Use the topic buttons to sort the problems by general topic area - Use the search window to find problems at specific grade levels, for example, enter 'Grade:3' will show all problems at an estimated grade level of 3 in math skills.
Problem 692: Exploring Interplanetary Dust with Solar Probe-Plus
Students examine the impact frequency of dust grains in the vicinity of the Solar Probe orbit around the sun, and estimate how many impact will occur during the mission.
Students use solar storm data near Earth to estimate how often the spacecraft will encounter solar storms and estimate how much power will be lost from the solar panels due to radiation damage.
Students work with the masses of various spacecraft systems expressed as fractions, and create and solve algebraic equations to determine the masses of these systems.
Problem 682:NASA’s Kepler Mission Detects 715 New Planets
[Grade:6-8 | Topics: percentage; histograms; population sampling; scaling and proportion ]
Category: All,Solar System,Universe
Students work with the statistics of the detected candidate planets to estimate the number of planetary systems in the Milky Way and the number of earth-sized planets.
Problem 681:A Practical Application of Vector Dot and Cross Products
[Grade:10-12 | Topics: vectors; dot and cross product; normal vectors; unit conversions ]
Category: All,Helio
Students work with coordinate vectors describing the corners of the roof of a house, calculate the area of the roof using dot products; calculate the normal vector to the roof using cross products; and the amount of sunlight striking the roof using dot products to determine how much solar power could be generated by solar panels on the roof.
Problem 680:A Pulsar Shot Out from a Supernova Explosion!
[Grade:6-8 | Topics: Scientific notation; speed=distance/time; unit conversions; density ]
Category: All,Stars
Students study the speed of a pulsar ejected from a supernova explosion, and describe what would happen if the dense star collided with a star like the sun.
Students work with vectors to determine a spacecrafts orientation relative to Earths magnetic field. They compute the expected strength of the magnetic field parallel and perpendicular to the spacecraft motion vector.
Problem 677:VAB-Navigating in a Magnetic Field Using Linear Equations
[Grade:8-10 | Topics: graphing linear equations; equation of line perpendicular to another line; geometry ]
Category: All,Magnetism
Students model spacecraft motion and the local magnetic field direction using two linear equations, then determine the line perpendicular to the spacecraft motion and the angle of motion relative to the magnetic field.
Problem 674:VAB - Exploring the Orbit of the Van Allen Probes
[Grade:7-10 | Topics: coordinate plotting; unit conversion; rates ]
Category: All,Helio,Solar System
Students explore the speed of the spacecraft in their orbit around Earth using coordinate graphing, time differences, pythagorean theorem and unit conversions.
Problem 673:VAB - An Improved Model for Van Allen Belt Radiation Dose
[Grade:9-11 | Topics: Polynomial equations; trigonometric equations; composite functions f(f(x)); estimating areas under curves]
Category: All,Helio
Students use a detailed model of the path of a satellite and the radiation dose rate along the path to calculate the total radiation dose to the spacecraft.
Problem 671:VAB - The Van Allen Probes and Radiation Dose
[Grade:8-10 | Topics: Unit conversion; rates]
Category: All,Helio
Students study radiation dose units and estimate the exposures for a human living on the gropund; an astronaut in the ISS, and the Van Allen belt environment.
Problem 670:VAB - Exploring the Third Belt with the Van Allen Probes
[Grade:9-12 | Topics: Intersection points of circles and ellipses; graphical and algebraic solutions]
Category: All,Helio
Students use the elliptical equation for the orbit of NASAs Van Allen Probes spaccecraft, and a circle representing the location of the new Van Allen belt, to find where they intersect along the orbit of the spacecraft.
Problem 669:VAB - Exploring the Third Belt with the Van Allen Probes
[Grade:9-12 | Topics: Intersection points of circles and ellipses; graphical and algebraic solutions]
Category: All,Helio
Students use the elliptical equation for the orbit of NASAs Van Allen Probes spaccecraft, and a circle representing the location of the new Van Allen belt, to find where they intersect along the orbit of the spacecraft.
Problem 669: HST - Exploring Two Nearby Stars to the Sun.
[Grade:9-12 | Topics: Working with quadratic equations; intersection points of quadratic functions]
Category: All,Helio,Stars
Students explore two nearby stars Ross 128 and Gliese 445 and determine when they will be the nearest stars to our sun by working with quaddratic equations that model their distances.
Problem 665: Kepler - Kepler’s Latest Count on Goldilocks Planets
[Grade:6-8 | Topics: percentages, bar graphs, estimation]
Category: All,Helio,Universe
Students examine the statistics of the latest candidate planets beyond our solar system, work with poercentages and a bar graph, and estimate the number of earth-like planets in our Milky Wy.
Problem 664: HST - The Sun’s Nearest Companions…At least for now!
[Grade:6-8 | Topics: Graphical data; finding minimum from a plotted curve]
Category: All,Helio,Stars
Students study a graph that models the distances from the sun of seven nearby stars over a 100,000 year time span. They determine the minimum distances and a timeline of which star will be the suns new closest neighbor in space in the next 80,000 years.
Problem 663: HST - The Hubble Search for the Farthest Galaxy in the Universe
[Grade:6-8 | Topics: working with simple equations; solving for X]
Category: All,Universe
Students learn about the recent discovery of z8_GND_5296 what may be the farthest known galaxy in our visible universe whose light left the galaxy when the universe was only 700 million years old. They use a simple linear equation to estimate the galaxys look-back time, and learn about the cosmological redshift.
Problem 661: SAGE- Measuring Stratospheric Ozone with SAGE-III
[Grade:6-8 | Topics: Unit conversion; reading a data graph ]
Category: All,Rockets
Students use a data graph to identify the ozone layer from its concentration of ozone, and use parts-per-million to compare ozone concentration to the atmosphere density.
Problem 660: SAGE- Some Basic Properties of the SAGE-III Instrument
[Grade:6-8 | Topics: Unit conversion; proportions ]
Category: All,Rockets
Students examine the mass, data, pointing accuracy and power of the SAGE-III instrument and use unit conversions to translate the units into pounds, watts and degrees.
Students explore how gas density is related to the average distances between molecules in the air using a simple geometric mode of a cube with 64 cells.
Problem 648: SAGE- Using Opacity to Find Aerosol Density
[Grade:6-8 | Topics: solving a system of linear equations; scientific notation]
Category: All,Rockets
Students examine a mathematical model based on the SAGE-III geometry and see how it leads to solving a system of linear equations to determine aerosol concentrations at different altitudes.
Problem 643: SAGE- The Sources and Sinks of Carbonyl Sulfide
[Grade:6-8 | Topics: Scientific notation; rates]
Category: All,Rockets
Students explore a molecule important in forming stratospheric aerosols. They calculate total rates of change from a table of sources and sinks, and estimate the change in the number of molecules per year.
Problem 641: SAGE- A Study of Aerosol Extinction in the Stratosphere
[Grade:6-8 | Topics: slope of a line; linear equations; forecasting]
Category: All,Rockets
Students work with a table of atmospheric extinction at different altitudes and latitudes to graph selected data and draw a straight line thrlough the graphed data to estimate the slope. They create a linear equation from the graph and use it to predict the extinction at a different altitude.
Problem 639: SAGE- Aerosol Sources in the Stratosphere
[Grade:6-8 | Topics: Rates; percentage; pie graphs]
Category: All,Rockets
Students examine the sources for aerosols in the atmosphere and determine their percentage contributions based upon their individual rates given in megatons/year.
Problem 634: History of Winter - What is a Snowballs Chance on Mars?
[Grade:9-12 | Topics: Graph analysis]
Category: All,Solar System
Students explore the phase diagrams for water and carbon dioxide and discover whether astronauts would be able to create snowballs on mars made from carbon dioxide ice.
Students create a 3-d model of the constellation Orion and explore how stars are located in space and how this perspective changes from different vantage points.
[Grade:6-8 | Topics: Graphing tabular data; determining the slope of a line; rates of change]
Category: All,Solar System,Rockets
Students plot the altitude, range and speed of the LADEE rocket launch and investigate rates of change including acceleration by graphing the tabular data and determining the slope of the graph using the definition of the slope of a line between two points.
