Space Math Problems Sorted by NASA Mission and Program

Advanced Composition Explorer (ACE)

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 ]

Cassini - Huygens

Problem 335: Methane Lakes on Titan Students use a recent Cassini radar image of the surface of Titan to estimate how much methane is present in the lakes that fill the image, and compare the volume to that of the fresh water lake, Lake Tahoe. [Grade: 6-8 | Topics: estimating irregular areas; calculating volume from area x height; scaled images ]

Problem 315: The Mysterious Hexagon on Saturn A curious hexagon formed by the Saturn polar jet stream, and photographed by the Cassini spacecraft, is used to determine wind speed and acceleration. [Grade: 6-9 | Topics: Measuring; Metric Units; speed=distance/time]

Chandra X-Ray Observatory

Problem 417: Estimating the Size and Mass of a Black Hole Students use a simple formula to estimate the size of a black hole located 3.8 billion light years from Earth, recently studied by NASA's Chandra and Swift satellites. [Grade: 8-10 | Topics: distance=speed x time] (PDF)

Problem 398: The Crab Nebula - Exploring a pulsar up close! Students work with a photograph to determine its scale and the time taken by light and matter to reach a specified distance. [Grade: 6-8 | Topics: Scale drawings; unit conversion; distance = speed x time] (PDF)

Dawn

Problem 434: Dawn Spacecraft Sees Asteroid Vesta Up-Close!
Students use an image of the asteroid to determine the diameters of craters and mountains using a millimeter ruler and the scale of the image in meters per millimeter. [Grade: 6-8 | Topics: scale, metric measurement] (PDF)

Problem 210: The Mathematics of Ion Rocket Engines Students learn about the basic physics of ion engines, calculating speeds. [Grade: 9-12| Topics: Scientific Notation; Algebra II; evaluating formulae.]

Deep Impact - EPOXI

Problem 387: A Mathematical Model of Water Loss from Comet Tempel-1 Students use data from the Deep Impact spacecraft to create a simple empirical model for predicting the rate of water loss from a comet based on actual data. [Grade: 8-10 | Topics: graphing; fitting a parabola to data; evaluating functions] (PDF)

Problem 383: Estimating the mass of Comet Hartley 2 using calculus.
Students use a recent image of the nucleus of Comet Hartley 2 taken by the Deep Impact/EPOXI camera and a shape function described by a fourth-order polynomial to calculate the volume of the comet's head using integral calculus. to estimate the volume of the comets nucleus, and its total mass, [Grade: 12 | Topics: Volume integral using disk method; scale model; scientific notation; unit conversion] (PDF)

Fermi Gamma-Ray Observatory

Problem 330: Fermi Detects Gamma-rays from the Galaxy Messier-82 Based on a recent press release, students work with a log-log plot to show that straight lines on this plot represent power-law functions. They use this fact to determine, by interpolation, the strength of the gamma-rays from this galaxy. [Grade: 10-12 | Topics: power-laws; log-log graphing; linear regression]

Problem 288: Fermi Observatory Measures the Lumps in Space Students use timing data obtained by the Fermi Observatory of a powerful gamma-ray burst 10 billion light years away, to determine how lumpy space is based on travel time delays between the lowest and highest-energy gamma-rays. [Grade: 9-12 | Topics: Scientific Notation; Evaluating an equation with multiple factors]

Galaxy Evolution Explorer (GALEX)

Problem 111: A Star Sheds a Comet Tail! The GALEX satellite captured a spectacular image of the star Mira shedding a tail of gas and dust nearly 13 light years long. Students use the GALEX image to determine the speed of the star, and to translate the tail structures into a timeline extending to 30,000 years ago. [Grade: 8-10 | Topics:Image scaling; Unit conversion; Calculating speed from distance and time]

Gravity Probe - B (GP-B)

Problem 421: The Lense-Thirring Effect Near the Sun and a Neutron Star Students work with a formula for the Lense-Thirring Effect and estimate how large it will be in orbit around our sun, and in the intense gravitational field of a dense neutron star. [Grade: 9-12 | Topics: algebra; scientific notation, angular measure] (PDF)

Problem 420: Gravity Probe B: Testing Einstein again! Students learn about the Lense-Thirring Effect, and calculate its magnitude near Earth's orbit using an algebraic equation with integer and fractional exponents. [Grade: 9-12 | Topics: algebra; scientific notation, angular measure] (PDF)

