Year 7: Problems 343 to 428

Problem 428: Meteorite Compositions: A matter of density
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: 8-10 | Topics: density; mass = density x volume; percentages] (PDF)

Problem 427: A Black Hole - Up Close
Students explore how the color of a light bulb changes as it gets close to a black hole, demonstrating the principle of the gravitational 'red shift'. [Grade: 9-12 | Topics: Evaluating an equation with one variable; square roots; metric units; nanometers] (PDF)

Problem 426: Black Holes - Hot Stuff!
Students explore the temperature of matter falling into a black hole using a simple equation to calculate the gas temperature at different distances. [Grade: 9-12 | Topics: Evaluating an equation with one variable; fractional exponents] (PDF)

Problem 425: Exploring a Full-sized Black Hole
Students explore how the speed of an orbiting satellite changes if it were near a black hole with five times the mass of our Earth. [Grade: 6-8 | Topics: Evaluating an equation with one variable; square roots; speed = distance/time; circumference of a circle] (PDF)

Problem 424: Exploring Black Holes
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. [Grade: 3-5 | Topics: working with a compass and metric ruler] (PDF)

Problem 423: The Moon as a Black Hole
Students draw a life-sized model of the Earth and Moon as two black holes to explore the actual sizes of these exotic astronomical bodies. [Grade: 3-5 | Topics: Working with a compass; metric ruler] (PDF)

Problem 422: Supercomputers: Getting the job done FAST! Students use a simple counting problem to explore how much faster a supercomputer is compared to as hand-calculation. [Grade: 6-8 | Topics: algebra] (PDF)

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

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

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

Problem 418: Supercomputers: Modeling colliding neutron stars! 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. [Grade: 8-10 | Topics: distance=speed x time; scale model; triangle and circle geometry; circumference] (PDF)

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

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

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

Problem 414: Radiation Dose and Distance Students explore the dosimetry from the Japan 2011 Earthquake and graph the decline of the radiation dose rates with distance from the nuclear reactors. [Grade: 9-12 | Topics: unit conversions; amount=rate x time; graphing Log-Log data] (PDF)

Problem 413: Exploring Nuclear Decay and Radiation Dose 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: 9-12 | Topics: unit conversions; amount=rate x time; Solving exponential equations in base-e] (PDF)

Problem 412: Radiation Dose and Dose Rate 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] (PDF)

Problem 411: Lifestyles and Radiation Dose 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] (PDF)

Problem 410:Exploring Radiation in your Life 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. [Grade: 6-8 | Topics: unit conversions; amount=rate x time] (PDF)

Problem 409: The 2011 Japan Earthquake Rocks the Earth 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: 9-12 | Topics: Algebra; evaluating an equation] (PDF)

Problem 408: Estimating the Speed of a Tsunami 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. [Grade: 6-8 | Topics: Time arithmetic; time zones; speed = distance/time] (PDF)

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

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

Problem 405: Discovering Earth-like Worlds by their Color 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 [Grade: 6-8 | Topics: graphing tabular data; interpreting graphical data] (PDF)

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

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

Problem 402: Kepler- Earth-like planets by the score! II 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: 6-8 | Topics: Percentage; re-scaling sample sizes] (PDF)

Problem 401: Kepler - Earth-like planets by the score! I Students use recent Kepler satellite data to estimate the number of Earth-like planets in the Milky Way galaxy. [Grade: 6-8 | Topics: Percentage; histograms; Re-scaling sample sizes] (PDF)

Problem 400: The Most Distant Objects in the Universe Students use a table of the most distant known events and objects in the universe to create a timeline of the universe soon after the Big Bang. [Grade: 6-8 | Topics: Working with millions and billions; elapsed time] (PDF)

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

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

Problem 397: The Changing Pace of Global Warming Students work with a table of global temperatures to forecast the temperature change by 2050 using a linear extrapolation. [Grade: 8-10 | Topics: Graphing tabular data; linear extrapolation; equation of a line y=mx+b] (PDF)

Problem 396: Kepler 10b - A matter of gravity Students use the measured properties of the Earth-like planet Kepler 10b to estimate the weight of a human on its surface. [Grade: 8-10 | Topics: Evaluating formulas; mass = density x volume; volume of a sphere; scientific notation] (PDF)

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

Problem 394: Probing the lunar core using seismology Students learn about the geometry needed to determine the diameter of the lunar core using a simplified model. [Grade: 9-10 | Topics: Geometry; Properties of Inscribed Arcs] (PDF)

