One Variable- Students work with equations like '4.3 = 3.26D' to solve for D in a numer of simple astronomical problems involving distances, speed and temperature conversion. [Grade: 6-8 | Skills: equations in one variable; multiplication; division; decimals]
Problem 163: Time Intervals - Students calculate time intervals between a number of astronomical events, from milliseconds to years. [Grade: 3-5 | Skills: Time calculations; unit conversions; decimal math]
Problem 162: Areas and Probabilities- Students explore how area and probability are related in working out meteor impact and 'stormy day' problems. [Grade: 4-6 | Skills: Working out all possible outcomes for a set of events; fractions and percentages]
Problem 161: Earth and Moon to Scale- Students create a scale model of trhe Earth-Moon system and compare with artistic renditions and actual NASA spacecraft images. [Grade: 4-6| Skills: Decimals; scaling and similarity]
Problem 160: The Relative Sizes of the Sun and Stars- Students work through a series of comparisons of the relative sizes of the sun compared 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 | Skills: working with fractions; scale models]
Problem 159: Galaxies to Scale - Students explore the relative sizes of the Milky Way compared to other galaxies to create a scale model of galaxies, similar to the methods in Problem 161. [Grade: 4-6 | Skills: working with fractions; scale models]
Problem 158: The Solar Neighborhod within 17 Light Years - Students create a scale model of the local solar neighborhood and determine the shortest travel distances to several stars. [Grade: 6-8 | Skills: Plotting polar coordinates using a ruler and compass; decimal math]
Problem 157: Space Shuttle Launch Trajectory - I - Students use the parametric equation for the altitude and range for an actual Shuttle launch to determine the speed and acceleration of the Shuttle during launch and orbit insertionh [Grade: 11-12 | Skills: Algebra; Calculus; Parametric Equations; Differentiation
Problem 156: Spectral Classification of Stars- Students use actual star spectra to classify them into specific spectral types according to a standard ruberic. [Grade: | Skills: Working with patterns in data; simple sorting logic
Problem 155: Tidal Forces: Let 'er rip! - Students explore tidal forces and how satelites are destroyed by coming too close to their planet. [Grade: 7-10| Skills: Algebra; number substitution]
Problem 154: Pan's Highway and Saturn's Rings - Students use an image from the Cassini spacecraft to determine how large the satellite Pan is, and the scale of Saturn's rings using a millimeter ruler. [Grade: 4-6 | Skills:Finding the scale of an image; measurement; unit conversion]
Problem 153: Number Sentence Puzzles - Students are presented with three number sentences such as 145 + N = 375, and asked to select which 'spacy' word problem they belong to. [Grade: 3-4 | Skills: Number skills and problem solving]
Problem 152: The Hubble Law - Students plot the speed and distance to 7 galaxies and by deriving the slop of the linear model for the data points, obtain an estimate for the expansion rate of the universe known as Hubble's Constant. [Grade: 6-8 | Skills: Plotting data; determining the slope of the data;]
Problem 151: Time Zone Math - Students learn about time zones and perform simple clock calculations using common United States and European time zones. [Grade: 3-5 | Skills: time units; addition, subtraction]
Problem 150: Cosmic Bar Graphs - Students interpret simple bar graphs taken from astronomical data. [Grade: 3-5 | Skills: finding maxima and minima; fractions; extrapolating data]
Problem 149: Equations with One Variable - Students solve formulas of the form 2001 = 1858 + 11x to find 'X'. [Grade: 3-5 | Skills: addition, subtraction, multiplication, division; solving simple equations]
