National Aeronautics and Space Administration

Problem 507: Exploring the Launch of the Falcon 9
Students use data from the launch of the Falcon 9 booster to determine its speed and acceleration. [Grade: 6-8 | Topics: speed=distance/time; Time calculations] (PDF)

Problem 493: Fun with Gears and Fractions
Students learn about how simple fractions are used to describe gears and gear trains that reduce or increase speed. [Grade: 4-7 | Topics: multiplying simple fractions] (PDF)

Problem 472: Investigating Juno's Elliptical Transfer Orbit
Students use the Standard Formula for an ellipse to study the elliptical orbit of the Juno spacecraft, and relate specific properties of the ellipse to features of the spacecrafts trajectory such as aphelion, perihelion, and ellipticity. [Grade: 9-12 | Topics: formula for an ellipse; semi-major and minor axis] (PDF)

Problem 471: Investigating the Launch of the Juno Spacecraft
Students use a series of images from a launch video to determine the scale of each image and determine the speed of the rocket as it leaves the gantry. [Grade: 6-8 | Topics: scale models; speed = distance/times] (PDF)

Problem 470: The Launch of the Juno Spacecraft - Ascent to orbit
Students use tabulated altitude and range data following the launch of the Juno mission, to determine the speed of the rocket as it travels to arth orbit. [Grade: 6-8 | Topics: scale models; speed = distance/time] (PDF)

Problem 469: Solar Energy and the Distance of Juno from the Sun
Students use the formula for an ellipse, along with the inverse-square law to create a mathemartical model that predicts the declining solar power produced by Junos solar panels as the spacecraft travels from Earth to Jupiter. [Grade: 9-12 | Topics: algebra; trigonometry; distance formula] (PDF)

Problem 463: A Simple Fuel Gauge in a Cylindrical Tank
Rockets use fuel tanks that can be approximated as cylinders. In this simple geometric exercise, students work the formula for the volume of a cylinder to add a fuel gauge at the right level to indicate how much fuel remains. [Grade: 7-9 | Topics: VOlume of cylinder; proportions] (PDF)

Problem 459: A piece of history - space shuttle thermal tiles
Students explore volume density and mass using the Space Shuttle thermal tiles. Get your own free tile from NASA too! [Grade: 6-8 | Topics: mass = density x volume; metric conversion] (PDF)

Problem 457: The Interplanetary Voyage of MSL
Students use the properties of ellipses to determine the formula for the Hohmann Transfer Orbit taking the Mars Science Laboratory to Mars in 2012 [Grade: 10-11 | Topics: time=distance/speed; scale models; metric math; properties of ellipses] (PDF)

Problem 456: The Launch of the Mars Science Laboratory (MSL) in 2011
Students use a sequence of launch images to determine the Atlas V's launch speed and acceleration. By determining the scale of each image, they estimate average speeds during the first 4 seconds after lift-off. [Grade: 8-10 | Topics: time=distance/speed; scale models; metric math] (PDF)

Problem 455: The Night Launch of STEREO in 2006
An example of old news seen in a different way! Students use a spectacular time-lapse photo of the launch of the STEREO mission obtained by photographer Dominic Agostini in 2006 to study parabolic curves. [Grade: 8-10 | Topics: time=distance/speed; scale models; metric math; equation of a parabola; curve fitting] (PDF)

Problem 442: Modeling the Atmospheric Re-entry of UARS
Students graph the altitude of the UARS satellite in the weeks before re-enrty to explore the accelerating effects of atmospheric drag. They create a mathematical model that fits the data, and use this to make their own prediction of the re-entry date. [Grade: 8 - 11 | Topics: graphing data; linear equations; exponential and power functions] (PDF)

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] (Questions Only)

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)

Problem 436: Space Shuttle Challenger Deploys the INSAT-1B Satellite
Students use a sequence of images to determine the launch speed of the satellite from the Space Shuttle cargo bay. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 435: Apollo-17 Lanuch from Lunar Surface
Students use a sequence of images to determine the speed of ascent of the Apollo-17 capsule from the lunar surface. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 433: Space Shuttle Atlantis - Plume Speed
Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 432: Space Shuttle Atlantis - Exhaust Speed
Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 431: Space Shuttle Atlantis - Launch Speed
Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 430: Space Shuttle Atlantis - Ascent to Orbit
Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. [Grade: 6-8 | Topics: scale, metric measurement, speed=distance/time] (PDF)

Problem 419: The Space Shuttle: Fly me to the moon? Students discuss the popular misconception that the Space Shuttle can travel to the moon by examining the required orbit speed change and the capacity of the Shuttle engines to provide the necessary speed changes. [Grade: 6-8 | Topics: amount = rate x time ] (PDF)

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 282: Exploring the Ares 1-X Launch: The Hard Climb to Orbit Students learn about the energy required to send a payload into orbit by studying the Ares 1-X rocket launch. [Grade: 8-10 | Topics: Algebra II]

Problem 281: Exploring the Ares 1-X Launch: Energy Changes Students learn about kinetic and potential energy while studying the Ares 1-X rocket launch. [Grade: 8-10 | Topics: Algebra II]

Problem 280: Exploring the Ares 1-X Launch: Parametrics Students learn about parametric equations to determine the path of the Ares 1-X rocket. [Grade: 8-10 | Topics: Algebra II; Parametric Equations]

Problem 279: Exploring the Ares 1-X Launch: Downrange Distance Students learn about the path of the Ares 1-X test launch and calculate its downrange landing distance in the Atlantic Ocean. [Grade: 8-10 | Topics: Algebra; Significant Figures; Metric to English Conversion]