Problem 606: Global Warming and the Sun’s Evolving Luminosity
[Grade:9-12 | Topics: working with equations; eliminating common variables; functions]
Category: All,Helio,Solar System,Universe
Students work with two functions that relate the brightness of the sun to its age L(t), and the temperature of earth to the suns brightness, T(L) to create a new function that gives the temperature of earth over time T(t).
Problem 605: The Solar System Beyond the Orbit of Neptune
[Grade:9-12 | Topics: volume of a disk; density = number/volume ]
Category: All,Helio,Solar System
Students compute the volume and density of the Kuiper Belt located beyond the orbit of Neptune, and estimate how far apart the objects are located compared to the earth-sun distance.
Problem 603: The Temperature of Earth without Carbon Dioxide
[Grade:9-12 | Topics: evaluating functions; trigonometry; surface area of a sphere ]
Category: All,Solar System
Students study a computer model to determine the temperature of Earth if there were no carbon dioxide in the atmosphere. They also determine the albedo of earth given different amounts of ice cap coverage determined by the computer model.
Students work with centrifugal forces to calculate the acceleration of County Fair rides; rotating spacecraft and the acceleration of rockets to see if artificial gravity can be created.
Problem 596: Distance Traveled Under Free Fall by Gravity
[Grade:6-8 | Topics: solving for X; quadratic monomials; square roots]
Category: All,Miscellaneous
Students explore accelerated motion and distance traveled using an equation that related distance to time-squared, and solve the equation under various conditions.
Students explore how the angular sizes of the moons of Jupiter depend on the actual sizes and distances from the observer, and can sometimes allow eclipses of the sun as viewed from Europa.
Problem 590: Magnetic Storms, Aurora and the Kp Index
[Grade:3-5 | Topics: averaging; percentage; working with tables ]
Category: All,Helio,Magnetism
Students use simple math, percentage and probability to estimate how common intense magnetic storms are by using the magnetic Kp index and its statistics.
[Grade:6-8 | Topics: Surface aea of a sphere; rates; scientific notation]
Category: All,Solar System
Students examine how volcanic activity on Jupiters satellite Io can lead to fresurfacing the entire moon in less than a million years covering all new craters.
Problem 567:Exploring Parabolas - The shape of a satellite dish
[Grade:9-12 | Topics: geometry; properties of parabolas]
Category: All,Helio
Students use the equation for a parabola to determine the focus location for a solar cooker and a sound amplifier dish given their diameters and depths.
Problem 566:Exploring Light Brightness and the Inverse Square Law
[Grade:6-8 | Topics: graphing tabular data; surface area of a sphere; ]
Category: All,Miscellaneous
Students collect data and explore the inverse square law using a light meter. They deduce the formula for the brightness of a lamp given its distance and wattage.
Problem 564:Exploring the Stars in Orion - Light Year Madness
[Grade:6-8 | Topics: time lines; time interval calculations; time = distance/speed ]
Category: All,Stars
Students explore the light year and its relationship to light travel time for observing events in different parts of space.When would colonists at different locations observe the star Betelgeuse become a supernova?
Students explore the collision of two galaxies and estimate from their present speed, separation and acceleration how long it will be before they have collided.
Problem 550:Comparing the Rings of the Outer Planets
[Grade:6-8 | Topics: scale model; proportions; number line ]
Category: All,Solar System
Students compare the dimensions of the rings of Jupiter, Saturn, Uranus and Neptune to the radius of each planet, and the location of the break up Tidal Limit to test an idea of how the rings may have formed.
[Grade:3-5 | Topics: measurement; scales; proportions; metric measure; bar graphs]
Category: All,Solar System
Students use a Cassini image of Saturns rings to calculate the sizes of the smallest rings, and how their thicknesses change with distance from Saturn.
[Grade:9-12 | Topics: volume of a ring and a sphere; scientific notation]
Category: All,Solar System
Students explore the volume and mass of the rings of saturn to estimate the number of ring particles and their separations, and the radius of the equivalent spherical body.
[Grade:6-8 | Topics: volume of spheres; proportions]
Category: All,Solar System
Students estimate the average arrival time of large asteroids that impacted the moon. They work with the formula for the volume of a sphere to estimate how much additional mass was added to the moon and Earth durung this era.
[Grade:3-5 | Topics: integer arithmetic; positive and negative numbers]
Category: All,Helio
Students solve 10 problems using positive and negative numbers, addition, subtraction and multiplication to find the missing words in a short essay about solar storms.
Problem 536:Exploring a Possible InSight Landing Area on Mars
[Grade:6-8 | Topics: degree measure; latitude and longitude; working with scaled images; metric measure]
Category: All,Solar System
Students work with latitude and longitude and scaled images of mars to locate the InSight proposed landing area, and describe the terrain of the landing area.
Students use scaled images of a proposed InSIght landing area and a scaled image of an urban neighborhood on Earth to compare the sizes of familiar things with the unfamiliar martian landscape.
Students are introduced to the Moment Magnitude marsquake scale which gives a logarithmic index for marsquakes of differing energies. They calculate two examples of marsquakes and meteor impacts and compare their Moment Magnitude.
[Grade:8-10 | Topics: Pythagorean Theorem, Algebra; scientific notation; areas of spheres and circles ]
Category: All,Solar System
Students devive a basic equation for the distance to the horizon on a spherical body using the Pythagorean Theorem and a bit of algebra. The estimate the number of cell towers needed to cover Mars.
Students work with logarithmic scales to explore the relationship between the energy of an marsquake and its logarithmic index, which is similar to the Richter Scale used for earthquakes.
Students explore how insulation works to reduce heat flow. They convert a verbal description of a formula expressed in proportions, and use it to calculate why aluminum pots heat faster than steel pots, and how we can determine the properties of martian soil from heat flow and temperature changes.
Problem 526:Exploring Temperature Change in Earth’s Outer Crust
[Grade:6-8 | Topics: fahrenheit and celsius degrees; rates of change]
Category: All,Solar System
Students explore the rate of temperature change in the crust of Earth and Mars and learn about units expressed as degrees C/km. They calculate how hot the ground will be at various depths, and how gold miners must deal with extreme heat.
[Grade:5-7 | Topics: working with time units; creating a timeline]
Category: All,Rockets
Students learn about scheduling many events along a timeline (breakfast, packing, driving, etc ) by planning a family trip where the family members have to arrive at the airport for a flight that leaves at a specific date and time.
Students work with proportions and scaling to discover the size of the supernova remnant compared to the distance from the Sun to the nearest star Alpha Centauri. The also work with time and speed calculations to estimate the speed of the supernova compared to the International Space Station.
[Grade:3-5 | Topics: Time intervals; time calculations by addition and subtraction]
Category: All,Solar System
Students work with simple time calculations to explore how the length of a day on Earth and MArs differm and how this affects how scientists navigate the Curiosity Rover on the martian surface.
Problem 513: The Remarkable Gamma Ray Burst GRB 130427A
[Grade:8-10 | Topics: surface area of sphere; scientific notation]
Category: All,Stars
Students work with the surface area of a sphere, metric conversions and scientific notation to calculate the total power of this distant supernova event.
Problem 510: Planck Mission Sees the Ancient Universe Clearly
[Grade:6-8 | Topics: scale and proportion; angular measure]
Category: All,Universe
Students work with an image of the universe when it was 370,000 years old and determine from simple scaling and proportions the sizes of the features seen in the image compared to the Milky Way.
Problem 508: The InSight Seismographic Station - Wave arrival times
[Grade:6-8 | Topics: speed=distance/time; Time calculations; circumference of a circle]
Category: All,Solar System,Rockets
Students work with the circumference of Mars and the speed of shock waves in the martian crust to estimate the arrival times of the waves at the InSight Lander.
Students explore the gravity field of the moon, and the behavior of simple pendulum clocks in places on the moon where the local gravity is slightly different.
[Grade:8-10 | Topics: percercentages, scientific notation; volume of a disk]
Category: All,Stars,Universe
Students explore the Fermi Gamma-Ray Observatory's confirmation of the idea that supernova are the sources of cosmic rays in the Milky Way. They use a simple model to estimate how many supernova are needed to account for the current number of cosmic rays in the galaxy.
