This web page contains problem sets for the Weekly Space Science Problem program. The goal of these problems is to teach students about space weather by using mathematics. To learn more about space weather and why it is important, visit the Human Impacts of Space Weather website at www.solarstorms.org.
IMAGE satellite program (2004-2006)
Hinode satellite program (2006-2008)
We have compiled the 20 most interesting problems in books that we publish each year in PDF format. The files are about 3 Megabytes long:
For the complete set of individual problems visit our:- Archive for 2004-2005 Contains 38 problems
- Archive for 2005-2006 Contains 26 problems
- Archive for 2006-2007 Contains 37 problems
Hinode satellite program (2006-2008)
This Week's Problems:
Problem 144 Chandra Exploring Angular Size[PDF] - Grade level: 7 - 10 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. [Skills:Scientific Notation; degree measurement; physical size=distance x angular size.]
Problem 143 NEAR So..How big is it? - Asteroid Eros surface [PDF] - Grade level: 4 - 7 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. [Skills: Scaling; multiplication, division; metric measure]
Previous Problems:
Problem 142 Black Holes---Part VIII[PDF] - Grade level: 7 - 10 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. [Skills:Scientific Notation; Working with equations in one variable to first and second power.]
Problem 141 Spitzer Exploring a Dusty Young Star [PDF] - Grade level: 4 - 7 Students learn about how dust emits infrared light and calculate the mass of dust grains from a young star in the nebula NGC-7129. [Skills: Algebra I; multiplication, division; scientific notation]
Problem 140 Black Holes---Part VII[PDF] - Grade level: 7 - 10 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. [Skills:Scientific Notation; Working with equations in one variable to first and second power.]
Problem 139 Mars Orbiter How Big Is It? - Mars [PDF] - Grade level: 4 - 7 Students use an image of a crater wall on mars to investigate ancient water gullies discovered in 2008 by the Mars Orbiter. [Skills:image scales; metric measurement; division and multiplication; decimals]
Problem 138 Black Holes---Part VI[PDF] - Grade level: 7 - 10 Tidal forces are an important gravity phenomenon, but they can be lethal to humans in 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. [Skills:Scientific Notation; Working with equations in one variable to first and second power.]
Problem 137 Chandra / XMM Black Holes---Part V[PDF] - Grade level: 7 - 10 Students explore how Kepler's Third Law can be used to determine the mass of a black hole, or the mass of the North Star: Polaris. [Skills:Scientific Notation; Working with equations in one variable to first and second power.]
Problem 136 Chandra / XMM Black Holes---Part IV[PDF] - Grade level: 7 - 10 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 = 2.83 M, and energy is estimated from E = mc^2. [Skills:Scientific Notation; Working with equations in one variable to first and second power.]
Problem 135 Cassini - How Big is It? - Io and Jupiter.[PDF] - Grade level: 4 - 7 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. [Skills:image scaling; multiply, divide, work with millimeter ruler]
Problem 134 The Last Total Solar Eclipse--Ever![PDF] - Grade level: 7 - 10 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. [Skills:Simple linear equations]
Problem 133 Mars Orbiter - How Big is It? - The Mars Rover.[PDF] - Grade level: 4 - 7 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. [Skills:image scaling; multiply, divide, work with millimeter ruler]
Problem 132 Black Holes - III[PDF] - Grade level: 8 - 12 Students learn about how gravity distorts time near a black hole and other massive bodies. [Skills:Simple linear equations; scientific notation]
Problem 131 QuickBird Satellite - How Big is It? - Las Vegas up close.[PDF] - Grade level: 4 - 7 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. [Skills:image scaling; multiply, divide, work with millimeter ruler]
Problem 130 Black Holes - II[PDF] - Grade level: 8 - 12 Students learn about how gravity distorts time and causes problems even for the Global Positioning System satellites and their timing signals. [Skills:Simple linear equations; scientific notation]
Problem 129 Lunar Orbiter - How Big is It? - The Moon up close.[PDF] - Grade level: 4 - 7 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. [Skills:image scaling; multiply, divide, work with millimeter ruler]
Problem 128 Black Holes - I[PDF] - Grade level: 8 - 12 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. [Skills:Simple linear equations; scientific notation]
Problem 127 Lunar Orbiter - How Big is It? - The Moon up close.[PDF] - Grade level: 4 - 7 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. [Skills:image scaling; multiply, divide, work with millimeter ruler]
Problem 126 Mars Reconnaissance Orbiter - How Big is It? - A Martian Avalanche![PDF] - Grade level: 4 - 7 Students work with a satellite 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! [Skills:image scaling; multiply, divide, work with millimeter ruler]
Problem 125 International Space Station - How Big is It? - Washington DC up close.[PDF] - Grade level: 4 - 7 Students work with an image taken by ISS astronauts to determine image scale, and search for the smallest things seen in a photograph. [Skills:image scaling; multiply, divide, work with millimeter ruler]
Problem 124 The Moon's Atmosphere![PDF] - Grade level: 8-10 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. [Skills:volume of sphere, shell; density-mass-volume; unit conversions]
Problem 123 A Trillion Here...A Trillion There[PDF] - Grade level: 5-9 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. [Skills:add, subtract, multiply, divide.]
