Technology to Explore Deep SpaceRick Kang 1-97
Scientific Use of Digitaized Data - a sampler
Goal: Estimate the distance to galaxy M101 by using simple geometry.
Suggestion: Quickly read through the entire exercise so that you have a grasp of the nature of the project. Then come back and work out the details.
Method: Use concept of ratio of apparent size to distance to relate galaxy at known distance that displays a particular diameter, to galaxy at UNKNOWN distance that displays a different diameter.
Tools:Digitized images of known and unknown galaxies (images must be of same scale - we furnish several images here), ruler, calculator, pencil and paper. (Use image analysis software if you wish to download the images, enhance contrast, and count actual pixels.)
Astronomy Background:Galaxies are pancake or football-like volumes in space that possess huge gravitational fields, hence collect lots of matter, including hydrogen gas, one of the early building blocks of our known Universe. Over time, much of this gas becomes stars, the stars cook up all the chemical elements of our Periodic Table, and use these elements to produce lots of planets and who knows how many intelligent life forms who may be going through this same exercise at this very moment.
You can think of a galaxy as a "star city", not that unlike the city you live in, where your house would represent a star, and your family members represent planets and moons of your star's solar system. The major problem with this comparison is that typical galaxies contain billions of stars, whereas typical cities contain only a few thousand houses.
Galaxies are huge, typically hundreds of thousands of light years in diameter, perhaps the largest scale "building blocks" of the Universe. They are separated by even greater distances, hence are very difficult to study: Appearing faint since their starlight is dimmed out by the time it reaches us, due to the fanning out of the light rays, and appearing tiny due to the perspective of distance, typically millions to billions of light years away. Fortunately, the sensitivity of the modern CCD (Charge Coupled Device) Electronic Camera allows professional and amateur astronomers to easily capture dim light from distant galaxies, and the digitized images that are created lend themselves to analysis.
Distances to galaxies are still in question, hence astronomers continue to explore better ways to find out the size of our inter-galactic community since this information will help reveal the size, age, large-scale structure, and behavior of our Universe. Our project is a "first approximation" at estimating distance, to demonstrate that anyone, using current technologies, can do some real astronomy!
Background of Measuring Concept: We know, intuitively and observationally, that due to perspective, when we step back twice as far from an object, like a table, the table's width appears to decrease. You can hold a finger near your eye, using the finger as a ruler, and try measuring the "angular diameter" (width) of several objects at various distances within your room or outside your window. The question is whether there is an actual numerical relationship of the increase in distance to the decrease in apparent width, like half, or third, etc. Perform some experiments to try to establish the nature of the relationship, like try backing up two times, three times, four times, etc. the distance and recording the change in width. Develop your "Law of Proportions".
Now check the first image, titled "Bottles". These are identical 7-Up bottles, placed 10, 20, and 30 feet away from the camera. Use your ruler to carefully measure the height or width of the bottles or their labels on the screen (be careful not to actually touch the computer screen... that might damage or smear the screen) and see if you can verify the relationship (If you elect to download the image, perhaps you can actually count pixels using your image processing software).
What did you come up with? When you doubled the distance, by what factor did the width change? How about when you tripled the distance? Here's a question to check your understanding of our plan: If you now see a bottle or object that appears ten times smaller than the object you first looked at that was at a known distance, say 25 feet away, how much farther away is the new object? What do you do to the 25 to get your answer?
On To The Galaxies:
Our "Standard Galaxy", M31, the great Andromeda Galaxy:
Examine the image titled "Galaxy M31". How wide is M31? What problem do you have in making this measurement? Can you enhance contrast to better define the galaxy's boundaries? The distance to M31 was determined fairly accurately several dozen years ago by famous astronomer Edwin Hubble. How did he do this? He was able to locate and measure the pulsation rate and magnitude (brightness) of several Cepheid Variable Stars within the galaxy. Several dozen years before that, Harvard data analysts Annie Jump Cannon and Henrietta Swan Leavitt discovered that Cepheid Variables pulsate with a rate proportional to their absolute magnitude (actual brightness). Knowing the absolute magnitude by observing the pulse rate (after spectroscopically classifying the star as a Cepheid), and measuring the apparent (visible) magnitude, the "inverse square law" (how brightness drops by the square of the distance from the light source) yielded a distance of about 2.2 million light years to M31 (most other galaxies are too far to allow distinguishing individual stars, so this method has severe intergalactic limitations).
Your measurement: Now, examine the image titled "Galaxy M101" and measure how many pixels wide this galaxy appears (can you find the galaxy in the image?) You are the astronomer. What kinds of decisions and problems did you encounter in making your measurement? Remember, science involves good observations, but there isn't any right nor wrong answer, only data upon which you develop logical conclusions. Use the "Law of Proportions" that you developed in the first step to calculate your estimated distance to M101 by comparing the widths of M31 and M101 and using Hubble's known distance to M31.
Find the professionally determined distance, see how yours compares. What error factors are involved, could be reduced? What major assumption did you have to make to use this method of determining distance to galaxies? Think of some other observational tests on the galaxies that you might make to determine if your assumption is harmless to the accuracy of your calculation or if you need to make some adjustments to your final estimate. Remember, science is about observations, not facts! Who knows how far away M101 is, I haven't been to M101 recently, have you?
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