Students examine how often a large meteor should be visible like the one that exploded over Russia on February 14, 2013. This asteroid had a mass of 10,000 tons and injured over 1000 people.
[Grade:7-8 | Topics: Graphing in the XY plane; midpoint formula; tangent lines to curves]
Category: All,Magnetism
Students graph a magnetic field line in the First Quadrant, then calculate the segment midpoints using the Midpoint Formula, and then draw tangent lines at each midpoint to determine compass direction.
[Grade:6-8 | Topics: graphing in XY plane; reflection symmetry]
Category: All,Magnetism
Students plot points along a magnetic field line in the First Quadrant, then use reflection symmetry to complete the field line shape in all four quadrants.
Problem 494: The Close Encounter to the Sun of Barnards Star
[Grade:12 | Topics: Derivitives and minimization]
Category: All,Helio,Stars
Students use parametric equations and calculus to determine the linear equation for the path of Barnards Star, and then determine when the minimum distance to the sun occurs
Students plot data for the orbiting planet and determine its orbit period. They use this in a simple formula to determine its distance, then they estimate its surface temperature at this distance.
[Grade:6-8 | Topics: Cartseian graphs; ordered pairs and coordinates; distance = speed x time; metric measure ]
Category: All,Solar System
Students plot the position of the Curiosity Rover on a cartesian grid covering the satellite image of the landing area. They use the 2-point distance formula to determine how far the rover traveled between stops, and determine it speed.
Problem 490: LL Pegasi - A Perfect Spiral in Space
[Grade:6-8 | Topics: Distance = speed x time; unit conversions; evaluating formulas ]
Category: All,Stars
The star LL Persei is ejecting gas like a sprinkler on a lawn. Every 800 years the gas makes one complete orbit, and over time forms a spiral patteri in space. Students explore the timing of this pattern and estimate the size and age of this gas.
Problem 489: The Van Allen Probes and the location of Dawn Chorus - III
[Grade:6-8 | Topics: Linear equations; solving systems of equations; graphical solutions ]
Category: All,Helio,Rockets
The location of the Chorus signal from each of the Van Allen Probes spacecraft is given by a linear equation that represents the direction along which the signal is detected by each spacecraft. Students solve the two linear equations for the common intersection point representing the location of the Chorus signal in space. This can be done graphically by plotting each linear equation, or solved algebraically.
Students use hypothetical information from the twin RBSP spacecraft to triangulate the location of the Chorus signal near Earth using angle measurements, graphing and protractors to identify the intersection point of the CHorus signals.
Problem 482: Exploring Density, Mass and Volume Across the Universe
[Grade:9-12 | Topics: Density=mass/volume; scientific notation; unit conversion; metric math ]
Category: All,Universe
Students calculate the density of various astronomical objects and convert them into hydrogen atoms per cubic meter in order to compare how astronomical objects differ enormously in their densities.
Students explore Kepler's Third Law and estimate the orbit period of a hypothetical sixth moon using the distance:period law. They also determine the mass of Pluto using the orbit data, including the recently discovered fifth moon (P5) of Pluto by the Hubble Space Telescope.
Students explore the Gale Crater landing area and calculate rover distances to various way stations to determine the round trip distance and travel time.
Problem 478: The Grail and LRO Encounter in Lunar Orbit
[Grade:9-12 | Topics: formula for an ellipse; semi-major and minor axis]
Category: All,Solar System
Students explore the May 31, 2012 encounter between NASA's Grail and LRO spacecraft in orbit around the moon. Will the Grail/Ebb spacecraft be able to photograph the LRO spacecraft as it passes-by?
Students use the equation for tidal disruption to explore the stability of a star encountering a black hole, and a satellite of Saturn. Why are there no large satellites of Saturn inside the ring system?
Problem 472: Investigating Juno's Elliptical Transfer Orbit
[Grade:9-12 | Topics: formula for an ellipse; semi-major and minor axis]
Category: All,Rockets
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.
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.
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.
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.
Students use simple statistics to determine the solar flare frequency during the last 11-year sunspot cycle to estimate the time between X-class flares during the current sunspot cycle
Students use two images of the solar storm during March 2012 to estimate the speed of the solar wind and a coronal mass ejection. They also estimate arrival times for the CME at Earth and Neptune.
Students use simple fraction arithmetic to determine the relative sizes of several new planets recently discovered by the Kepler mission, and compare these sizes to that of Jupiter and Earth.
Students work with a scaled drawing of 26 large moons in the solar system, and together with an exercise in using simple fractions, explore the relative sizes of the moons compared to Earth.
Problem 463: A Simple Fuel Gauge in a Cylindrical Tank
[Grade:7-9 | Topics: VOlume of cylinder; proportions]
Category: All,Miscellaneous
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.
The recently-confirmed Earth-like planet Kepler-22b by the Kepler Observatory is a massive planet orbiting its star in the temperature zone suitable for liquid water. This problem explores the gravity and mass of this planet, and some implications for playing baseball on its surface!
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; equation of a parabola; curve fitting]
Category: All,Rockets
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.
Students work with a scaled drawing of the orbit of the moon and the asteroid trajectory to predict where the asteroid will be relative to earth and the orbit of the moon.
Problem 450: Mapping Dark Matter in a Distant Cluster
[Grade:8-10 | Topics: Volume of a sphere; shells; density]
Category: All,Universe
Students explore the changing density of dark matter within a distant cluster of galaxies to see if the density of dark matter is uniform inside the cluster.
Students use ozone data for the Arctic region between 1979 and 2011 to graph the tabulated data, perform simple regression analysis, and forecast trends into the future. How much will there be in the year 2030?
Problem 442: Modeling the Atmospheric Re-entry of UARS
[Grade:8 - 11 | Topics: graphing data; linear equations; exponential and power functions]
Category: All,Miscellaneous
Students graph the altitude of the UARS satellite in the weeks before re-entry 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.
Problem 441: Exploring the new planet Kepler 16b called 'Tatooine'
[Grade:8-10 | Topics: angle measure; tangent]
Category: All,Solar System,Stars
Using the tangent function, students estimate the angular diameter and separation of the two stars in the Kepler 16 binary system as viewed from the planet's surface...if it had one!!
Students use a recent image obtained by the LRO spacecraft to estimate how far astronauts walked to get to various points in the landing area. They also estimate how many craters are in this area and the average impact time between crater events.
The planet CoRot2b is losing mass at a rate of 5 million tons per second. Students estimate how long it will take for the planet to lose its atmosphere
Problem 434: Dawn Spacecraft Sees Asteroid Vesta Up-Close!
[Grade:6-8 | Topics: scale, metric measurement]
Category: All,Solar System,Rockets
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.
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.
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.
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.
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.
The latitude, longitude, elapsed time and distance traveled are provided in a table. Students use the data to determine the daily and hourly speed of a leatherback turtle as it travels from New Zealand to California across the Pacific Ocean.
Problem 428: Meteorite Compositions: A matter of density
[Grade:8-10 | Topics: density; mass = density x volume; percentages]
Category: All,Helio
Astronomers collect meteorites to study the formation of the solar system 4.5 billion years ago. In this problem, students study the composition of a meteorite in terms of its density and mass, and the percentage of iron and olivine to determine the volumes occupied by each ingredient.
[Grade:3-5 | Topics: working with a compass and metric ruler]
Category: All,Helio
Students compare the sizes of the planets in our solar system if they were actually black holes. They use a compass and metric ruler to create circles that are the actual sizes of the 'black hole' planets.
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.
Students learn about the Lense-Thirring Effect, and calculate its magnitude near Earth's orbit using an algebraic equation with integer and fractional exponents.
Problem 419: The Space Shuttle: Fly me to the moon?
[Grade:6-8 | Topics: amount = rate x time ]
Category: All,Solar System,Rockets
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.
Problem 418: Supercomputers: Modeling colliding neutron stars!
[Grade:8-10 | Topics: distance=speed x time; scale model; triangle and circle geometry; circumference]
Category: All,Universe
Students use a series of time-lapse images calculated using a supercomputer to determine the speed of collision of two neutron stars, and whether they will form a black hole afterwards.
