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Distances and Models Your Name_______ Objectives of this lab exercise: After completing this exercise you should -  Understand measuring tools  Learn how astronomers are able to determine distances to celestial objects  Understand the vast dimensions of the universe and how to scale those dimensions to build a model Part I – Exploring everyday measuring tools [6 points] Science is all about measuring. One of the most important parts of doing astronomy is measuring distances, angles, and luminosity of celestial objects. In Astronomy the distances are huge and unimaginable. You might ask yourself the question “How can you gather information about an object that is so far away that you cannot reach it? For example, how do we know if a star is far away, but very bright, or close to Earth and relatively dim? Before we start with exploring astronomical distances you will investigate how you measure things in everyday life, and what tools you can use. 1. List at least 10 tools that you use for measuring things in your everyday life. Some everyday measuring tools include, scales, measuring tape, rulers, meter stick, measuring cup, measuring spoons, gps, clock, speedometer, stopwatch. 2. If you were going to measure the area of your room what kind of measuring tools might you use? In order to measure the area of my room I would probably use a measuring tape or a meter stick. Part II – Measuring distant objects [24 points] Parallax as explained in the pre-lab activity, is an interesting way of measuring the distance of an object by how much it appears to move when viewed against a much more distant background from one location, then another ( the distance between the locations is called the baseline ) . 3. Print a paper meter stick and tape it to your arm so that your chin can rest on the “0” mark. With your other hand hold a pencil or pen at the 50 cm mark. Then shut first one eye, then the other and observe how the pencil moves against objects in the background. Describe what happens. The pencil appears to move to the right when I close my left eye and it seems to stand still when I close my right eye. 4. Move the pencil closer, to the 25 cm mark. What happens to the motion of the pencil now when you first close one eye and then the other? Can you quantify the difference? Is the motion apparently twice as much as it was before? Five times as much? Write your answers 1

Pencil 50 cm from eyes. Distant object or wall eyes below. The pencil appears to move significantly more but to the left when I close my left eye and it still remains motionless when I close my right eye. 5. Now move the pencil to about the 100 cm end of the paper meter stick or as far as it can get from your eyes. Again quantify the motion compared to when the pencil was at the 50 cm position. The pencil barley moves and shifts only slightly when my left eye closes and continues to remain motionless when I close my right eye. 6. The pencil at 50 cm is shown below. Explain how the drawing would change for the 100 cm and 25 cm situations. In particular describe how the parallax angle, the angle between the two sight lines, changes as the distance of the pencil from the eyes changes. Does the angle double when the distance doubles? To perform this task use the insert shapes feature in your word program and draw the appropriate lines in the figure below. Use different colors for the two cases. 7. Parallax can be accurately measured if you have the right tools. What kinds of instruments would improve your experiment? I think a piece of string tied to the pencil would have helped me better determine the amount the pencil shifted and a protractor could be used to determine the angle of the shift. 8. Parallax is the first step on the ladder to measure distance to the stars . What kind of baseline do you think astronomers use to measure distance to the nearby stars? List some possibilities below. Astronomers use the distance of the sun from the earth as a baseline to measure the distance to nearby stars. Part III – Stellar magnitudes [10 points] The apparent brightness of stars is rated on a scale based on that developed by Hipparchus about 150 years B.C.E. That system classified stars from 1 to 6. Stars classified 1 were the brightest in the sky, 6 were near the limit of what can be observed with the naked eye. The modern scale includes 2

10. -Cygni (Deneb) is the upper left star in the Summer Triangle (see photo below) and the main α star in the Swan. Its apparent magnitude is 1.25 and the distance to Deneb is 993 parsec. Calculate the absolute magnitude for Deneb. What does this tell you about the nature of Deneb? 993=10((1.25)-M+5)/5  4965=(12.5-10M+50)  4902.5=-10M  M =-490.25 Absolute magnitude can tell us how luminous a star is and if 1 is the most luminous then Deneb is very luminous. Part IV – How big is the universe? Realm of the Earth and Moon [30 points] We will begin by shrinking the Earth to a two – inch diameter circle, then scaling other objects close to earth to see how they compare. Earth has a diameter of approximately 12756 km. We will use the metric system measurements for all astronomical objects today. Since one inch is 2.54 cm, it would be more consistent with the metric system to think of this a 5 cm universe. However, since the United States still doesn’t use the metric standard, most of us are used to thinking in terms of inches and feet and have a better idea of what an inch is (about the length of your thumb from top joint to tip) than what a cm is. Now do the math. In this realm 2 inches = 12756 km and the Moon is 3475 km in diameter, so how many inches in diameter would it be in our two inch Earth/Moon system? ¿ earth ∈ 2 − inch model ¿ earth ∈ kilometers = ¿ Moon ∈ 2 − inch model ¿ Moon ∈ kilometers 4

or, putting in the numbers 2 ∈ ¿ 12756 km = x 3475 km ¿ so x = 2 ( 3475 12756 ) inches ( the km units cancel). In other words the moon’s diameter is about .54 inches, or about ¼ the diameter of the Earth. Do the same process to calculate the distance the Moon is from Earth. In this case x is the distance of Moon from Earth in the model, but you will now need to use the fact that the Moon is about 384403 km away from Earth on average when measuring from the centers of Earth and Moon. Now we have: 2 inches 12756 km = x 384403 km Doing the math we get x = 2 (384403/12756) or 60 inches . Since 1 foot = 12 inches that is about 5 feet away. Other sizes and distances In this model, where the Earth is 2 inches across, the Sun is about 18 feet in diameter (imagine a round, glowing mini-van!) and is 1800 feet, or about 6 football fields away from Earth Realm of the Sun The next stage of this exercise is to shrink the Sun down to a 2 inch diameter. The Sun is approximate 1400000 km in diameter. Write this number in scientific notation. 11. Sun’s diameter in scientific notation : 1.4 x10 6 We use the same routine to calculate Earth’s size in this model: 2 ∈ ¿ 1400000 km = x 12756 km ¿ Finish finding Earth’s diameter and then distance in this model: 12. Calculated size of Earth in model: x=2(12756/1400000) x=0.018in 13. Calculated distance of Earth from Sun in this model: x=212.857in Other objects and distances shrunk to this scale:  Earth Size - A grain of salt, with a dust-speck Moon 1/2 inch away from it 5

 Light Travel Time - It would take 100,000 years for a beam of light to cross our galaxy and 2.5 million years for light to travel from the Andromeda Galaxy to us. Conclusion questions [Grade points: 15] 1. The absolute magnitude, M, is defined as the apparent magnitude a star would have if it were placed 10 parsecs from the Sun. But wouldn’t it be more correct to measure this distance from the Earth? Does it make a difference whether we measure this distance from the Sun or from the Earth? It would make a difference, the measurements would be inaccurate because earth orbits around the sun which would meaning the position of the earth constantly changes making it impossible to get accurate measurements. 2. Explain how this exercise has impacted your thinking about the size and importance of Earth in the universe. I learned that despite the fact that the universe is so big the amount we can observe and research is like a grain of sand on the beach. 3. Given what you have learned in the 2-inch universe exercise, what do you think the likelihood is of interstellar travel by humans in spaceships? Explain your reasoning. I don’t think interstellar travel will become common anytime soon however I do think one day we will explore the universe more with better robots like the mars rover. I can’t see humans in space anytime soon however I do think it might be a common occurrence one day in the far future. 7