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

Problem 392: Exploring the DNA of an organism based upon arsenic. Students estimate the increase in the mass of the DNA from an arsenic-loving bacterium in which phosphorus atoms have been replaced with arsenic. [Grade: 8-10 | Topics: Integer math; percentages] (PDF)

Problem 391: Investigating the atmosphere of Super-Earth GJ-1214b 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. [Grade: 6-8 | Topics: graphing functions; evaluating functions for given values; volume of a sphere; mass = densityxvolume] (PDF)

Problem 390: X-rays from hot gases near the black hole SN1979c Students use two functions to estimate the size of a black hole from the gas emitting x-rays which is flowing into it. [Grade: 8-10 | Topics: Functions; substitution; evaluation] (PDF)

Problem 389: Estimating the diameter of the SN1979c black hole 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 [Grade: 6-8 | Topics: evaluating linear functions; integer math; metric units] (PDF)

Problem 388: Hubble Detects More Dark Matter 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' [Grade: 8-10 | Topics: evaluating functions; Scientific notation] (PDF)

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

Problem 386: Whacky Spacecraft Orbits - They only seem crazy!
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. [Grade: 6-8 | Topics: distance=speedxtime; scientific notation; unit conversion] (PDF)

Problem 385: Gamma Ray Bubbles in the Milky Way
Students use the recent Fermi image of the gamma ray bubbles in the nucleus of the Milky Way to study their sizes and other properties. [Grade: 8-10 | Topics: scale model; scientific notation; unit conversion] (PDF)

Problem 384: Detecting the Most Distant SUpernova in the Universe
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. [Grade: 6-8 | Topics: Analyzing a graph; interpreting mathematical models] (PDF)

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

Problem 382: Estimating the mass and volume of Comet Hartley 2.
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. [Grade: 8-10 | Topics: volume of a sphere and cylinder; scale model; scientific notation; unit conversion] (PDF)

Problem 381: The Cosmological Redshift - Changing the light from a galaxy.
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: 8-10 | Topics: solving a simple equation for X] (PDF)

Problem 380: Seeing the Distant Universe Clearly
Students calculate the angular sizes and scales of distant objects to study how different sized telescopes see details with varying degrees of clarity. [Grade: 7-9 | Topics: solving a simple equation for X; angular measure; Scientific Notation] (PDF)

Problem 379: Exploring the Cosmos with Supercomputers
Students use two images created by a supercomputer calculation to explore the size and accuracy of computer models of the distanct universe. [Grade: 7-9 | Topics: scale model; proportions; Scientific Notation] (PDF)

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

Problem 377: Deep Impact: Approaching Comet Hartley-2
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. [Grade: 8-10 | Topics: linear modeling from data; inverse-square law] (PDF)

Problem 376: The Earth-like Planet Gliese 518g
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. [Grade: 3-5 | Topics: scale models; measurement] (PDF)

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

Problem 374: Deep Impact - Closing In on Comet 103P/Hartley 2
Students use the Tangent formula to figure out the angular size of the comet at closest approach, and the scale of the HRI camera image. [Grade: 8-10 | Topics: Scaled images; trigonometry; angle measure] (PDF)

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

Problem 372: LRO Determines Lunar Cratering History
Students count large craters on an LRO coded image of the lunar surface to estimate whether the impacting asteroids that produced the largest craters were from the same population of asteroids during the two different epocs of impacts. [Grade: 6-8 | Topics: Scaled images; probability; percentages] (PDF)

Problem 371: Close Encounters of the Asteroid Kind!
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. [Grade: 8-10 | Topics: Evaluating a base-10 power function; graphing; astronomical brightness scale] (PDF)

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

Problem 369: Scaling Up the Webb Space Telescope Mirror
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. [Grade: 8-10 | Topics: Properties of Hexagons and triangles; counting; evaluating a formula; tiling] (PDF)

Problem 368: The Hexagonal Tiles in the Webb Space Telescope Mirror
Students learn about the Webb Space Telescopes segmented mirror by studying the geometry of hexagons. [Grade: 8-10 | Topics: Properties of Hexagons and triangles; counting] (PDF)

Problem 367: Significant Figures...Oh My!
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: Significant figures; rounding; decimal math; scientific notation; evaluating a function] (PDF)

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

Problem 365: Terra Spies a Major Glacier Break-up
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: 8-10 | Topics: image scales; speed = distance/time; unit conversions] (PDF)

Problem 364: The Cometary Planet HD209458b
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: Scientific Notation; volume of a sphere; density; rates] (PDF)

