# National Aeronautics and Space Administration

## Year 2: Problems 39 to 64

Problem 64 Solar Activity and Satellite Mathematics - When solar storms cause satellite problems, they can also cause satellites to lose money. The biggest source of revenue from communications satellites comes from transponders that relay television programs, ATM transactions and many other vital forms of information. They are rented to many different customers and can cost nearly \$2 million a year for each transponder. This activity examines what happens to a single satellite when space weather turns bad! [Grade level: 4-6 | Topics: Decimals; money; percents]

Problem 63 Solar Activity and Tree Rings - What's the connection? - Trees require sunlight to grow, and we know that solar activity varies with the sunspot cycle. Can an average tree sense solar activity cycles and change the way it grows from year to year? 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 Excell Spreadsheet Data File. [Grade level: 4-6 | Topics: Spreadsheets and technology; decimal math]

Problem 62 Star light...Star bright - A question of magnitude! - Since the time of the ancient Greek astronomer Hipparchus, astronomers have measured and cataloged the brightness of stars according to the 'apparent magnitude scale'. This activity lets students experience this peculiar numbering system where bright stars have small numbers (even negative: our sun is a -26 magnitude!) and faint stars have large numbers (faintest stars are +29 magnitudes). 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: 4-6 | Topics: Positive and negative numbers; decimal math]

Problem 61 Drake's Equation and the Search for Life...sort of! - Way back in the 1960's Astronomer Frank Drake invented an equation that helps us estimate how much life, especially the intelligent kind, might exist in our Milky Way. It has been a lively topic of discussion in thousands of college astronomy courses for the last 30 years. In this simplified version, your students will get to review what we now know about the planetary universe, and come up with their own estimates. The real fun is in doing the research to track down plausible values (or their ranges) for the factors that enter into the equation, and then write a defense for the values that they choose. Lots of opportunity to summarize basic astronomical knowledge towards the end of an astronomy course, or chapter. [Grade level: 6-8 | Topics: decimal math; evaluating functions for given values of variables]

Problem 60 When is a planet not a planet? - In 2003, Dr. Michael Brown and his colleagues at CalTech discovered an object nearly 30% larger than Pluto, which is designated as 2003UB313. It is also known unofficially as Xenia, after the famous Tv Warrior Princess! Is 2003UB313 really a planet? In this activity, students will examine this topic by surveying various internet resources that attempt to define the astronomical term 'planet'. How do astronomers actually assign names to astronomical objects? Does 2003UB313 deserve to be called a planet, or should it be classified as something else? What would the new classification mean for asteroids such as Ceres, or objects such as Sedna, Quaoar and Varuna? [Grade level: 6-8 | Topics: Non-mathematical essay; reading to be informed]

Problem 59 Getting A Round in the 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. Thanks to many Internet image archives this activity can be expanded to include dozens of small bodies in the solar system to enlarge the research data for this problem. Only a few example images are provided, but these are enough for the student to get a rough answer! [Grade level: 6-8 | Topics: Data analysis; decimals; ratios; graphing]

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 57 Asteroids and comets and meteors - Oh My! - Astronomers have determined the orbits for over 30,000 minor planets in the solar system, with hundreds of new ones discovered every year. Working from a map of the locations of these bodies within the orbit of Mars, students 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: 4-6 | Topics: Scale model; Decimal math; Interpreting 2-D graph]

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 55 Essays by Starlight - Being an astronomer is far more than just knowing facts and measurements. Sometimes you can learn important things about the universe by listening to your own feelings. Song lyrics are often a great stimulus for thinking about space in a different way. Students will select three song lyric fragments from popular Rock songs and write a short essay for each of them. The challenge is to explain what the songs make you think of, from both a human and an astronomical point of view! [Grade level: 4-6 | Topics: Non-mathematical essay]

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 53 Astronomy: A Moving Experience! - Objects in space move. To figure out how fast they move, astronomers use many different techniques depending on what they are investigating. In this activity, you will measure the speed of astronomical phenomena using the scaling clues and the time intervals between photographs of three phenomena: A supernova explosion, a coronal mass ejection, and a solar flare shock wave. [Grade level: 6-8 | Topics: Finding the scale of an image; metric measurement; distance = speed x time; scientific notation]

Problem 52 Measuring the size of a Star Cluster - Astronomers often use a photograph to determine the size of astronomical objects. The Pleiades is a famous cluster of hundreds of bright 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: 4-6 | Topics: Online research; Finding the scale of an image; metric measurement; decimal math]

Problem 51 Sunspots Close-up and Personal - 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: Finding the scale of an image; metric measurement; decimal math]

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]

Problem 48 Scientific Notation - An Astronomical Perspective. - Astronomers use scientific notation because the numbers they work with are usually..astronomical in size. 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. They will learn about the planet Osiris, how long it takes to download all of NASA's data archive, the time lag for radio signals to Pluto, and many more real-world applications. [Grade level: 8-10 | Topics: Scientific notation; decimal math]

Problem 47 Discovering the Milky Way by Counting Stars. - It is common to say that there are about 8,000 stars visible to the naked eye in both hemispheres of the sky, although from a typical urban setting, fewer than 500 stars are actually visible. 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 number is a lower-limit to the roughly 250 to 500 billion stars that may actually exist in the Milky Way. [Grade level: 4-6 | Topics: Tallying data; decimal math]

Problem 46 A Matter of Perspective. - Why can't we see aurora at lower latitudes on Earth? 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: Geometric proofs]

Problem 45 Theories, Facts, Beliefs...Oh My! - It is very common to confuse the definitions for Theory, Hypothesis, Fact, Law and Belief. This causes all sorts of problems when scientists and non-scientists speak to each other, or when reporters try to explain the latest discoveries. 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!! [Grade level: 9-11 | Topics: Non-mathematical essay; reading to be informed]

Problem 44 Interstellar Distances with the Pythagorean Theorem - If you select any two stars in the sky and calculate how far apart they are, you may discover that even stars that appear to be far apart are actually close neighbors in space. 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. Requires a calculator and some familiarity with algebra and square-roots. [Grade level: 9-11 | Topics: Decimal math; Pythagorean Theorem; square root]

Problem 43 An Interplanetary Shock Wave On November 8, 2000 the sun released a coronal mass ejection that traveled to Earth, and its effects were detected on Jupiter and Saturn several weeks later. In this problem, students will use data from this storm to track its speed and acceleration as it traveled across the solar system. [Grade level: 6-10 | Topics: Time calculations; distance = speed x time ]

Problem 42 Solar Storms in the News - Students will use a newspaper archive to explore how reporters have described the causes of aurora since the 1850's. They will see how some explanations were popular for a time, then faded into oblivion, as better scientific explanations were created. [Grade level: 6-10 | Topics: Online research; tallying data]

Problem 41 Solar Energy in Space 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. [Grade level: 7-10 | Topics: Area of an irregular polygon; decimal math]

Problem 40 Why do stars rise in the East? Students will follow a step-by-step geometric construction procedure to creats 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, and that the angle turned by the Earth equals the amount of apparent sky position change by a fixed star in the sky. [Grade level 9-10 | Topics: Geometric proof]

Problem 39 Solar Storm Timeline How long does a solar storm last? How fast does it travel? Students will examine an event timeline for a space weather event and use time addition and subtraction skills to calculate storm durations and speeds. [Grade level: 7-9 | Topics: time math; decimal math; speed = distance/time]