# National Aeronautics and Space Administration

## Year 8: Problems 429 to 478

Problem 478: The Grail and LRO Encounter in Lunar Orbit
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? [Grade: 9-12 | Topics: formula for an ellipse; semi-major and minor axis] (PDF)

Problem 476: SpaceX launches the First Commercial Rocket to the ISS
Students detemine the volume of the Dragon capsule using the volume formula for a cone. [Grade: 9-12 | Topics: Volumes of 3-d objects; cones; evaluating functions] (PDF)

Problem 475: Exploring Tidal Forces: Black holes and Saturns rings
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? [Grade: 9-12 | Topics: Evaluating equations; scientific notation] (PDF)

Problem 474: MESSENGER Explores the Interior of Mercury
Students work with a simple spherical core and shell model to determine the interior structure of mercury and the size of its dense iron core. [Grade: 9-12 | Topics: working with volumes of speheres; mass = density x volume] (PDF)

Problem 473: MESSENGER Explores the Mass of Mercury
Students use the orbit of NASA's MESSENGER spacecraft to determine the mass of Mercury. [Grade: 9-12 | Topics: working with equations with integer powers and solving for specified values; scientific notation] (PDF)

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

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

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

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

Problem 468: How Common are X-Class Solar Flares?
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 [Grade: 5-7 | Topics: mean, median, percentage] (PDF)

Problem 467: Estimating Magnetic Field Speeds on the Sun
Students use two images from the Solar Dynamics Observatory to estimate the speed of the X-class solar flare on March 6, 2012. [Grade: 6-8 | Topics: speed=distance/time; scale model; metric measurement] (PDF)

Problem 466: Exploring the Solar Wind and Coronal Mass Ejections
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. [Grade: 3-5 | Topics: scale models; proportions; fractions] (PDF)

Problem 465: Comparing Planets Orbiting other Stars
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. [Grade: 3-5 | Topics: scale models; proportions; fractions] (PDF)

Problem 464: Big Moons and Small Planets
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. [Grade: 3-5 | Topics: scale models; proportions; fractions] (PDF)

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

Problem 462: Using a Gravity Lens to Weigh a Cluster of Galaxies
Students explore how the geometry of a gravity lens can be used to measure the mass of the object producing the gravity. [Grade: 9-12 | Topics: algebra; Scientific Notation] (PDF)

Problem 461: Cassini Delivers Holiday Treats from Saturn
Students explore proportions and angular size using images of Saturn's moons Titan and Dione [Grade: 7-9 | Topics: scale models; proportions] (PDF)

Problem 460: Fermi Explores the High-Energy Universe
Students work with percentages to explore the identities of the 1873 gamma-ray sources detected by NASAs Fermi Observatory [Grade: 6-8 | Topics: percentages; pie graphs] (PDF)

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

Problem 458: Playing Baseball on the Earth-like Planet Kepler-22b!
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! [Grade: 8-10 | Topics: scale models; proportions; scientific notation; metric math; Evaluating equations] (PDF)

Problem 457: The Interplanetary Voyage of MSL
Students use the properties of ellipses to determine the formula for the Hohmann Transfer Orbit taking the Mars Science Laboratory to Mars in 2012. [Grade: 10-11 | Topics: Geometry: properties of ellipses] (PDF)

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

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

Problem 454: The Closest Approach of Asteroid 2005YU55 - III
Students work with the equation of a circle and line to find the orbit intersection points, midpoint, and closest distance to earth. [Grade: 8-10 | Topics: time=distance/speed; scale models; metric math] (PDF)

Problem 453: The Closest Approach of Asteroid 2005YU55 - II
Students work with the properties of circles and angular measure to see where the moon will be at the start of the asteroid encounter. [Grade: 6-8 | Topics: angular measure; time=distance/speed; scale models; metric math] (PDF)

Problem 452: The Closest Approach of Asteroid 2005YU55 - I
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. [Grade: 6-8 | Topics: time=distance/speed; scale models; metric math] (PDF)

Problem 451: The Spectacular Cat's Eye Planetary Nebula
Students measure the diameter of the nebula and use speed information to estimate the age of the nebula [Grade: 6-8 | Topics: time=distance/speed; scale models; metric math] (PDF)

Problem 450: Mapping Dark Matter in a Distant Cluster
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. [Grade: 8-10 | Topics: Volume of a sphere; shells; density] (PDF)

Problem 449: A simple model for the origin of Earth's ocean water
Students create a simple model of the arrival of water to Earth using three sizes of cometary bodies and their arrival rates. [Grade: 8-10 | Topics: volume of a sphere; rates of change] (PDF)

Problem 448: The Declining Arctic Ice Cap During September
Students graph the change in Arctic ice surface area, and perform linear and quadratic regressions to model and forecast trends. [Grade: 9-11 | Topics: Statistics; Regression; graphing tabular data] (PDF)

Problem 447: The Arctic's Vanishing Ozone Layer
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? [Grade: 9-11 | Topics: Regression; graphing tabular data] (PDF)

Problem 446: Arctic Ozone Hole Continues to Grow in 2011
Students estimate the area of the Arctic ozone hole, and work with the concept of parts-per-million to estimate total ozone volume lost. [Grade: 6-8 | Topics: Area of rectangle; volume; percentage] (PDF)

Problem 445: LRO - The relative ages of lunar surfaces
Students examine two Apollo landing areas using images from the LRO spacecraft to estimate the relative ages of the two regions using crater counting. [Grade: 6-8 | Topics: scale; histogramming] (PDF)

Problem 444: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - II
Students determine how often the two stars Kepler 16 A and B will line up with Tatooine on the same day of the year. [Grade: 6-8 | Topics: comparing two sequences of numbers; patterns, Least Common Multiple] (PDF)

Problem 443: Predicting the Transits of the Stars Kepler-16A and 16B from Tatooine - I
Students explore the orbit speeds of Tatooine and Kepler-16B and predict how often the two stars line up with the planet to create an 'eclipse'. [Grade: 6-9 | Topics: angle measure; angular speed] (PDF)

Problem 442: Modeling the Atmospheric Re-entry of UARS
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. [Grade: 8 - 11 | Topics: graphing data; linear equations; exponential and power functions] (PDF)

Problem 441: Exploring the new planet Kepler 16b called 'Tatooine'
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!! [Grade: 8-10 | Topics: angle measure; tangent] (PDF)

Problem 440: LRO explores the Apollo 12 landing area on the moon
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. [Grade: 6-8 | Topics: image scale; metric measurement] (PDF)

Problem 439: Chandra Sees a Distant Planet Evaporating
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 [Grade: 6-8 | Topics: Scientific Notation; Rate = Amount/Time] (PDF)

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

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

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

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

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

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

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

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

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

Problem 429: Tracking a Sea Turtle from Space
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. [Grade: 4-6| Topics: scale, metric measurement, speed=distance/time] (PDF)