Lab 1 Measuring and Scales

AST 195 Measuring and Scales Objectives: After completing this lab, you should be able to: 1. Use the metric system to a. Make length measurements b. Convert between measurements within the metric system 2. Design and construct scale models (drawings) 3. Understand the use of multiple model representations 4. Understand and use units specific to Astronomy and the various structures the units are associated with Introduction: Metric Measuring The metric system is fundamental to work in science. In this class, you will be using the metric system exclusively. Once you are used to it, the metric system is actually easier to use than the everyday English system (technically called the US Customary System). In reality, you are familiar with the metric system; you use it every time you spend a penny. The “cent” is from the fact that there are 100 cents in one dollar. In the same way, there are 100 centi meters in one meter. Centi is the prefix that means 1/100. Each metric prefix simply represents a power of 10. Each prefix can be used with any base unit (meters, seconds, grams, etc.) So, just as one can say “1 millimeter,” one could say “1 millisecond.” In both cases, there would be 1/1000 of the meter or the second. The most common metric prefixes you will be using are centi and milli. They both represent parts of the unit you are using. Generally, you will be measuring lengths, so you need to be familiar with centimeters (cm) and millimeters (mm). There are two different ways to think about the meaning of these two prefixes. They are summarized in table 1 Prefix Substitution Meter stick centi 1 cm = 1/100 meter 100 cm = 1 meter milli 1 mm = 1/1000 meter 1000 mm = 1 meter With prefixes representing numbers greater than 1, the substitution process works better. For example, you could say 1 km = 1000 m. The k stands for kilo which represents 1000, so just substitute the 1000 for the k in the expression. Page 1 of 12 Table 1

Reading and Using a Metric Ruler Generally, you will be using a ruler (just a short meter stick) to make your measurements. Metric rulers have large divisions marked in centimeters (cm). Remember, centimeters are hundredths (1/100 = .01) of a meter. Each centimeter is divided into ten smaller divisions that are millimeters (mm). Remember, millimeters are thousandths of a meter (1/1000 = . 001). At times you will notice that your measurements land in between two tick marks. In this case split the difference and choose the value halfway between them. The example below would be written 17.5 mm. It is more than 17 mm but not quite 18 mm, but we don’t have any finer tick marks to judge whether it is 17.6 mm or 17.8 mm, so we record it as 17.5 mm ± 0.5 mm. Scales In Astronomy, you will be looking at object sizes and distances that are so great, they cannot fit into the room (or even on the earth). To help understand objects that cannot be dealt with directly, scientists develop models to help visualize the objects. In many cases, a scale model is the most useful. The simplest scale model is a drawing. An example of an everyday scale drawing is a map. Different scales give you different sizes of maps representing the same area. One of the problems in astronomy is finding the scale that is most appropriate when dealing with various objects. For example, a scale that would allow you to put all the planets in the solar system on a single sheet of paper, would make all the planets so small that you couldn’t even see them. Assume on a map, you look at the legend (scale) and (in metric!) you find 1 cm = 100 km. The scale factor then is: 100 km/cm. The scale factor is simply a ratio that compares one size to another. In this case, you are comparing the size on the scale to the actual size of the Page 2 of 12 Millimeter divisions Figure 1 Centimeter cm

Determining the Scale The final problem generally encountered with making a scale drawing of something is deciding what scale to use. To determine the scale to use, you need to think about the largest object or distance to be represented and the size of the model you can use. For example, let’s assume you want to draw a scale model of a room on a sheet of paper. Assume the room is 9 m by 14 m. Step 1: Measure the piece of paper. The longest side is just under 28 cm. Step 2: The longest size you need to fit is 14 m, so your scale factor is 28 cm = 14 m. This can also be expressed as 2 cm = 1 m. Or, 1 cm on your scale will represent ½ meter in reality and this can be expressed as 1 cm = 0.5 m. Step 3: Determine the size you will draw the model: 9 m × 1 cm 0.5 m = 18 cm or 9 m × 2 cm / m = 18 cm 14 m × 1 cm 0.5 m = 28 cm or 14 m × 2 cm / m = 28 cm The two different ways of writing the scale factors and even the actual processes are equivalent. Making a scale model As your first example in making a scale drawing, you will look at a selected portion of the solar system. The size of a planet is generally given in terms of its diameter or its radius. Page 4 of 12 Figure 2 A diameter is the distance across a circle or sphere through the center. A radius is the distance from the center to the edge. The radius will equal one- half the diameter.

