Challenge: HOW FAR ARE THE STARS?

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1 Challenge: HOW FAR ARE THE STARS? TEACHERÕS NOTES In this investigation, students are challenged to determine the distance to a star using only the telescope and a simple software tool for measuring the brightness of the star. This activity introduces several fundamental ideas: The distance to the stars, which is central to determining the size and scale of the universeé and to appreciating our place in it. The inverse-square law, used widely throughout physical science. Scientific notation, which is basic to physical science. Experimental and interpretive skills that are fundamental to most scientific investigation. BEFORE YOU BEGIN It is critical to set the context for this investigation, so that the result (the distance to a star) is meaningful to students. A suggested context is to have students discuss and explore the challenges of communicating with or visiting life forms in other star systems. Students will discover that the extreme distance to even the closest stars poses an impressive barrier to travel and communication. Students should be familiar with our own solar system (sun and planets) before beginning this activity. It is important for students to understand that the stars are suns like our own Sun; stars give off their own light, unlike planets, which merely reflect light from the star they orbit. The activity assumes, but does not discuss, that Ònothing can travel faster than lightó. STARTING A DISCUSSION WITH YOUR STUDENTS You might begin this investigation by having students express their thoughts about life beyond our solar system. Do you think there IS life elsewhere in the universe? Would it matter to you if there were or were not? Why? From the Ground Up! (Draft ) -1- Smithsonian Astrophysical Observatory

2 TEACHERÕS GUIDE TO THE CALCULATIONS: (Refer to the Go Figure! page) Here are actual figures for a typical investigation of the distance to the star HD , using the MicroObservatory telescopes and the Sky Image Processor: Brightness of the star: 16,000 counts in 10 seconds Brightness of the Sun: 3.05 x 10 8 counts in 0.1 second. CORRECT FOR EXPOSURE: So for a 10 second exposure, the Sun WOULD have had 3.05 x counts for the Sun compared to 16,000 for the star CORRECT FOR THE SUN FILTERS: The filters cut down the sunõs light by another factor of So the real comparison is: 3.05 x counts for the Sun vs. 16,000 counts for the star. The square root of these relative brightnesses gives the relative distances of Sun and star. The square root of (3.05 x / 16,000) is about 1.2 x 10 7 or 12 million. Thus the star is 1.2 x 10 7 times further than the sun Ð i.e., 12 million times further than the Sun. That is, the star is 12 million x 93 million miles away, or about 1000 trillion miles from Earth. There are about 6 trillion miles in a light-year, the distance that light travels in one year. So the star HD is about 150 light-years from Earth. From the Ground Up! (Draft ) -2- Smithsonian Astrophysical Observatory

3 Challenge: HOW FAR ARE THE STARS? The distance to the stars holds the key to big questions about the universe. THE CHALLENGE: Astronomers have been studying a star in the constellation Pegasus that appears similar to our own Sun. They believe the star is orbited by planets, perhaps bearing life. Your company, Investigation Inc., has been asked by the United Nations to explore the possibility of traveling beyond our own solar system to visit this star system (called HD ). The U.N. also wants you to explore the possibility of communicating with any life forms that might exist there. Your challenge is to use the telescope to determine the distance to the star system. Using your findings, report on the following: How long would it take to reach the star by spaceship? Could we communicate with beings in nearby star systems? The distance to the stars bears on all these questions, and is a basic yardstick for our mission to measure the size of the universe. THE PLAN: In this challenge, weõll assume that we know the distance to our own star, the Sun: ItÕs about 93 million miles away. WeÕll also use the fact that the further away a source of light is, the dimmer it appears. In fact, the brightness of an object decreases as the SQUARE of its distance. For example, if the Sun were 10 times further away from us, it would appear 100 times dimmer. (If it were 1000 times further away, how much dimmer would it appear?) We can use this fact to estimate the distance to a sun-like star -- that is, a star believed to put out just as much light as our own sun. First, weõll use the telescope to compare the BRIGHTNESS of our sun with the brightness of the From the Ground Up! (Draft ) -3- Smithsonian Astrophysical Observatory

