A.4 The Solar System Scale Model

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1 CHAPTER A. LABORATORY EXPERIMENTS 25 Name: Section: Date: A.4 The Solar System Scale Model I. Introduction Our solar system is inhabited by a variety of objects, ranging from a small rocky asteroid only a few meters in diameter to the Sun whose diameter is 1,390,000 km. Each object has its own unique characteristics. This lab is a brief tour of the solar system and will help you become familiar with our neighboring planets. II. Reference The Nine Planets ( III. Materials Used calculator geometric compass meter stick large piece of paper IV. Activities How Big Are Other Planets? Planets come in various sizes. How big are other planets, such as Mars, compared to the Earth? Because planets are so much larger than objects we regularly interact with, we will use a scale model to get a more intuitive feel for the sizes of objects in the solar system. Let us shrink the solar system so that the diameter of the Earth becomes 1 cm; i.e., we will use a scale factor of 1 cm equals 13,000 km. 1 To find the scaled size of a planet in cm, divide the actual distance in km by the scale factor 13,000 km/cm. For example, Mercury s diameter is 4,900 km. Then, ( ) 1 cm Mercury s scaled diameter = 4, 900 km = 0.38 cm. (A.5) 13, 000 km 2 Find the scaled diameters for all planets and Sun and complete the following table. 3 What is the largest planet? Smallest? 4 Draw a circle corresponding to the scaled diameter of each planet on a large piece of paper using a compass.

2 26 CHAPTER A. LABORATORY EXPERIMENTS Planet Table A.10: The scaled diameters of planets. Actual Scaled Planet Actual diameter diameter diameter (km) (cm) (km) Mercury 4, Saturn 120,000 Scaled diameter (cm) Venus 12,000 Uranus 51,000 Earth 13, Neptune 50,000 Mars 6,800 Pluto 2,300 Jupiter 140,000 Sun 1,400,000 Venus Sun Mercury 1 AU Earth Mars Figure A.12: The inner solar system.

3 CHAPTER A. LABORATORY EXPERIMENTS 27 How Far Away Is Pluto? Planets do not collide with each other because the solar system is mostly empty and because the planets circle around the Sun at different distances at different rates. The path of a planet around the Sun is called its orbit. All planets orbit the Sun in the same direction as the Earth (counterclockwise as seen from above the north pole). To measure the distance from the Sun to a planet, astronomers use the distance standard called the astronomical unit (AU). One AU is defined as the average distance between the Sun and the Earth, 150 million km. 1 AU = km (A.6) In astronomical units, the distance from the Sun to Mercury can be expressed as 0.39 AU. In this part of the lab you are going to experience the vast size of our solar system. 1 The solar system is a big place. It is too big for us appreciate its size in the classroom. So, let us shrink the entire solar system. This time we are going to pick a scaling factor such that the Earth is 1 mm in diameter, ie. 13,000 km equals 1 mm in our scale model. The distance between the Sun and the planet (or the orbital radius) in the scaled solar system can be found by using this conversion to convert from kilometers into millimeters. For example, ( ) ( ) 1 mm 1 m Earth s orbital radius = km = 12, 000 mm = 12 m. (A.7) 13, 000 km 1000 mm 2 While we could do the above conversion for each planet, there is an easier way. We know that the Earth s actual distance of 1 AU is the same as 12 m in our scaled model. The scaled orbital radius to a particular planet can then be more easily found by multiplying the scaled radius for the Earth (= 12 m) by the actual orbital radius of the planet in astronomical units. Calculate the scaled orbital radii for all planets and record in Table A Next, you are going to express all distances in terms of your average stride size. In a hallway, mark a starting point and casually walk forward 10 strides. Mark the ending point. Using a meter stick, measure the total distance between the starting and ending point. Divide this distance by 10 to determine your average stride size. 4 Divide the distance between the Sun and the Earth in the shrunken solar system by the average stride. Now you have the Earth s distance from the Sun in the unit of your stride. We can find the distance from the Sun to another planet by multiplying the distance in the astronomical unit by the number of strides to the Earth. For example, suppose the distance to the Earth is equal to 18 strides. Then, the distance to Saturn is 5 Complete the third column of Table A strides 9.54 = 172 strides. 6 Go outside and take a piece of chalk with you. Find a straight section of sidewalk. Mark the position of the Sun. 7 Take an appropriate number of strides toward Mercury. Mark the position on the ground with chalk. Keep walking till you are at the Venus position. Keep marking the positions of the planets up to Saturn. While doing this, recall that in this scale model, the Earth is only 1 mm in diameter!

4 28 CHAPTER A. LABORATORY EXPERIMENTS Table A.11: The scaled orbital radii of planets. Planet Actual radius (AU) Scaled radius (m) Scaled radius (strides) Mercury 0.39 Venus 0.72 Earth Mars 1.52 Jupiter 5.20 Saturn 9.54 Uranus Neptune Pluto Table A.12: Average stride. Total Average distance stride size (m) (m)

5 CHAPTER A. LABORATORY EXPERIMENTS 29 8 Describe what happens to the distance between two consecutive planets as you walk away from the Sun. How Old Would I Be On Mercury? Each planet takes a different amount of time to orbit around the Sun. We call that time a year or the orbital period. It takes the Earth days to go around the Sun once. In contrast, it takes only 88.0 days for Mercury. Therefore, one Mercury-year is equal to 88.0 days. Similarly, one Jupiter-year is equal to 11.9 Earth-years. 1 Convert your age in the Earth-years to Mercury-years. your age in Mercury-years = (your age in Earth-years) ( ) 365 days 1 Earth-year ( ) 1 Mercury-year 88.0 days (A.8) 2 Repeat the conversion for other planet-years. Table A.13: Your age on other planets Planet Orbital period (Earth-years) Your age (planet-year) Mercury 88.0 days Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto 225 days 365 days 687 days 11.9 years 29.5 years 84.0 years 165 years 248 years

6 30 CHAPTER A. LABORATORY EXPERIMENTS V. Questions 1. A typical person walks at 4.8 km/h. At this speed, how long does it take you to get to the Moon? The orbital radius of the Moon is 384,000 km. 2. The nearest star to our solar system is Alpha Centauri. It is over 7,000 times the distance between the Sun and Pluto. Find the distance to Alpha Centauri in the scaled model of the solar system in which the Earth s diameter is 1 mm. 3. Now imagine that you are asked to create a model of the solar system that can fit on a single sheet of paper along its long axis. If the paper is 279 mm long, what scaling factor should you use such that Pluto s orbit just fits on the sheet of paper? How big would the Earth be in this scale model? VI. Credit To obtain credit for this lab, you need to turn in appropriate tables of data, observations, calculations, graphs, and a conclusion as well as the answers to the above questions. Do not forget to label axes and give a title to each graph. Show your work in calculations. A final answer in itself is not sufficient. Don t leave out units. In the conclusion part, briefly summarize what you have learned in the lab and possible sources of error in your measurements and how they could have affected the final result. (No, you cannot just say human errors explain what errors you might have made specifically.) You may discuss this with your lab partners, but your conclusion must be in your own words.