Hinode Solar Observatory

Problem 362: Hinode Discovers the Origin of White Light Flares
A study of the magnetic energy of a flare[Grade: 9-12 | Topics: Image scale; Algebra; Scientific Notation] (PDF)

Problem 105: The Transit of Mercury As seen from Earth, the planet Mercury occasionally passes across the face of the sun; an event that astronomers call a transit. From images taken by the Hinode satellite, students will create a model of the solar disk to the same scale as the image, and calculate the distance to the sun. [Grade: 9-11 | Topics:image scales; angular measure; degrees, minutes and seconds]

Hubble Space Telescope

Problem 399: A Galactic City in the Far Reaches of the Universe Students work with an image of a distant cluster of galaxies to determine its scale compared to nearby galaxies. [Grade: 6-8 | Topics: Scale; proportion; metric measurement; unit conversion] (PDF)

Problem 395: Death Stars Some stars create super-flares that are capable of eliminating life on planets that orbit close to the star. Students learn about these flares on common red-dwarf stars and compare them to flares on our own sun [Grade: 6-9 | Topics: Scientific Notation; percentages; rates of change] (PDF)

Interstellar Boundary Explorer (IBEX)

Problem 274: IBEX Uses Fast-moving Particles to Map the Sky! Students learn about Kinetic Energy and how particle energies and speeds are related to each other in a simple formula, which they use to derive the speed of the particles detected by the IBEX satellite. [Grade: 8-10 | Topics: Algebra I, Scientific notation]

Problem 273: IBEX Creates an Unusual Image of the Sky Students create an image of the sky by using a Bingo-like technique of tallying particles in various sky directions using a simple 5x5 grid. [Grade: 6-8 | Topics: Counting, tallying]

Imager for Magnetosphere to Auroral Global Exploration (IMAGE)

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 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]

Kepler Exoplanet Transit Explorer

Problem 416: Kepler probes the interior of red giant stars Students use the properties of circular arcs to explore sound waves inside stars. [Grade: 8-10 | Topics: geometry of circles and arcs; distance=speed x time] (PDF)

Problem 403: The Goldilocks Planets - Not too hot or cold Students use a table of the planets discovered by the Kepler satellite, and estimate the number of planets in our Milky Way galaxy that are about the same size as Earth and located in their Habitable Zones. They estimate the average temperature of the planets, and study their tabulated properties using histograms. [Grade: 6-8 | Topics: Averaging; histogramming] (PDF)

Lunar Orbiter

Problem 129: How Big is It? - The Moon up close. Students work with an image taken by the Lunar Orbiter III spacecraft to determine image scale, and search for the smallest things seen in a photograph. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Problem 127: How Big is It? - The Moon up close. Students work with an image taken by the Lunar Orbiter IV spacecraft to determine image scale, and search for the smallest things seen in a photograph. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]

Lunar Reconnissance Orbiter (LRO)

Problem 378: LRO Makes a Temperature Map of the Lunar South Pole
Students use the published LRO temperature map to study the scale of the south polar region, the sizes of its craters, and estimate the volume of water-ice that may be present in the Shackleton Crater. [Grade: 7-9 | Topics: Volume of a circular disk; scale models] (PDF)

Problem 372: LRO Determines Lunar Cratering History
Students count large craters on an LRO coded image of the lunar surface to estimate whether the impacting asteroids that produced the largest craters were from the same population of asteroids during the two different epocs of impacts. [Grade: 8-10 | Topics: Scaled images; histograming; inference] (PDF)

Manned Space Programs - Apollo, ISS, Shuttle, Ares

Problem 438: The Last Flight of the Space Shuttle Endeavor
Students use tabular data and graphing to determine the launch speed and acceleration of the Space Shuttle from the launch pad. [Grade: 6-8 | Topics: tabular data, graphing, metric measurement, speed=distance/time] (PDF)

Problem 437: Saturn V Rocket Launch Speed and Height
Students tabular data to determine the launch speed of the Saturn V rocket from the launch pad. [Grade: 6-8 | Topics: tabular data, graphing, metric measurement, speed=distance/time] (PDF)

Magnetosphere Multi-Scale Mission (MMS)

Problem 113: NASA Juggles Four Satellites at Once! Students will learn about NASA's Magnetospheric Multi-Scale (MMS) satellite mission, and how it will use four satellites flying in formation to investigate the mysterious process called Magnetic Reconnection that causes changes in Earth's magnetic field. These changes lead to the production of the Northern and Southern Lights and other phenomena. From the volume formula for a tetrahedron, they will calculate the volume of several satellite configurations and estimate the magnetic energy and travel times for the particles being studied by MMS. [Grade: 8-10 | Topics: Formulas with two variables; scientific notation]

Mars Rovers, Orbiters, etc.