Problem 363: Celestial Fireworks Near NGC3603
This young star cluster, barely one million years old, is furiously evaporating the clouds of interstellar gas and dust from which it formed. [Grade: 9-12 | Topics: Scientific Notation; evaluating functions; density] (PDF)

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

Problem 361: The Sky is Falling? Well...not quite!
The recent report that the upper atmosphere has collapsed is investigated [Grade: 9-12 | Topics: Algebra; Scientific Notation; exponential functions] (PDF)

Problem 360: Kepler's First Look at 700 Transiting Planets
A statistical study of the 700 transits seen during the first 43 days of the mission. [Grade: 6-8 | Topics: Percentages; area of circle] (PDF)

Problem 359: The Most Massive Stars Known
A study of the lifespans of the most massive stars known. [Grade: 9-12 | Topics: Scaling and proportions; Evaluating a function] (PDF)

Problem 358: A Flyby of Asteroid Lutetia
The Rosette mission flew by an asteroid. An application of the Pythagorean Theorem and angular size.[Grade: 6-8 | Topics: image scale; Pythagorean Theorem; rates] (PDF)

Problem 357: The Fastest Sea Level Rise in the United States
Global climate change is causing measurable sea level changes. Which part of the United States is sinking the fastest? [Grade: 6-8 | Topics: fitting linear equations to graphical data] (PDF)

Problem 356: Calculating Molecular Mass
Students count hydrogen, carbon and oxygen atoms in a molecule of adefovir dipivoxil and calculate its mass and formula.[Grade: 6-8 | Topics: Counting; Scientific Notation] (PDF)

Problem 355: Astronaut Bone Loss
From a graph, students predict how much bone loss an astronaut experiences during a long-duration stay in space.[Grade: 6-8 | Topics: Rates; linear equations] (PDF)

Problem 354: Earth's Polar Wander - The Chandler Wobble
Students plot the circular shape of the track of the North Pole during a 2-year period and estimate the speed of movement. [Grade: 6-8 | Topics: Graphing ordered pairs] (PDF)

Problem 353: Dwarf Planets and Kepler's Third Law
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. [Grade: 9-12 | Topics: Fitting functions to data; Evaluating a polynomial] (PDF)

Problem 352: Exponential Functions and Atmospheric 'Scale heights'
A study of the way a planet's atmosphere changes as its temperature is changed using exponential functions. [Grade: 9-12 | Topics: Scientific Notation; evaluating exponential functions; Optional calculus] (PDF)

Problem 351: Counting Atoms in Molecules
Students count the number of atoms of various elements in a molecule of inositol nicotinate to deduce the molecule's formula and mass. [Grade: 3-5 | Topics: Counting; multiplication] (PDF)

Problem 350: Estimating the Temperatures of Exoplanets
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.[Grade: 9-12 | Topics: Equation of ellipse; evaluating functions] (PDF)

Problem 349: Exoplanet Orbits and the Properties of Ellipses
Given the formula for the orbits of newly-discovered planets, students determine the basic properties of the elliptical orbits for the planets. [Grade: 9-12 | Topics: Properties of ellipses] (PDF)

Problem 348: Taking a Log-Log Look at the Universe
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.[Grade: 9-12 | Topics: Base-10 logarithms; graphing logarithmic data] (PDF)

Problem 347: More Molecular Madness!
Students count the number of atoms in a molecule of ciprofloaxcin to determine its chemical formula and mass. [Grade: 3-5 | Topics: Counting; multiplication] (PDF)

Problem 346: The International Space Station and a Sunspot: Exploring angular scales
An amateur photograph of the International Space Station crossing in front of the sun is analyzed to determine the scales of sunspots. [Grade: 9-12 | Topics: Similar triangles; angular measure] (PDF)

Problem 345: How many stars are there?
A starfield image taken by the 2MASS survey is analyzed to estimate how many stars are in the sky. [Grade: 6-8 | Topics: Scaling; unit conversion; angular measure] (PDF)

Problem 344: Hubble Spies an Asteroid - Yes it does move!
The track of an asteroid in a Hubble image of a cluster of galaxies is analyzed to determine speed of the asteroid.[Grade: 6-8 | Topics: Scaling; unit conversion; speed=distance/time] (PDF)

Problem 343: The Oldest Lunar Rocks
A list of the ages of the oldest lunar rock samples is grouped into families with about the same average ages to estimate the age of the lunar mare. [Grade: 3-5 | Topics: Ordering numbers; averaging] (PDF)