4 star. Then, knowing the DISTANCE to our own sun, weõll use the inverse-square law to determine the distance to the star. WHAT YOUÕLL NEED: SunÕs distance: You need to know that the Sun is about 93 million miles from Earth. Image of Sun: YouÕll need a MicroObservatory image of the Sun so that you can compare its brightness with the brightness of your target star. WeÕve archived an image for you that other students have taken, at this URL: Left: Our star, the Sun. Right: The star HD is the brightest star in this picture. It's just to the right and above the center of the picture. Can you find this star using the telescope? The Sun image is a 0.1 sec exposure. It was taken with the grey filter (Òneutral density 4Ó) filter in place, which allows only 10-4 of the light hitting it to pass through, and also with an external sun filter which cuts down the light by anothr factors of.0001 (i.e., 10-4 ). The Sun was 15 degrees above the horizon. Coordinates of target star: YouÕll also need how to find the star HD Its Òsky addressó is listed below in the ÒScope it Out!Ó section. Included there are the sky addresses (coordinates) of several other sun-like stars you can investigate. Software to measure brightness: A convenient image-processing program that lets you measure the brightness of an object in the image is the Sky Image Processor. ItÕs available for download at: A guide to using this program to measure brightness is attached below. From the Ground Up! (Draft ) -4- Smithsonian Astrophysical Observatory

5 FOR THE RECORD: YOUR PREDICTIONS Before you determine the distance to your target star, make a prediction about what youõll find, using the following scale model: In this model, use a grape to represent the size of our Sun. (The Sun is almost 1 million miles in diameter, so on this scale, 1 grape = 1 million miles.) The planet Earth in this model would be about 3 feet from the Sun; the planet Saturn would be more than 6 feet from the Sun. In this scale model, how far from the Sun would you guess the nearest star is? Feet? Yards? Miles? HD is a bit too faint to be seen by eye, but can easily be seen with a pair of binoculars. How far would you guess it is in this scale model? Feet? Yards? Miles? From a dark location in the countryside, the night sky seems filled with countless stars. How many INDIVIDUAL stars do you think you can make out with your naked eye. That is, if you counted all the stars you can see, how many would there be? stars From the Ground Up! (Draft ) -5- Smithsonian Astrophysical Observatory

6 ÔSCOPE IT OUT: USING THE TELESCOPE Finding your target star: Use the telescope to take an image of the star HD The coordinates for the star are: R.A. = 22 hr min, DEC=18 deg. 53 min When you get your image, use the photo on a page above to identify which star is HD You can also investigate the sun-like stars listed below. No one knows whether they have planets around them or, if they do, whether the planets contain life. To identify the star in your image you can refer to the star charts here (under construction) or find star charts on the Web. STAR 1: HR483 (RA=01 hr 40.6 min DEC=42 31') STAR 2: Lambda Serpentis (RA=15 hr 45.9 DEC=7 23') STAR 3: Beta Canum Venaticorum (RA=12 hr 33.2' DEC=41 25') Time of night to take exposure: Does it matter how high in the sky the star is? Think of what happens to the apparent brightness of the sun when it is high in the sky, compared to sunset or sunrise. In the same way, will your measurement of the sun-like starõs brightness be affected by how high or low it is in the sky? Should the star be at the same height in the sky as the Sun for a fair comparison? If not, how will it affect your result? Filter: Use the ÒclearÓ filter (which is no filter at all). Exposure time: Use an exposure time of about 10 seconds, and make sure you write down the exposure time you use. Does it matter what exposure time I use? Yes! The longer your exposure time, the brighter the star in your image will appear. So youõll need to record your exposure time along with the measured brightness of your star. Choose an exposure time that gives you a good image of the star, but is not so bright that the image SATURATES: That is, every pixel in your image should be below 4095, when measured by an image processing program. (See appendix for an explanation.) When youõve got your image, use the image processing program to measure the brightness of your target star and the brightness of the Sun. (Use the instructions appended below. Then enter your data on the DATA PAGE. From the Ground Up! (Draft ) -6- Smithsonian Astrophysical Observatory

7 DISTANCE TO A STAR: DATA PAGE First enter the data for your reference star, the Sun, including the brightness you measure from the Sun image: REF. STAR BRIGHTNESS EXPOSURE FILTER DISTANCE (name) (in flux units) (in secs.) (factor) (in miles) Sun Then enter the name and the brightness you measure for your target star (HD or other sun-like star). To determine the star's distance, use the Go Figure! sheet. TARGET STAR BRIGHTNESS EXPOSURE FILTER DISTANCE (name) (in flux units) (in secs.) (factor) (in miles) The Sun was at an altitude of 15 degrees above the horizon. My star was at an altitude of degrees above the horizon. QUALITY CONTROL: How many images of the same star should you take to be confident in the REPRODUCIBILITY of your results? How close are your measurements to each other? From the Ground Up! (Draft ) -7- Smithsonian Astrophysical Observatory