Problem 393: Taking a stroll around a martian crater! Students use a recent photograph of a crater on Mars to estimate its circumference and the time it will take NASAs Opportunity Rover to travel once around its edge. [Grade: 6-8 | Topics: scale model; distance = speedxtime; metric measure] (PDF)

Problem 237: The Martian Dust Devils Students determine the speed and acceleration of a martian dust devil from time laps images and information about the scale of the image. [Grade: 6-8 | Topics: scales; Determining speed from sequential images; V = D/T

Mercury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER)

Problem 415: Mercury and the Moon - Similar but different Students explore the mass and volume of mercury compared to the moon by using the formula for a sphere and scale changes. [Grade: 8-10 | Topics: scale; volume of a sphere; mass = density x volume] (PDF)

Problem 121: Ice on Mercury? Since the 1990's, radio astronomers have mapped Mercury. An outstanding curiosity is that in the polar regions, some craters appear to have 'anomalous reflectivity' in the shadowed areas of these craters. One interpretation is that this is caused by sub-surface ice. The MESSENGER spacecraft hopes to explore this issue in the next few years. In this activity, students will measure the surface areas of these potential ice deposits an calculate the volume of water that they imply. [Grade: 8-10 | Topics:Area of a circle; volume, density, unit conversion]

Near Earth Asteroid Rendezvous (NEAR)

Problem 143: So..How big is it? - Asteroid Eros surface Students calculate the scale of an image of the surface of the asteroid Eros from the NEAR mission, and determine how big rocks and boulders are on its surface. [Grade: 4 - 7 | Topics: Scaling; multiplication, division; metric measure]

Radiation Belt Storm Probe (RBSP)

Problem 204: The Mass of the Van Allen Radiation Belts- Students graph some magnetic field lines in polar coordinates, then estimate the volume and mass of the Belts using the formula for a torus. [Grade: 9-12| Topics: Algebra II.]

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]

Ramaty High Energy Solar Spectroscopic Imager (RHESSI)

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]

Solar and Heliospheric Observatory (SOHO)

Problem 299: Changing Perspectives on the Sun's Diameter Students compare two images of the sun taken by the SOHO satellite to measure the apparent diameter change from different earth obit locations in the winter and summer. [Grade: 6-8 | Topics: measurement; parallax; metric units; percentage change]

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]

Solar Dynamics Observatory (SDO)

Problem 337: SDO Reveals Details on the Surface of the Sun Students use a spectacular colored image of the Sun to calculate the scale of the image in kilometers per millimeter, and then search for the smallest features relative to the size of Earth. [Grade: 6-8 | Topics: image scales; proportions]

Problem 336: SDO: Measuring the Speed of an Eruptive Prominence Students use recent First Light images of the Sun from SDO to calculate the speed of a prominence using a sequence of scaled images and computing position shift over the time interval of the images. [Grade: 6-8 | Topics: image scales; speed=distane/time ]

Solar Probe Plus

Problem 373: Solar Probe Plus - Having a hot time near the sun!
Students use a simple equation to estimate the temperature reached by the Solar Probe Plus spacecraft as it gets close to the sun. [Grade: 8-10 | Topics: Evaluating a function; square roots and forth roots] (PDF)

Problem 366: Solar Probe Plus - Working with angular diameter
Students use the tangent formula to determine the angular diameter of the sun as seen by the Solar Probe Plus spacecraft as it approaches the sun. [Grade: 8-10 | Topics: angular measure; tangent formula; angular size] (PDF)

Spitzer Space Telescope

Problem 278: Spitzer Studies the Distant Planet Osiris Students learn about the density of the planet HD209458b, also called Osiris, and compare it to that of Jupiter. [Grade: 8-10 | Topics: Spherical volumes; density; Scientific Notation;]