Problem 417: Estimating the Size and Mass of a Black Hole
[Grade:8-10 | Topics: distance=speed x time]
Category: All,Universe
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:9-12 | Topics: unit conversions; amount=rate x time; graphing Log-Log data]
Category: All,Miscellaneous
Students explore the dosimetry from the Japan 2011 Earthquake and graph the decline of the radiation dose rates with distance from the nuclear reactors.
Problem 413: Exploring Nuclear Decay and Radiation Dose
[Grade:9-12 | Topics: unit conversions; amount=rate x time; Solving exponential equations in base-e]
Category: All,Miscellaneous
Students compare the dose rates measured from the same location in Japan on two different days, then determine the half-life of the radioisotope causing the radiation exposure by comparing the derived half-life with those of Cesium-137 and Iodine-131.
[Grade:6-8 | Topics: unit conversions; amount=rate x time]
Category: All,Miscellaneous
Students use radiation measurements across Japan to calculate the total absorbed doses from the 2011 nuclear reactor failures. They also calculate the total dose for passenger trips on jets and the Concorde.
[Grade:6-8 | Topics: unit conversions; amount=rate x time]
Category: All,Miscellaneous
Students see how the kind of lifestyle you lead determines most of your annual absorbed radiation dose. Some factors are under your control, and some are not.
[Grade:6-8 | Topics: unit conversions; amount=rate x time]
Category: All,Miscellaneous
Students use a pie grap to calculate the total dose and dose rate for various factors that determine your annual radiation exposure while living on Earth.
Problem 409: The 2011 Japan Earthquake Rocks the Earth
[Grade:9-12 | Topics: Algebra; evaluating an equation]
Category: All,Miscellaneous
Using a simple physical model, students explore the principle by which the Japan Earthquake of 2011 caused Earth's rotation to spin up by 1.8 microseconds.
[Grade:6-8 | Topics: Time arithmetic; time zones; speed = distance/time]
Category: All,Miscellaneous
Students use the tsunami arrival times and earthquake start time for the devastating 2011 Japan Earthquake to estimate the speed of a tsunami as it crosses the Pacific Ocean to make landfall in Hawaii and California.
Problem 406: Growing Grapes in the Middle of the Desert
[Grade:6-8 | Topics: areas of irregular regions; unit conversion]
Category: All,Solar System
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
Students use recent measurements of the reflected light from solar system bodies to graph their colors and to use this in classifying new planets as Earth-like, moon-like or Jupiter-liike
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.
Problem 403: The Goldilocks Planets - Not too hot or cold
[Grade:6-8 | Topics: Averaging; histogramming]
Category: All,Solar System,Universe
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.
Students use recent Kepler satellite data summarized in tabular form to estimate the number of planets in the Milky Way galaxy that are about the same size as our Earth, and located in their Habitable Zones were liquid water may exist.
[Grade:6-9 | Topics: Scientific Notation; percentages; rates of change]
Category: All,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
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.
Problem 391: Investigating the atmosphere of Super-Earth GJ-1214b
[Grade:6-8 | Topics: graphing functions; evaluating functions for given values; volume of a sphere; mass = densityxvolume]
Category: All,Miscellaneous
Students investigate a simple model for the interior of an exoplanet to estimate the thickness of its atmosphere given the mass size and density of the planet.
Problem 389: Estimating the diameter of the SN1979c black hole
[Grade:6-8 | Topics: evaluating linear functions; integer math; metric units]
Category: All,Universe
Students use simple equations to learn about the various definitions for the sizes of black holes in terms of their event horizons, last photon orbit, and last stable particle orbit radii, and apply this to the recently discovered 'baby' black hole in the galaxy M-100
Students learn about how astronomers estimate the amount of invisible dark matter in a cluster of galaxies by comparing its visible mass against the speeds of the galaxies to 'weigh' the cluster'
Problem 387: A Mathematical Model of Water Loss from Comet Tempel-1
[Grade:8-10 | Topics: graphing; fitting a parabola to data; evaluating functions]
Category: All,Solar System
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.
Problem 386: Whacky Spacecraft Orbits - They only seem crazy!
[Grade:6-8 | Topics: distance=speedxtime; scientific notation; unit conversion]
Category: All,Solar System
Students investigate the loopy orbit of the THEMIS/Artemis spacecraft as they are being inserted into lunar orbit. To save fuel, their orbits take them on a complicated path in space.
Problem 384: Detecting the Most Distant SUpernova in the Universe
[Grade:6-8 | Topics: Analyzing a graph; interpreting mathematical models]
Category: All,Stars,Universe,Rockets,Telescopes
Students use a graph to compare the brightness of supernova produced by three different masses of stars, and predict whether the Webb Space Telescope can see them.
Problem 383: Estimating the mass of Comet Hartley 2 using calculus.
[Grade:12 | Topics: Volume integral using disk method; scale model; scientific notation; unit conversion]
Category: All,Solar System
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,
Problem 382: Estimating the mass and volume of Comet Hartley 2.
[Grade:8-10 | Topics: volume of a sphere and cylinder; scale model; scientific notation; unit conversion]
Category: All,Solar System
Students use a recent image of the nucleus of Comet Hartley 2 taken by the Deep Impact/EPOXI camera and a simple geometric 'dumbell' model based on a cylinder and two spheres, to estimate the volume of the comets nucleus, and its total mass.
Problem 381: The Cosmological Redshift - Changing the light from a galaxy.
[Grade:8-10 | Topics: solving a simple equation for X]
Category: All,Universe
Students learn about the redshift unit of measurement in astronomy, and solve a simple linear equation to explore how the light from very distant galaxies is reddened compared to nearby galaxies.
[Grade:7-9 | Topics: solving a simple equation for X; angular measure; Scientific Notation]
Category: All,Universe,Telescopes
Students calculate the angular sizes and scales of distant objects to study how different sized telescopes see details with varying degrees of clarity.
Problem 378: LRO Makes a Temperature Map of the Lunar South Pole
[Grade:7-9 | Topics: Volume of a circular disk; scale models]
Category: All,Solar System
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.
Problem 377: Deep Impact: Approaching Comet Hartley-2
[Grade:8-10 | Topics: linear modeling from data; inverse-square law]
Category: All,Solar System
Students use data for the brightness of Comet Hartley-2 measured by the Deep Impact spacecraft to create a linear equation for its approach distance, and use the inverse-square law to estimate its brightness on October 13, 2010.
Students use data for the Gliese 581 planetary system to draw a scaled model of the locations and sizes of the discovered planets. They also identify the location and span of the Habitable Zone for this planetary system.
Problem 375: Terra Satellite Measures Dangerous Dust
[Grade:8-10 | Topics: unit conversion; scientific notation; mass=densityxvolume]
Category: All,Miscellaneous
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.
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.
Problem 371: Close Encounters of the Asteroid Kind!
[Grade:8-10 | Topics: Evaluating a base-10 power function; graphing; astronomical brightness scale]
Category: All,Solar System,Telescopes
On September 8, 2010 two small asteroids came within 80,000 km of Earth. Their small size of only 15 meters made them very hard to see without telescopes pointed in exactly the right direction at the right time. In this problem, based on a NASA press release, students use a simple formula to calculate the brightness of these asteroids from their distance and size.
Problem 370: 6-fold Symmetry and the Webb Space Telescope Mirror
[Grade:8-10 | Topics: Properties of Hexagons; rotation symmetry; counting; tiling]
Category: All,Rockets,Telescopes
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
Problem 369: Scaling Up the Webb Space Telescope Mirror
[Grade:8-10 | Topics: Properties of Hexagons and triangles; counting; evaluating a formula; tiling]
Category: All,Rockets,Telescopes
Students learn about the Webb Space Telescopes segmented mirror and determine the area of the mirror along with scaled up versions of this mirror using the formula for the area of a hexagon, and the properties of tiling a surface with hexagons.
Students work with the basic rules of significant figures to evaluate a formula. Exercises also ask students to state the number of SFs in some simple numbers for review.