Problem 122 Hubble - XZ Tauri's Super CME![PDF] - Grade level: 8-10 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. [Skills:Calculate image scale; speed from distance and time; mass:volume:density]
Problem 121 MESSENGER - Ice on Mercury?[PDF] - Grade level: 8-10 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. [Skills:Area of a circle; volume, density, unit conversion]
Problem 120 Benford's Law [PDF] - Grade level: 8-10 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. [Skills:Calculating frequency tables; Histogramming; Statistics]
Problem 119 GALEX - A Star Sheds a Comet Tail! [PDF] - Grade level: 8-10 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. [Skills:Image scaling; Unit conversion; Calculating speed from distance and time]
Problem 118 STEREO-An Application of the Parallax Effect[PDF] - Grade level: 8-10 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. [Skills:Pythagorean Theorem; square-root; solving for variables]
Problem 117 SOHO - CME Kinetic Energy and Mass[PDF] - Grade level: 8-10 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. [Skills:time calculation; Evaluating a simple equation; solving for variables]
Problem 116 STEREO - The Comet Encke Tail Disruption Event[PDF] - Grade level: 8-10 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. [Skills:time calculation; finding image scale; calculating speed from distance and time]
Problem 115 A Mathematical Model of the Sun[PDF] - Grade level: 8-10 Students will use the formula for a sphere and a shell to calculate the mass of the sun 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. [Skills: scientific notation; volume of a sphere and a spherical shell; density, mass and volume.]
Problem 114 The Heliopause...a question of balance[PDF] - Grade level: 8-10 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. [Skills: Formulas with two variables; scientific notation; spreadsheet programming]
Problem 113 MMS - NASA Juggles Four Satellites at Once![PDF] - Grade level: 8-10 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. [Skills: Formulas with two variables; scientific notation]
Problem 112 HINODE - How fast does the sun spin?[PDF] - Grade level: 5-9 Students will use two x-ray images of the sun taken by the Hinode satellite to determine how fast the sun rotates. [Skills:calculating map scales; time calculations; unit conversion]
Problem 111 Scientific Notation III[PDF] - Grade level: 5-9 In this continuation of the review of Scientific Notation, students will perform simple multiplication and division problems with an astronomy and space science focus. [Skills:Scientific notation - multiplication and division]
Problem 110 Scientific Notation II[PDF] - Grade level: 5-9 In this continuation of the review of Scientific Notation, students will perform simple addition and subtraction problems. [Skills:Scientific notation - addition and subtraction]
Problem 109 Scientific Notation I[PDF] - Grade level: 5-9 Scientists use scientific notation to represent very big and very small numbers. In this exercise, students will convert some 'astronomical' numbers into SN form. [Skills:Scientific notation - conversion from decimal to SN]
Problem 108 THEMIS - A Problem in Satellite Synchrony[PDF] - Grade level: 5-9 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. [Skills:multiplication; Greatest Common Multiple]
Problem 107 Monster Sunspots![PDF] - Grade level: 5-9 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. [Skills:multiplication; calculating length from image scale]
Problem 106 Oscillating Spheres[PDF] - Grade level: 9-11 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. [Skills:Algebra; calculating with a formula]
Problem 105 HINODE - The Transit of Mercury[PDF] - Grade level: 9-11 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. [Skills:image scales; angular measure; degrees, minutes and seconds]
Problem 104 HINODE - Loopy Sunspots![PDF] - Grade level: 9-11 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. [Skills:image scales; cylinder volume calculation; scientific notation; unit conversions]
Problem 103 HINODE - The Mysterious Solar Micro-Flares![PDF] - Grade level: 6-9 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. [Skills:image scales; area calculation; unit conversions]
Problem 102 HINODE - How fast does the sun rotate?[PDF] - Grade level: 6-9 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'. [Skills:image scales; time calculations; speed calculations, unit conversions]