8 DISTANCE TO A STAR: GO FIGURE! YouÕve measured the apparent brightness of your target star, and also the brightness of your reference star, the Sun. How do you use these numbers to determine the distance to your target star? You can use a relationship between brightness and distance, called the Òinverse square law.ó It says that the apparent brightness of a light source decreases with the square of its distance to the observer. For example, a light source 3 times further away will appear only 1/9 as bright: (Apparent brightness) proportional to (1/ distance) 2 (Can you figure out from the diagram the reason for this relationship?) Comparing the Sun and the target star: Or in terms of distance: So first figure out how much DIMMER than the Sun the target star is. Then take the square root. ThatÕs how much FURTHER the target star is. From the Ground Up! (Draft ) -8- Smithsonian Astrophysical Observatory

9 You've measured the apparent brightness of both the Sun and the target star from your MicroObservatory telescope images. But you can't compare these brightnesses directly. Why not? To make a FAIR comparison, you have to CORRECT for the fact that the Sun image was taken with a much shorter exposure, and with a filter that cut down on most of it light. In other words, you need to know: how bright would you have measured the Sun if its exposure time and filter were the SAME as the target star? CORRECTING THE SUN'S MEASURED BRIGHTNESS: Original brightness of Sun you measured from the Sun image: (flux units) Correction 1: Brightness of the Sun you WOULD measure if you had used the SAME EXPOSURE as target star: (flux units). (To answer this, think: how much more light do you capture if you leave the shutter open, say, 100 times as long?) Correction 2: Brightness you WOULD measure if, IN ADDITION, the image had not used the Sun filters which let through only 10-8 of the Sun's light: (flux units). (Without these filters, the Sun's light would have melted the telescope!) Now you can make a FAIR comparison of the brightness of the Sun and your measured brightness of the target star. Use your (corrected) measurements, and the relationship between brightness and distance discussed above. How many times further away from us than our Sun is your target star?: Target star is times further than the Sun. Distance to the target star in miles: (miles) From the Ground Up! (Draft ) -9- Smithsonian Astrophysical Observatory

10 INTRODUCING THE ÒLIGHT-YEARÓ. Distances beyond our own solar system are so huge that it makes no sense to measure them in units of miles Ð the numbers would be too large to work with easily. Astronomers use a measure of distance called the Òlight-year.Ó ItÕs the distance that light travels in a year. How far is a light-year? Light travels at 186,000 miles per second, and there are about 32,000,000 seconds in a year. So a light-year is (186,000 mi./sec.) x (32,000,000 sec.) = about 6 trillion miles! How far is your target star in light-years?: (light-years) IS THAT RIGHT?: SOURCES OF ERROR? ItÕs a good idea to look critically at your results. What are the possible sources of error in your result? For example, what factors could affect the brightness of your image? Are there unavoidable errors in your measurements? How do you think these factors affected the overall accuracy of your result? The Art of Science: WHATÕS THE ÒRIGHT ANSWERÓ? Sorry! In the real world, there is no Òright answeró Ð there are only results. After all, the universe doesnõt come with a manual. But not all results are created equal: Some experimental methods are better than others, and some experiments are carried out more carefully than others. Determining how good your results are Ð when nature doesnõt provide a ÒtextbookÓ answer to check against Ð is one of the real challenges of being an investigator. Compare your result with the results of other students or professional researchers. How do they stack up? Determining the distance to astronomical objects is a challenge even for the professionals, and thereõs an uncertainty even in their results! From the Ground Up! (Draft ) -10- Smithsonian Astrophysical Observatory

11 DISTANCE TO A STAR: MAKING SENSE Modeling the Universe. In your scale model of the solar system using a grape as the Sun: If you use a second grape to represent your target star, then how far away should you put it from the Sun? Telescope as time machine. Particles of light travel at 186,000 miles per second. How long does it take a particle of light to reach the Earth from your target star? What year did the light that you captured with the telescope actually leave the star? Does that mean you are looking back in time? In what way can you use the telescope as a Òtime machineó? E.T. Phone Home? Suppose there are intelligent beings on a planet orbiting your target star. How long would it take for a message from them to reach the Earth? How long would a return message from Earth take to reach the star system? How long would a typical phone conversation take if you could "call" the star system? Travel to the stars? Today's fastest spacecraft travel at less than 100,000 miles per hour. How long would it take to reach your target star? Do you think it would ever be possible to reach the star system using a spacecraft? Amazing space. What do you make of the fact that you can see such incredible distances in space, even with the unaided eye? From the Ground Up! (Draft ) -11- Smithsonian Astrophysical Observatory