[Grade:8-10 | Topics: image scales; speed = distance/time; unit conversions]
Category: All,Miscellaneous
Students use two images from the Terra MODIS instrument to determine the scale of the glacier and the number of cubic kilometers and gallons of fresh water that were 'calved'
[Grade:9-12 | Topics: Scientific Notation; volume of a sphere; density; rates]
Category: All,Solar System,Stars,Telescopes
Astronomers using NASA's Hubble Space Telescope have confirmed that this gas giant planet is orbiting so close to its star its heated atmosphere is escaping into space.
[Grade:9-12 | Topics: Fitting functions to data; Evaluating a polynomial]
Category: All,Helio
Students plot the distance versus period relationship for planets and minor bodies in the solar system and fit it to two functions to determine Kepler's Third Law.
Problem 350: Estimating the Temperatures of Exoplanets
[Grade:9-12 | Topics: Equation of ellipse; evaluating functions]
Category: All,Miscellaneous
Students review the basic properties of ellipses by exploring the orbits of newly-discovered planets orbiting other stars. They also use a simple formula to determine the temperatures of the planets from their orbits.
The size and mass of various astronomical objects is plotted on a Log-Log graph to explore the various physical scales in the universe, and what combinations are excluded.
Problem 342: The Rate of Oil Leakage in the Gulf Oil Spill of 2010
[Grade:6-8 | Topics: unit conversions; rates; image scale]
Category: All,Miscellaneous
Students use still images from a video of the oil emitted by the leaking British Petrolium oil well in the Gulf of Mexico to estimate the rate of oil leakage in gallons per day.
Problem 341: Recent Events: A Perspective on Carbon Dioxide
[Grade:6-8 | Topics: unit conversions; rates ]
Category: All,Solar System
Students compare the carbon dioxide generated by the 2010 Icelandic volcano and the Gulf Oil Spill to see the relative contributions to the atmosphere of a natural and man-made catastrophe.
Problem 337: SDO Reveals Details on the Surface of the Sun
[Grade:6-8 | Topics: image scales; proportions]
Category: All,Helio
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.
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: estimating irregular areas; calculating volume from area x height; scaled images ]
Category: All,Solar System
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.
Problem 334: Solar Dynamics Observatory: Working with Giga, Tera, Peta and Exabytes
[Grade:8-12 | Topics: powers of ten; time conversion: seconds, minutes, days, years]
Category: All,Helio,Rockets
The recent launch of SDO will bring high definition TV to the study of the sun's surface details. This also means a HUGE amount of data will have to be processed every day to handle the torrent of information. This activity works with the prefixes giga, tera, peta and exa to familiarize students with how to interpret these quantities in a practical setting.
Problem 333: Hubble: Seeing a Dwarf Planet Clearly
[Grade:8-12 | Topics: scales and ratios; volume of sphere; density=mass/volume]
Category: All,Solar System
Based on a recent press release, students use the published photos to determine the sizes of the smallest discernible features and compare them to the sizes of the 48-states in the USA. They also estimate the density of Pluto and compare this to densities of familiar substances to create a 'model' of Pluto's composition. A supplementary Inquiry Problem asks students to model the interior in terms of two components and estimate what fraction of Pluto is composed of rock or ice.
Problem 332: Hubble: The Changing Atmosphere of Pluto
[Grade:10-12 | Topics: properties of ellipses; evaluating an algebraic function ]
Category: All,Solar System
Based on a recent press release, students determine the aphelion and perihelion of Pluto's elliptical orbit using the properties of ellipses, then calculate the temperature of Pluto at these distances to estimate the thickness of Pluto's atmosphere and its changes during its orbit around the sun.
Problem 331: Webb Space Telescope: Detecting dwarf planets
[Grade:9-12 | Topics: Evaluating square-roots and base-e exponentials]
Category: All,Helio,Solar System,Rockets
The 'JWST' will be launched some time in 2014. One of its research goals will be to detect new dwarf planets beyond the orbit of Pluto. In this problem, students use three functions to predict how far from the sun a body such as Pluto could be detected, by calculating its temperature and the amount of infrared light it emits.
Problem 330: Fermi Detects Gamma-rays from the Galaxy Messier-82
[Grade:10-12 | Topics: power-laws; log-log graphing; linear regression]
Category: All,Universe
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.
Problem 328: WISE: F(x)G(x): A Tale of Two Functions
[Grade:10-12 | Topics: Power-law functions; domain and range; graphing; areas under curves; integration]
Category: All,Miscellaneous
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.
Problem 327: WISE: Exploring Power-law Functions Using WISE Data
[Grade:10-12 | Topics: areas; functions; histograms; unit conversion; power-laws; integration]
Category: All,Stars
Based on a recent press release of the 'First Light' image taken with NASA's new WISE satellite, students explore a practical application of a power law function to count the number of stars in the sky. An additional calculus-level problem is included for advanced students.
[Grade:8-12 | Topics: Volume of a thin disk; Algebra 1; Evaluating a definite integral; power-law]
Category: All,Solar System
Based on a recent press release, students calculate how often asteroids collide in the Asteroid belt using a simple formula. Students estimate belt volume, and asteroid speeds to determine the number of years between collisions. They also investigate how the collision time depends on the particular assumptions they made. An 'extra' integration problem is also provided for calculus students.
[Grade:4-6 | Topics: Counting; graphing; area of a square]
Category: All,Stars
Students count squares on a Bizarro Star to study the transit of a planet, and determine the diameter of the planet. This demonstrates the basic principle used by NASA's Kepler satellite to search for Earth-sized planets orbiting distant stars.
The Deep Impact spacecraft flew by the Comet Tempel-1 in 2005. Students determine the form of a function that predicts the changing apparent size of the comet as viewed from the spacecraft along its trajectory.
[Grade:11-12 | Topics: Piecewise functions; integral calculus]
Category: All,Universe
Students use a piecewise function that estimates how many quasars are found in a given area of the sky. The function is integrated to determine the estimated total number of quasars across the entire sky.
[Grade:10-12 | Topics: Algebra, limiting form of functions; derivitives]
Category: All,Stars,Universe
Students examine a simple model of the rotation of a galaxy to investigate how fast stars orbit the centers of galaxies in systems such as the Milky Way and Messier-101.
Students use an image from the LRO satellite of the Apollo-11 landing area, along with a power-law model of cratering, to determine what fraction of the landin garea was safe to land upon.
Problem 317: The Global Warming Debate and the Arctic Ice Cap
[Grade:9-11 | Topics: Modeling data with linear equations; forecasting]
Category: All,Solar System,Universe
Students use graphical data showing the area of the Arctic Polar Cap in September, and compare this to surveys of what people believe about global warming. Simple linear models are used to extrapolate when we will lose half of the Arctic polar cap, and when the belief in climate change will reach zero.
Students count craters on a piece of the Wide Field Planetary Camera recovered from the Hubble Space Telescope in 2009. They determine the cratering rate and use this to predict how many impacts the solar panels on the International Space Station experiences each day.
Using a millimeter ruler and a sequence of images of a gaseous shell between 2000 and 2005, students calculate the speed of the material ejected by Supernova 1987A.
[Grade:9-12| Topics: ALgebra; Scientific Notation; Unit conversions]
Category: All,Universe
Two simple equations allow students to compute the temperature and energy of matter soon after the Big Bang, and compare these with energies available at the LHC.
The Large Hadron Collider collides protons at very high energy to create new forms of matter. Students explore unit conversions related to energy and mass.
This problem extends student understanding of volume to include higher-dimensional spheres and their unusual properties. A simple recursion relation is used to calculate the volume formulas for spheres in dimensions 4 through 10.
Problem 308: The Higgs Boson and the Mystery of Mass
[Grade:10-12 | Topics: Properties of functions; polynomials; Critical points]
Category: All,Miscellaneous
The search for the Higgs Boson is underway at the Large Hadron Collider (LHC). In this problem, students explore how the mass of this particle is believed to depend on the energies used to form it by studying a simple quartic polynomial.
Students explore how long it takes to form a small planet from a collection of asteroids in a planet-forming disk of matter orbiting a star based on a very simple physical model.
Problem 302: How to Build a Planet from the Inside Out
[Grade:9-11 | Topics: Geometry; volume; scientific notation; mass=density x volume]
Category: All,Solar System
Students model a planet using a spherical core and shell with different densities. The goal is to create a planet of the right size, and with the correct mass using common planet building materials.
