 | This web page contains problem sets in PDF format having to do with the universe. |
Problem 285: Chandra Sees the Most Distant Cluster in the 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. [Grade: 9-12 | Topics: Algebra I; Solving for X; Scientific notation]
Problem 239: Counting Galaxies with the Hubble Space Telescope Students use an image of a small area of the sky to estimate the total number of galaxies in the universe visible from Earth. [Grade: 8-10 | Topics: area, angular measure]
Problem 233: The Milky Way: A mere cloud in the cosmos- Students compare the average density of the Milky Way with the density of the universe. [Grade: 8-10 | Topics: Volume of disk, density, scientific notation]
Problem 230: Galaxy Distances and Mixed Fractions- Students use the relative distances to nearby galaxies expressed in mixed numbers to determine distances between selected galaxies. [Grade: 3-5 | Topics: Basic fraction math.]
Problem 222: Kelvin Temperatures and Very Cold Things- Students convert from Centigrade to Fahrenheit and to Kelvin using three linear equations. [Grade: 5-8 | Topics: Evaluating simple linear equations for given values.]
Problem 219: Variables and Expressions from Around the Cosmos- Students evaluate linear equations describing a variety of astronomical situations. [Grade: 6-8 | Topics: Evaluating simple one-variable equations.]
Problem 213: Kepler: The hunt for Earth-like planets- 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. [Grade: 6-8 | Topics: Area of circle; ratios; percents.]
Problem 212: Finding Mass in the Cosmos- 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. [Grade: 9-12| Topics: Scientific Notation; Algebra II; parametric equations]
Problem 196: Angular Size and velocity- 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. [Grade: 8-10| Topics: Geometry; Angle measurement]
Problem 192: The Big Bang - Cosmic Expansion - Students explore the expansion of the universe predicted by Big Bang cosmology [Grade: 10-12| Topics: Algebra, Integral Calculus]
Problem 191: Why are hot things red? - Students explore the Planck Function using graphing skills, and calculus for experts, to determine the relationship between temperature and peak wavelength. [Grade: 10-12| Topics: Algebra, graphing, differential calculus]
Problem 186: Collapsing Gas Clouds and Stability- Students use the derivative to find an extremum of an equation governing the pressure balance of an interstellar cloud. [Grade: 11-12| Topics: differentiation; finding extrema; partial derivitives]
Problem 170: Measuring Star Temperatures- 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. [Grade: 6-8 | Topics: algebra, graph analysis]
Problem 160: The Relative Sizes of the Sun and Stars- Students work through a series of comparisons of the relative sizes of the sun compablack 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]
Problem 159: Galaxies to Scale - Students explore the relative sizes of the Milky Way compablack to other galaxies to create a scale model of galaxies, similar to the methods in Problem 161. [Grade: 4-6 | Topics: working with fractions; scale models]
Problem 152: The Hubble Law - 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. [Grade: 6-8 | Topics: Plotting data; determining the slope of the data;]
Problem 150: Cosmic Bar Graphs - Students interpret simple bar graphs taken from astronomical data. [Grade: 3-5 | Topics: finding maxima and minima; fractions; extrapolating data]
Problem 146 Black Hole Power 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. [Grade: 9 - 11 | Topics:Scientific Notation; Spherical shells; density; power]
Problem 144 Exploring Angular Size 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. [Grade: 7 - 10 | Topics:Scientific Notation; degree measurement; physical size=distance x angular size.]
Problem 136 Black Holes---Part IV 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: 7 - 10 | Topics:Scientific Notation; Working with equations in one variable to first and second power.]
Problem 128 Black Holes - I 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: 8 - 12 | Topics:Simple linear equations; scientific notation]
Problem 123 A Trillion Here...A Trillion There 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: 5-9 | Topics:add, subtract, multiply, divide.]
Problem 111 Scientific Notation III 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 - multiplication and division]
Problem 110 Scientific Notation II In this continuation of the review of Scientific Notation, students will perform simple addition and subtraction problems. [Grade: 5-9 | Topics:Scientific notation - addition and subtraction]
Problem 109 Scientific Notation I 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:Scientific notation - conversion from decimal to SN]
Problem 58 How many stars are there? - For thousands of years, astronomers have counted the stars to determine just how vast the heavens are. Since the 19th century, 'star gauging' has been an important tool for astronomers to assess how the various populations of stars are distributed within the Milky Way. In fact, this was such an important aspect of astronomy between 1800-1920 that many cartoons often show a frazzled astronomer looking through a telescope, with a long ledger at his knee - literally counting the stars through the eyepiece! 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. [Grade level: 6-8 | Topics: Positive and negative numbers; histogramming; extrapolating data]
Problem 56 The Sombrero Galaxy Close-up - The Sombrero Galaxy in Virgo is a dazzling galaxy through the telescope, and has been observed in detail by both the Hubble Space Telescope and the Spitzer Infrared Observatory. This exercise lets students explore the dimensions of this galaxy as well as its finest details, using simple image scaling calculations. [Grade level: 9-11 | Topics: Finding the scale of an image; measurement; decimal math]
Problem 54 Exploring Distant Galaxies - Astronomers determine the redshifts of distant galaxies by using spectra and measuring the wavelength shifts for familiar atomic lines. The larger the redshift, denoted by the letter Z, the more distant the galaxy. In this activity, students will use an actual image of a distant corner of the universe, with the redshifts of galaxies identified. After histogramming the redshift distribution, they will use an on-line cosmology calculator to determine the 'look-back' times for the galaxies and find the one that is the most ancient galaxy in the field. Can students find a galaxy formed only 500 million years after the Big Bang? [Grade level: 6-8 | Topics: Decimal math; using an online calculator; Histogramming data]
Problem 50 Measuring the Speed of a Galaxy. - Astronomers can measure the speed of a galaxy by using the Doppler Shift. By studying the spectrum of the light from a distant galaxy, the shift in the wavelength of certain spectral lines from elements such as hydrogen, can be decoded to give the speed of the galaxy either towards the Milky Way or away from it. In this activity, students will use the formula for the Doppler Shift to analyze the spectrum of the Seyfert galaxy Q2125-431 and determine its speed. [Grade level: 6-8 | Topics: Interpolating data in a graph; decimal math]
Problem 49 A Spiral Galaxy Up Close. - Astronomers can learn a lot from studying photographs of galaxies. In this activity, 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. They will also use the internet or other resources to fill-in the missing background information about this galaxy. [Grade level: 6-8 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]