12 SEEING THE LIGHT: FROM THE STARS TO YOU Each image you take with the MicroObservatory telescope is made of thousands of tiny dots. (If you look closely, you can see them.) The dots are called pixels (for "picture elements"); they form an array 650 dots wide by 500 dots high, and each dot is black, white, or some shade of grey. Where do these dots come from, and what do they mean? Here's how light gets from outer space to your classroom: 1. Light from the stars enters the MicroObservatory telescope and is focused onto a small silicon chip. 2. The silicon chip is divided into an array of thousands of individual "wells," each of which senses the light that falls on it. The array is 650 wells by 500 wells on a side. Each well senses the amount of light that falls on it, and electronically converts it into a number from 0 to 4095: the more light, the higher the number. If no light falls on a well, it gets the number 0. If the well fills up ("saturates") with light, it gets the number For example, a well with the number 3000 has received twice as much light as one with the number Thus the telescope sends your image over the Internet in the form of numbers. Each image consists of 650 x 500 numbers (that equals 325,000 numbers!), and each number is somewhere between 0 and This array of numbers makes it all the way to your computer. Your image processor reconstructs the image from these numbers. Each number becomes a dot, called a pixel (for "picture element"). The number zero becomes a black dot. The number 4095 becomes a white dot, and the numbers in between are dots with different shades of grey. (There's a catch here: The image contains 4096 shades of grey, but your computer monitor can only display about 256 shades of grey. Therefore, you have to tell the computer how to convert the numbers in your image file into the greys that you see on the screen. This is called image processing.) 6. When you measure the brightness of a portion of your image, you are measuring (adding up) all the numbers in that portion of the image. Since the numbers are PROPORTIONAL TO the amount of light that fell on the chip, these numbers allow you to COMPARE the brightness of two different objects. In short, the chip in the telescope converts light into numbers, and your computer turns the numbers back into dots of light. From the Ground Up! (Draft ) -12- Smithsonian Astrophysical Observatory

13 HOW TO MEASURE BRIGHTNESS USING THE SKY IMAGE PROCESSOR PROGRAM Access and download the Sky Image Processor program from the World Wide Web at this address: Launch the program on your computer Note that there are TWO menu items named ÒFILEÓ (this is very confusing). Always use the second FILE menu (the one next to the VIEW menu). To Open your image: First make sure the image you are processing is in FITS image format. (Not sure? The telescope returns images in both GIF and FITS formats. See the MicroObservatory GET IMAGE page for how to download your image in FITS format.) Next, make sure your image is LABELED as a FITS image: The name of the image should end in.fits IMPORTANT: The SIP processor will ONLY recognize and open a file if its name ends in Ò.FITSÓ or Ò.FITÓ or Ò.FTSÓ such as Ògalaxy.FITSÓ Be sure your FITS file name ends in.fits! Open your image by selecting, under FILE, the choice Open Image File From UserÕs Machine. To Process your image: First make sure the object you want is actually in your image: Under VIEW, select Automatic Contrast Adjustment. To improve your image, select under VIEW the Change Image Parameters option. IMPORTANT: Processing your image will change how bright your target object LOOKS on the screen, but it will NOT change how bright the object is measured to be by SIP. That is, the SIP program measures the ORIGINAL PIXEL VALUES in your image, NOT the adjusted brightness on the screen. Therefore a dim image can still be measured to be bright and vice versa: The measured brightness of your image is independent of how you did the image processing. Measuring brightness. Under the ANALYZE menu, select Determine Centroid or Instrumental Magnitude of an Object. Move the green box to your target object using the center x and center y controls in the dialog window. Open the width of the green box so that it just covers the object you are measuring and a tiny bit more. Now move the red box to a part of the image that appears pretty blank Ð no stars or other galaxies. Select a width equal to or similar to the green box if you can Ð but smaller is also okay. This box measures the BACKGROUND brightness of From the Ground Up! (Draft ) -13- Smithsonian Astrophysical Observatory

14 your image, in counts per pixel. (Since itõs an average, the size of your box shouldnõt affect your results too much.) Reading results. Read off the Òobject fluxó at the bottom of the control window. This is your result. NOTE: The sun image is so large and bright that the reading you get should have an ÒEÓ followed by a number. This stands for Òexponent (number)ó. For example, 3.565E8 represents x 10 8 or million. What does it mean? The program has summed the brightness of each pixel in your green object box, and subtracted the background based on your red background box. Note what happens if you move the background box to coincide with your object box. The flux goes to zero, because your background is now as large as your target brightness! NOTE: The program reads pixels counts from your original image file, NOT from the screen. Therefore, processing your image Ð changing its brightness or contrast on screen, does NOT affect the brightness measurement described here. From the Ground Up! (Draft ) -14- Smithsonian Astrophysical Observatory