Students use tabulated data for the number of days in a year from 900 million years ago to the present, to estimate the rate at which an Earth day has changed using a linear model.
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:9-12 | Topics: Scientific Notation; evaluating simple formulas; unit conversion]
Category: All,Stars,Universe
Students use a simple formula to calculate how much power is produced by black holes of various sizes as they absorb matter from nearby stars and gas clouds.
Problem 290: The Apollo-11 Landing Area at High Resolution
[Grade:9-12 | Topics: metric measurement; scaling; A = B/C]
Category: All,Miscellaneous
Students use recent images made by the LRO satellite to estimate distances, crater sizes, and how many tons of TNT were needed to create some of the craters by meteor impact.
Students use an image of sound waves produced by a massive black hole to determine wavelength, and comparisons with musical scale to find how many octaves this sound wave is below the wavelength of middle-C.
Problem 288: Fermi Observatory Measures the Lumps in Space
[Grade:9-12 | Topics: Scientific Notation; Evaluating an equation with multiple factors]
Category: All,Miscellaneous
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: Geometry; volumes; mass=density x volume]
Category: All,Solar System
Students use information about the plume created by the LCROSS impactor to estimate the (lower-limit) concentration of water in the lunar regolith in a shadowed crater.
Problem 285: Chandra Sees the Most Distant Cluster in the Universe
[Grade:9-12 | Topics: Algebra I; Solving for X; Scientific notation]
Category: All,Universe
Students work with kinetic energy and escape velocity to determine the mass of a distant cluster of galaxies by using information about its x-ray light emissions.
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.
Students estimate the amount of water on the moon using data from Deep Impact/EPOXI and NASA's Moon Mineralogy Mapper experiment on the Chandrayaan-1 spacecraft.
Problem 274: IBEX Uses Fast-moving Particles to Map the Sky!
[Grade:8-10 | Topics: Algebra I, Scientific notation]
Category: All,Rockets
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.
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.
Problem 271: A Simple Model for Atmospheric Carbon Dioxide
[Grade:10-12 | Topics: Algebra I, rates of change, differential calculus]
Category: All,Solar System
Students work with the known sources of increasing and decreasing carbon dioxide to create a simple model of the rate of change of atmospheric carbon dioxide.
Problem 270: Modeling the Keeling Curve with Excel
[Grade:11-12 | Topics: Algebra II, properties of functions, Excel Spreadsheet]
Category: All,Solar System
Students create a mathematical model of the growth curve of atmospheric carbon dioxide using an Excel Spreadsheet, and create a future forecast for 2050.
Students work with a common unit to describe the number of objects in a population. Other related quantities are the part-per-thousand, part-per-million and part-per-billion.
Problem 267: Identifying Materials by their Reflectivity
[Grade:6-8 | Topics: percentage, interpreting tabular data, area ]
Category: All,Solar System
The reflectivity of a material can be used to identify it. This is important when surveying the lunar surface for minerals, and also in creating 'green' living environments on Earth.
[Grade:8-10 | Topics: unit conversion, scientific notation]
Category: All,Solar System
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 and quantify the energy required for liquid water to exist under various conditions.
Students examine a map of the Apollo-11 landing area and determine how well various features will be visible to the Lunar Reconnaissance Orbiter high-resolution camera.
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.
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, Law of Cosines, V = D/T]
Category: All,Helio,Rockets
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.
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:8-10 | Topics: combining positive and negative mixed numbers; fractions]
Category: All,Rockets
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:3-6 | Topics: integers; counting similar things; fractions; percentages ]
Category: All,Miscellaneous
Students count the number of atoms in a simple molecule and work out some basic fractions, percentages and masses. They also complete the chemical formula for the compound.
[Grade:8-10 | Topics: geometry, similar triangles, proportions]
Category: All,Miscellaneous
A critical concept in astronomy is angular size, measured in degrees, minutes or arc-seconds. This is a review of the basic properties of similar triangles for a fixed angle.
Students measure a Hubble image of the famous Eagle Nebula 'Pillars of Creation' to determine the sizes of various features compared to our solar system
Satellite experience drag with the atmosphere, which eventually causes them to burn up in the atmosphere. Students study various forecasts of the altitude of the Hubble Space Telescope to estimate its re-entry year.
[Grade:6-8 | Topics: scale; ratios; angle measure; right triangles]
Category: All,Helio,Solar System
Students use the latest image from the Lunar Reconnaissance Orbiter of the Apollo-11 landing site to explore lunar features at 1-meter resolution, and determine the solar elevation angle.
Students work with the differential form of the Pythagorean Theorem to determine the basic integral formula for arc length, then evaluate it for a parabola, logrithmic spiral and normal spiral. They evaluate the length of the spiral track on a CDrom.
Problem 225: Areas Under Curves; An astronomical perspective-
[Grade:6-8 | Topics: Adding areas in bar graphs.]
Category: All,Solar System
Students work with a bar graph of the number of planet discoveries since 1995 to evaluate the total discoveries, as areas under the graph, for various combinations of time periods.
Problem 224: Perimeters; Which constellation is the longest?-
[Grade:3-5 | Topics: perimeter of a curve; basic fractions; mixed numbers.]
Category: All,Stars
Students use tabulated data for the angular distances between stars in the Big Dipper and Orion to determine which constellation has the longest perimeter, and the average star separations.
Students examine the famous Krakatoa explosion, asteroid impacts on the moon, and geysers on Enceladus using three equations that describe the height of the plume and initial velocity, to answer questions about the speed of the debris and terminal height.
Students work with linear equations describing the rotation period of a pulsar, and evaluate the equations for various conditions. Students use the equations to predict intersection points in time.
Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder.
Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder.
Students study the energy ladders of an atom and work out, using differences between mixed numbers, the energy gained or lost by an electron as it moves up and down the ladder.
Problem 213: Kepler: The hunt for Earth-like planets-
[Grade:6-8 | Topics: Area of circle; ratios; percents.]
Category: All,Solar System,Stars
Students compare the area of a star with the area of a planet to determine how the star's light is dimmed when the planet passes across the star as viewed from Earth. This is the basis for the 'transit' method used by NASA's Kepler satellite to detect new planets.
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.
Problem 202: The Dawn Mission - Ion Rockets and Spiral Orbits-
[Grade: 9-12| Topics: Calculus - Arc lengths.]
Category: All,Rockets
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.
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: 6-10| Topics: Calculating image scales; Circle circumferences; Unit conversions; distance-speed-time]
Category: All,Solar System,Stars
Students study an image of the dust disk around the star Fomalhaut and determine the orbit period and distance of a newly-discovered planet orbiting this young star.
Students study a spectacular photo of the ISS passing across the face of the sun, and work out the angular sizes and speeds of the transit to figure out how long the event took in order to photograph it.
Problem 194: A Magnetic Case for 'What Came First?' -
[Grade: 6-8| Topics: Time calculations]
Category: All,Magnetism,Miscellaneous
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.
Students explore the Planck Function using graphing skills, and calculus for experts, to determine the relationship between temperature and peak wavelength.
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.
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.
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.
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: 6-8 | Topics: equations in one variable; multiplication; division; decimals]
Category: All,Miscellaneous
Students work with equations like '4.3 = 3.26D' to solve for D in a number of simple astronomical problems involving distances, speed and temperature conversion.
Problem 160: The Relative Sizes of the Sun and Stars-
[Grade:4-6 | Topics: working with fractions; scale models]
Category: All,Helio,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 | Topics: working with fractions; scale models]
Category: All,Universe
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.
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:4-6 | Topics:Finding the scale of an image; measurement; unit conversion]
Category: All,Solar System
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:6-8 | Topics: Plotting data; determining the slope of the data;]
Category: All,Universe
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.
Students calculate how much power is produced as matter falls into a rotating and a non-rotating black hole including solar and supermassive black holes.
Students examine the concept of angular size and how it relates to the physical size of an object and its distance. A Chandra Satellite x-ray image of the star cluster NGC-6266 is used, along with its distance, to determine how far apart the stars are based on their angular separations.
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:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.