Problem 272: Spitzer Telescope Discovers New Ring of Saturn! Students calculate the volume of the ring and compare it to the volume of Earth to check a news release figure that claims 1 billion Earths could fit inside the new ring. [Grade: 8-9 | Topics: Geometry, Algebra, volumn, scientific notation]

Solar Terrestrial Relations Observatory (STEREO)

Problem 404: STEREO Spacecraft give 360-degree Solar View Students use STEREO satellite images to determine which features can be seen from Earth and which cannot. They learn about the locations and changing positions of the satellites with respect to Earth's orbit. [Grade: 6-8 | Topics: angular measure, extrapolation; distance = speed x time] (PDF)

Problem 298: Seeing Solar Storms in STEREO - II Students explore the geometry of stereo viewing by studying a solar storm viewed from two satellites. [Grade: 10-12 | Topics: Geometry; Trigonometry]

Terra, Landsat, Earth Observatory

Problem 406: Growing Grapes in the Middle of the Desert Students use a dramatic Earth Observatory-1 satellite image of agriculture in Namibia to estimate the total cultivated area and water needs of grape growing under desert conditions [Grade: 6-8 | Topics: areas of irregular regions; unit conversion] (PDF)

Problem 375: Terra Satellite Measures Dangerous Dust
Students determine the number of dust particles inhaled by using a satellite map of the dust concentration and a calculation of the mass of a typical dust grain. [Grade: 8-10 | Topics: unit conversion; scientific notation; mass=densityxvolume] (PDF)

Problem 339: Terra Satellite Spies the Great Gulf Oil Catastrophe of 2010 Students use a Terra satellite image of the oil slick in the Gulf of Mexico to calculate its area, mass and thickness. [Grade: 6-8 | Topics: image scales; area of a circle; metric conversions ]

Time History of Events and Macroscale Interactions during Substorms (THEMIS)

Problem 201: Fly Me To the Moon! Students learn some basic principles and terminology about how spacecraft change their orbits to get to the moon. [Grade: 6-8| Topics: speed = distance/time; Pythagorean Theorem]

Problem 194: A Magnetic Case for 'What Came First?' Students create a timeline for events based on several data plots from the THEMIS program, and use their timeline to answer questions about the causes of magnetic storms. [Grade: 6-8| Topics: Time calculations]

Transition Region and Coronal Explorer (TRACE)

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 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]

Webb Space Telescope

Problem 407: Cryo-testing the Webb Space Telecope ISIM Students explore scaling by creating an enlarged geometric model of the ISIM to better appreciate the small changes due to expansion and contraction [Grade: 6-8 | Topics: scale models; proportions; unit conversion] (PDF)

Problem 370: 6-fold Symmetry and the Webb Space Telescope Mirror
Students learn about the Webb Space Telescopes segmented mirror and its rotational 6-fold symmetry due to tiling with hexagons. They identify groups of tiles that have identical optical properties [Grade: 8-10 | Topics: Properties of Hexagons; rotation symmetry; counting; tiling] (PDF)

Wide-Field Infrared Survey Explorer (WISE)

Problem 329: WISE and Hubble: Power Functions: A question of magnitude Students explore the function F(x) = 10^-ax and learn about the stellar magnitude scale used by astronomers to rank the brightness of stars. [Grade: 10-12 | Topics: base-10, evaluating power functions ]

Problem 328: WISE: F(x)G(x): A Tale of Two Functions Students use WISE satellite data to study a practical application of the product of two finctions by graphing them individually, and their product. A calculus-level problem is included for advanced students. [Grade: 10-12 | Topics: Power-law functions; domain and range; graphing; areas under curves; integration]

Wilkinson Microwave Anisotropy Probe (WMAP)

Problem 233: The Milky Way: A mere cloud in the cosmos- Students compare the average density of the Milky Way with the density of the universe. [Grade: 8-10 | Topics: Volume of disk, density, scientific notation]

Problem 192: The Big Bang - Cosmic Expansion - Students explore the expansion of the universe predicted by Big Bang cosmology [Grade: 10-12| Topics: Algebra, Integral Calculus]

X-ray Multi-Mirror mission (XMM)

Problem 136 : Energy Generation near Black Holes Students explore how much energy is generated by stars and gas falling into black holes. The event horizon radius is calculated from a simple equation, R = 2.95 M, and energy is estimated from E = mc^2. [Grade: 7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]