Problem 277: Deep Impact Comet Encounter Students learn about the Deep Impact experiment involving Comet Tempel-1, and how the path of an asteroid can be changed by using the Law of Conservation of Momentum. [Grade: 10-12 | Topics: Algebra; Scientific Notation; distance = speedxtime]

Problem 276: Solid Rocket Boosters and Thrust Students learn how solid rocket boosters work, and calculate the SRB Thrust Curve using a simple geometric model and 'counting squares'.. [Grade: 8-10 | Topics: Geometry, Cylindrical volumes and surface areas, Graphing data]

Problem 266: The Ares-V Cargo Rocket Students work with the equations for thrust and fuel loss to determine the acceleration curve of the Ares-v during launch. [Grade: 11-12 | Topics: Algebra II, properties of functions, differential calculus, Excel Spreadsheet]

Problem 260: Some Famous Unit Conversion Errors Students examine three famous unit conversion errors that led to catastrophic failures and near-death experiences. [Grade: 6-8 | Topics: unit conversion, metric measure]

Problem 256: A High-resolution Satellite Photo Students examine a satelite photo of the Tennessee Court House from the GEO-1 satellite and determine the sizes of familiar features in the image. [Grade: 6-8 | Topics: scale, ratios, proportions' angle measure, triangle geometry]

Problem 250: The Most Important Equation in Astronomy Students learn about how an instrument's ability to see details depends on its size and its operating wavelength - the key to designing any telescope or camera. [Grade: 8-10 | Topics: geometry, angle measure, scientific notation]

Problem 246: Evaluating Secondary Physical Constants Students evaluate complicated algebraic quantities that define important constants in physics with both integer and fractional exponents. [Grade: 10-12 | Topics: Algebra; significant figures, scientific notation]

Problem 245: Solid Rocket Boosters Students learn how SRBs actually create thrust, and study the Ares-V booster to estimate its thrust. [Grade: 8-10 | Topics: volume, area, unit conversions]

Problem 243: ISS - Orbit Altitude Changes Students read an essay describing the increases and decreases in the International Space Station orbit, and calculate the final orbit altitude after all the changes are applied. [Grade: 8-10 | Topics: combining positive and negative mixed numbers; fractions]

Problem 238: Satellite Drag and the Hubble Space Telescope Satellite experience drag with the atmosphere, which eventually causes them to burn up in the atmosphere. Students study various forecasts of the althtiude of the Hubble Space Telescope to estimate its re-entry year. [Grade: 8-10 | Topics: interpreting graphical data; predicting trends]

Problem 235: Scientific Data: The gift that keeps on giving! Students learn about gigabytes and terrabytes of data and the rates of data generation by NASA missions and how to store it. [Grade: 6-8 | Topics: metric units; rates; money]

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 ]

Problem 208: Optimization- Students determine the optimal dimensions of an hexagonal satellite to maximize its surface area given its desiblack volume. [Grade: 9-12| Topics: Calculus; differentiation ]

Problem 207: The STEREO Mission: getting the message across- Students learn about how the transmission of data is affected by how far away a satellite is for the two satellites in the STEREO constellation. [Grade: 6-8| Topics: multiplication; division; decimal numbers ]

Problem 206: Can You Hear me now? - Students learn about how the transmission of data is affected by how far away a satellite is, for a variety of spacecraft in the solar system [Grade: 6-8| Topics: multiplication; division; decimal numbers ]

Problem 202: The Dawn Mission - Ion Rockets and Spiral Orbits- Students determine the shape of the trajectory taken by a spacecraft using a constant-thrust ion motor using differential and integral calculus for arc lengths. [Grade: 9-12| Topics: Calculus - Arc lengths ]

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 195: Unit Conversions III- Students work with more unit conversions and use them to solve a series of practical problems in science and solar energy. [Grade: 6-10| Topics: unit conversions.]

Problem 193: Fluid Level in a Spherical Tank - Students explore the relationship between volume, and the height of fluid in a spherical tank as fluid is being drained at a constant rate. [Grade: 10-12| Topics: Algebra, differential calculus, related rates]

Problem 185: The International Space Station: Follow that graph!- Students use a plot of the orbit altitude of the ISS to pblackict its re-entry year after the peak of the next solar activity cycle. [Grade: 6-8| Topics: extrapolating a simple graph; estimation; forecasting]

Problem 171: Are U Really Nuts?- Students work with four unit conversion problems that are a bit tricky! [Grade: 6-8 | Topics: unit conversions]

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 insertion [Grade: 11-12 | Topics: Algebra; Calculus; Parametric Equations; Differentiation

Problem 108 THEMIS - A Problem in Satellite Synchrony - The THEMIS program uses five satellites in five different orbits to study Earth's magnetic field and its changes during a storm. This problem asks students to use the periods of the five satellites to figure out when all 5 satellites will be lined-up as seen from Earth. They will do this by finding the Greatest Common Multiple of the five orbit periods, first for the case of 2 or 3 satellites, which can be easily diagrammed with concentric circles, then the case for all five satellites together. [Grade level: 5-9 | Topics:multiplication; Greatest Common Multiple]

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 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 84 Beyond the black 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 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 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 Partity 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 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 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: 6 - 8 | Topics: area of irregular polygon; decimal math]

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 level: 7-9 | Topics: Geometry; time = distance/speed]

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. [Grade level: 7-9 | Topics: Graph analysis; Area calculation, unit conversions, extrapolation]

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 level: 7-9 | Topics: Plotting tabular data; graph analysis]

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 level: 7-9 | Topics: Area of irregular polygon; decimal math; unit conversions]

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 level: 7-10 | Topics: Area of hexagonal cylinder; decimal math; unit conversions]