Category: All,Universe
Matter that falls into a black hole heats up in an accretion disk, which can emit x-rays and even gamma rays visible from Earth. In this problem, students use a simple algebraic formula to calculate the temperature at various places in an accretion disk.
Students use Spitzer satellite data to learn about how dust emits infrared light and calculate the mass of dust grains from a young star in the nebula NGC-7129.
[Grade:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]
Category: All,Miscellaneous
If you fell into a black hole, how fast would you be traveling? Students use a simple equation to calculate the free-fall speed as they pass through the event horizon.
[Grade:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]
Category: All,Miscellaneous
Tidal forces are an important gravity phenomenon, but they can be lethal to humansin the vicinity of black holes. This exercise lets students calculate the tidal acceleration between your head and feet while standing on the surface of Earth...and falling into a black hole.
[Grade:7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]
Category: All,Stars
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:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
Students work with an image taken by the Cassini spacecraft of Jupiter and its satellite Io. They determine the image scale, and calculate the sizes of various features in the image.
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:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
Students work with an image taken by the Mars Orbiter satellite of the Spirit landing site. They determine the image scale, and calculate the sizes of various surface features from the image.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Miscellaneous
Students work with an image taken by the QuickBird imaging satellite of downtown Las Vegas, Nevada. They determine the image scale, and calculate the sizes of streets, cars and buildings from the image.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
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:8 - 12 | Topics:Simple linear equations; scientific notation]
Category: All,Universe
Students learn about the most basic component to a black hole - the event horizon. Using a simple formula, and scientific notation, they examine the sizes of various kinds of black holes.
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
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.
Problem 126: How Big is It? - A Martian Avalanche!
[Grade:4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
Category: All,Solar System
Students work with a Mars reconnissance Orbiter image to determine image scale, and search for the smallest things seen in a photograph.This avalanche was caught as it occurred on February 19, 2008!
[Grade:8-10 | Topics:volume of sphere, shell; density-mass-volume; unit conversions]
Category: All,Miscellaneous
Students learn about the moon's very thin atmosphere by calculating its total mass in kilograms using the volume of a spherical shell and the measured density.
Students learn to work with large numbers, which are the heart and soul of astronomical dimensions of size and scale. This activity explores the number 'one trillion' using examples drawn from the economics of the United States and the World. Surprisingly, there are not many astronomical numbers commonly in use that are as big as a trillion.
[Grade:8-10 | Topics:Calculate image scale; speed from distance and time; mass:volume:density]
Category: All,Helio,Stars,Rockets,Telescopes
Ordinarily, the SOHO satellite and NASA's STEREO mission spot coronal mass ejections (CMEs) but the Hubble Space Telescope has also spotted a few of its own...on distant stars! Students will examine a sequence of images of the young star XZ Tauri, and measure the average speed and density of this star's CME event between 1955 and 2000.
[Grade:8-10 | Topics:Area of a circle; volume, density, unit conversion]
Category: All,Miscellaneous
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:Calculating frequency tables; Histogramming; Statistics]
Category: All,Miscellaneous
Students will explore a relationship called Benford's Law, which describes the frequency of the integers 1-9 in various data. This law is used by the IRS to catch fradulent tax returns, but also applies to astronomical data and other surprising situations.
[Grade:8-10 | Topics:Image scaling; Unit conversion; Calculating speed from distance and time]
Category: All,Solar System,Stars
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.
Problem 118: An Application of the Parallax Effect
[Grade:8-10 | Topics:Pythagorean Theorem; square-root; solving for variables]
Category: All,Helio,Rockets
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:time calculation; Evaluating a simple equation; solving for variables]
Category: All,Helio,Stars
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.
Problem 116: The Comet Encke Tail Disruption Event
[Grade:8-10 | Topics:time calculation; finding image scale; calculating speed from distance and time]
Category: All,Helio,Solar System,Rockets
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: scientific notation; volume of a sphere and a spherical shell; density, mass and volume.]
Category: All,Helio
Students will use the formula for a sphere and a shell to calculate the mass of thesun 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.
Problem 114: The Heliopause...a question of balance
[Grade:8-10 | Topics: Formulas with two variables; scientific notation; spreadsheet programming]
Category: All,Helio
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.
Problem 113: NASA Juggles Four Satellites at Once!
[Grade:8-10 | Topics: Formulas with two variables; scientific notation]
Category: All,Magnetism
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:5-9 | Topics:Scientific notation - multiplication and division]
Category: All,Miscellaneous
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 - conversion from decimal to SN]
Category: All,Miscellaneous
Scientists use scientific notation to represent very big and very small numbers. In this exercise, students will convert some 'astronomical' numbers into SN form.
[Grade:5-9 | Topics:multiplication; Greatest Common Multiple]
Category: All,Magnetism
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:5-9 | Topics:multiplication; calculating length from image scale]
Category: All,Solar System
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:9-11 | Topics:Algebra; calculating with a formula]
Category: All,Stars
Many astronomical bodies have a natural period of oscillation. In this problem, students will use a simple mathematical model to calculate the period of oscillation of a star, a planet, and a neutron star from the estimated densities of these bodies.
[Grade:9-11 | Topics:image scales; angular measure; degrees, minutes and seconds]
Category: All,Helio,Solar System
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.
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:6-9 | Topics:image scales; area calculation; unit conversions]
Category: All,Helio
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; time calculations; speed calculations, unit conversions]
Category: All,Helio
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'.
Problem 100:The Sunspot Cycle - endings and beginnings -
[Grade level: 6-9 | Topics:graph reading; extrapolation; time calculations]
Category: All,Helio
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: 6-8 | Topics:image interpretation; eye-hand coordination; reading to be informed]
Category: All,Helio,Magnetism
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.
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).
Problem 95:A Study on Astronaut Radiation Dosages in SPace -
[Grade level: 9-11 | Topics:Graph analysis, interpolation, unit conversion]
Category: All,Rockets
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.
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 no one has thought about before? The Venn Diagramming activity is a key element of the activity and is reasonably challenging!
Problem 93:An Introduction to Radiation Shielding -
[Grade level: 9-11 | Topics: Algebra; Volume of a hollow cube; unit conversion]
Category: All,Miscellaneous
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.
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.
Students use the 'compound interest' formula to examine rates of growth for space mission costs, and the salaries of astronomers, with allowance for inflation.
This problem looks at some of the statistics of working in a field like astronomy. Students will read graphs and answer questions about the number of astronomers in this job area, and the rate of increase in the population size and number of advanced degrees.
Problem 89:Atmospheric Shielding from Radiation- III -
[Grade level: 11-12 | Topics: Evaluating an integral, working with exponential functions]
Category: All,Solar System
This is Part III of a 3-part problem on atmospheric shielding. Students use exponential functions to model the density of a planetary atmosphere, then evaluate a definite integral to calculate the total radiation shielding in the zenith (straight overhead) direction for Earth and Mars.
Problem 88:Atmospheric Shielding from Radiation- II -
[Grade level: 9-11 | Topics: Algebra I; evaluating a function for specific values]
Category: All,Miscellaneous
This is the second of a three-part problem dealing with atmospheric shielding. Students use the formula they derived in Part I, to calculate the radiation dosage for radiation arriving from straight overhead, and from the horizon. Students also calculate the 'zenith' shielding from the surface of Mars.
Problem 87: Atmospheric Shielding from Radiation- I -
[Grade level: 9-11 | Topics: Algebra II, trigonometry]
Category: All,Miscellaneous
This is the first part of a three-part problem series that has students calculate how much radiation shielding Earth's atmosphere provides. In this problem, students have to use the relevant geometry in the diagram to determine the algebraic formula for the path length through the atmosphere from a given location and altitude above Earth's surface.
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: Finding image scale; calculating time differences; calculating speed from distance and time]
Category: All,Helio
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.
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: 8-10 | Topics: arithmetic; unit conversions; surface area of a sphere) ]
Category: All,Solar System
In 2006, scientists identified 12 flashes of light on the moon that were probably meteorite impacts. They estimated that these meteorites were probably about the size of a grapefruit. How long would lunar colonists have to wait before seeing such a flash within their horizon? Students will use an area and probability calculation to discover the average waiting time.