Moon Moon Earth Moon Making other scale models Another way of making scale drawings is to compare one object to another. For example, how many moons would fit across the Earth? To determine this, we need to know the diameter of the Earth and the moon: Earth’s diameter: 12,756 km Moon’s diameter: 3,476 km To calculate how many moons would fit across the Earth, ask yourself how many times larger is the Earth’s diameter? Calculate it: 1.28 x 10 4 km divided by 3.5 x 10 3 km ~ 3.7 or about 4. We could model this as: Figure 3: About Four moons fit across the earth This method of comparing objects is particularly useful in terms of the Sun. The characteristics of a star may be given in terms of the radius of the Sun (R sun ) and the mass of the Sun (M sun ), for example; 3 R Sun and 10 M Sun . Models using distances and special units In astronomy, distances to various objects are of great interest. Modeling those distances is very important. Most of these distances are very large (at least in certain units) and so you will often see them expressed in scientific notation. To help make large numbers more convenient to work with, alternate units may also be used. One such unit is the Astronomical Unit (AU). An AU is defined as the average distance between the Earth and the Sun and is a very convenient unit to use when expressing distances within the Solar System. Although AU’s are useful for distances within the solar system, once you move out of the solar system, the numbers become unwieldy again. In astronomy, you will look at many structures even larger than our solar system. The next largest structure is a galaxy. A galaxy is a group of stars and planetary systems, dust, gas, etc. that all move around some Page 5 of 12 Moon

What is your scale factor? _____________________ Show your work below. 4. What size, in cm, would each object be in your drawing? Show your work. Sun: Earth: Jupiter: 5. Using the scale sizes determined in step 7, construct a drawing of these objects on a separate sheet of paper. (Use a compass if possible. If not, measure the diameters on the sheet and then hand-draw the best circle you can to represent the planet.) Remember, you may place the drawings inside each other. Many cities (Ithaca, NY and Gainesville, FL, for example) have a walking model of the solar system. Peoria, IL has a large model where you can drive between planets. We don’t have that much room, but assume you want to make a similar model on campus. You need to fit the solar system into the distance between the Oswald Building and the AT Building (to make a relatively straight line). Refer to figure 4 for a map of the campus. 6. What is the straight-line distance, in cm, between the left end of Oswald and the right side of the AT building? 7. What is this actual distance in meters? (Hint: the scale is given by the short line on the bottom of the map. Measure this and note how many meters it represents. Then use that as your scale factor to determine the actual distance.) Page 7 of 12

8. We will include the minor planet Pluto in our model of the solar system. Pluto’s average distance from the Sun is 39.5 AU. Determine the scale (use 1 AU = ? cm) you will need to be able to fit the solar system in the distance between the two points on the buildings given in step 9. Show your work. Calculate the scale distance to each object, in cm, according to your scale and place the values in Table 3. Show your work. Solar System Member Distance from the Sun (AU) Scale Distance (cm) Earth 1 Jupiter 5.2 Pluto 39.5 9. Put a dot representing the Sun at the left end of Oswald. Using the distances you found in Table 3, determine where the Earth, Jupiter, and Pluto would be. Clearly mark those places on the map (figure 4). Page 8 of 12 Table 3

10. Measure the line indicating the width of the galaxy and find the scale factor for Figure 5 . The scale of the drawing 1 cm = __________________ ly. 11. Locate the Sun in the picture. What is the distance from the Sun to the center of the galaxy? (The center is the point where the lines cross. You will need to measure and use the scale factor in order to answer the question.) Page 10 of 12 Figure 5

12. Table 4 lists five bright stars. What lettered dot (A through E) from figure 5 best represents the location of each star. Place the letter in the table. (You will use a letter more than once.) Star Distance from Sun (ly) Letter Sirius 9 Vega 26 Spica 260 Rigel 810 Deneb 1400 13. Are these stars inside or outside the galaxy? Explain. 14. One way of classifying objects is by use of a catalog where they are listed. One such catalog is the Messier catalog. Objects in the catalog are given “Messier numbers,” abbreviated M#. The objects often will also have common names, given below in parentheses. Table 5 lists three Messier Objects and their distances from the Sun. Find the letter of the dot (A through E) from the picture in figure 5 that best represents the location of each object. Place the letter in the table. (You may use a letter more than once.) Messier Object Distance from Sun (ly) Letter M45 (Pleiades) 380 M1 (Crab Nebula) 6300 M71 (Cluster) 12700 15. Are these Messier objects part of the galaxy? Explain. 16. Which letter, if any, might represent the LMC or SMC? Explain your choice. Page 11 of 12 Table 4 Table 5