Problem 80:Data Corruption by High Energy Particles -
[Grade level: 6-8 | Topics: Time and speed calculations; interpreting scientific data ]
Category: All,Helio
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.
Problem 77:Some Puzzling Thoughts about Radiation! -
[Grade level: 8-10 | Topics: Finding the roots of a quadratic equation; solving for X ]
Category: All,Miscellaneous
Students fill-in the blanks in an essay on radiation risks using a word bank tied to solving quadratic equations to find the right words from a pair of possible 'solutions'.
[Grade level: 6-8 | Topics: Unit conversion, arithmetic operations]
Category: All,Miscellaneous
This problem introduces students to a common radiation problem in our homes. From a map of the United States provided by the US EPA, students convert radon gas risks into annual dosages.
The relationship between the strength of a solar storm and the resulting magnetic disturbance on Earth is given as a series of equations. Students are asked to create new formulae based on these parametric these equations using the method of substitution.
[Grade level: 6-8 | Topics: decimals, unit conversion, graphing and analysis ]
Category: All,Solar System,Rockets
This math problem lets students examine the total radiation dosage that these explorers would receive on a series of 1000 km journeys across the martian surface. The students will compare this dosage to typical background conditions on earth and in the International Space Station to get a sense of perspective
Problem 72:Systems of Equations in Space Science -
[Grade level: 8-10 | Topics: decimals, solving systems of equations, matrix math, algebraic substitution ]
Category: All,Helio
This problem has students solve two problems involving three equations in three unknowns to learn about solar flares, and communication satellite operating power.
Problem 71:Are the Van Allen Belts Really Deadly? -
[Grade level: 8-10 | Topics: decimals, area of rectangle, graph analysis]
Category: All,Helio
This problem explores the radiation dosages that astronauts would receive as they travel through the van Allen Belts enroute to the Moon. Students will use data to calculate the duration of the trip through the belts, and the total received dosage, and compare this to a lethal dosage to confront a misconception that Apollo astronauts would have instantly died on their trip to the Moon.
Problem 70:Calculating Total Radiation Dosages at Mars -
[Grade level: 6-8 | Topics: decimals, area of rectangle, graph analysis]
Category: All,Solar System
This problem uses data from the Mars Radiation Environment Experiment (MARIE) which is orbiting Mars, and measures the daily radiation dosage that an astronaut would experience in orbit around Mars.
Problem 69:Single Event Upsets in Aircraft Avionics -
[Grade level: 8-10 | Topics: decimals, unit conversions, graph analysis]
Category: All,Miscellaneous
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.
Radiation dosages and exposure calculations allow students to compare several different ways that scientists use to compare how radiation exposure is delive black and accumulated over time.Like converting 'centimeters per sec' to 'kilometers per year' ,this activity reinforces student Topics in converting from one set of units to another.
[Grade level: 6-8 | Topics: fractions, decimals, unit conversions]
Category: All,Miscellaneous
Living on Earth, you will be subjected to many different radiation environments. This problem follows one person through four different possible futures, and compares the cumulative lifetime dosages.
[Grade level: 6-8 | Topics: decimals, unit conversions, graphing a timeline, finding areas under curves using rectangles]
Category: All,Solar System
Depending on the kind of career you chose, you will experience different lifetime radiation dosages. This problem compares the cumulative dosages for someone living on Earth, an astronaut career involving travel to the Space Station, and the lifetime dosage of someone traveling to Mars and back.
Problem 63 :Solar Activity and Tree Rings - What's the connection? -
[Grade level: 4-6 | Topics: Spreadsheets and technology; decimal math]
Category: All,Helio,Solar System
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 "weekly/tree.xls"Excell Spreadsheet Data File.
Students will calculate the brightness differences between stars using multiplication and division. Working with the number line will be a big help and math review!
[Grade level: 6-8 | Topics: Data analysis; decimals; ratios; graphing]
Category: All,Helio,Solar System
How big does a body have to be before it becomes round? In this activity, students examine images of asteroids and planetary moons to determine the critical size for an object to become round under the action of its own gravitational field.
In this activity, students will get their first taste of star counting by using a star atlas reproduction and bar-graph the numbers of stars in each magnitude interval. They will then calculate the number of similar stars in the sky by scaling up their counts to the full sky area.
Sudents will calculate the scale of the map, and answer questions about the distances between these objects, and the number that cross earth's orbit. A great, hands-on introduction to asteroids in the inner solar system! Links to online data bases for further inquiry are also provided.
[Grade level: 6-8 | Topics: Decimal math; using an online calculator; Histogramming data]
Category: All,Universe
Students will use an actual image of a distant corner of the universe, with the redshifts of galaxies identified to find a galaxy formed only 500 million years after the Big Bang.
[Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; distance = speed x time; scientific notation]
Category: All,Miscellaneous
In this activity, you will measure the speed of astronomical phenomena using the scaling clues and the time intervals between photographs of three phenomena:
[Grade level: 4-6 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]
Category: All,Stars
In this activity, students will determine the photographic scale, and use this to estimate the projected (2-D) distances between the stars in this cluster. They will also use internet and library resources to learn more about this cluster.
[Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; decimal math]
Category: All,Helio
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: Online research; Finding the scale of an image; metric measurement; decimal math]
Category: All,Universe
Students will compute the image scale (light years per millimeter) in a photograph of a nearby spiral galaxy, and explore the sizes of the features found in the image.
This collection of problems will have students reviewing how to perform multiplication and division with large and small numbers, while learning about some interesting astronomical applications.
Students will use data from a deep-integration image of a region of the sky in Hercules, observed by the 2MASS sky survey project to estimate the number of stars in the sky.
This problem will have students examine the geometry of perspective, and how the altitude of an aurora or other object, determines how far away you will be able to see it before it is below the local horizon.
[Grade level: 9-11 | Topics: Non-mathematical essay; reading to be informed]
Category: All,Miscellaneous
This activity presents 36 statements which the student is to evaluate as either a theory, law, fact, hypothesis or belief. Be prepared for some lively discussions!!
This activity lets students use the Pythagorean distance formula in 3-dimensions to explore stellar distances for a collection of bright stars, first as seen from Earth and then as seen from a planet orbiting the star Polaris.
[Grade level: 7-10 | Topics: Area of an irregular polygon; decimal math]
Category: All,Helio
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.
Students will follow a step-by-step geometric construction procedure to create a figure, and then use basic Euclidean postulates to prove that, because Earth rotates from west to east, stars must rise in the east and set in the west,
Students will examine an event timeline for a space weather event and use time addition and subtraction skills to calculate storm durations and speeds.
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.
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.
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.
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.
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.
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.
Students compare the dates of the largest sunspots since 1900 with the year of the peak sunspot cycle. They also compare superspot sizes with the area of earth.
[Grade:8 - 10 | Topics: Evaluating a function with two variables; completing tabular entries]
Category: All,Helio,Solar System
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.
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.
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:5 - 7 | Topics: Finding the scale of an image; measurement; decimal math]
Category: All,Miscellaneous
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:7 - 9 | Topics: Finding the scale of an image; decimal math; measurement]
Category: All,Miscellaneous
Students learn that the Pythagorean Theorem is more than a geometric concept. Scientists use a photograph taken by the IMAGE satellite to measure the size of Earth's plasmasphere region using a ruler and protractor.
Students work with positive and negative numbers to solve a crossword puzzle. Good exercise for pre-algebra review of adding and subtracting positive and negative numbers.
Problem 19: An Application of the Pythagorean Theorem
[Grade:8 - 10 | Topics: Squares and square-roots; Pythagorean Theorem in 3-D]
Category: All,Magnetism
This problem is an introduction to magnetism, which is a '3-dimensional vector', and how to calculate magnetic strengths using the Pythagorean Theorem.
Students learn about the spiral-shaped trajectories of charged particles moving in magnetic fields, and calculate some basic properties of this 'cyclotron' motion.
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.
Students learn about kinetic energy and how this concept applies to charged particles. They calculate the speed of a particle for various particle energies.
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.
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:7 - 9 | Topics: Volume of sphere; mass = density x volume; decimal math; scientific notation]
Category: All,Solar System
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).