DARE TO BE. FORMULA: e = distance between foci length of major axis VOCABULARY: ECCENTRIC. ellipse: eccentricity: focus (plural is foci): major axis:

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Amy Barber
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1 NAME: DATE: DARE TO BE ECCENTRIC INTRODUCTION: Have you ever heard the phrase dare to be different? Well that's what eccentricity is all about: deviating from the norm - or in other words, being different! Different is a relative term though, isn't it? To be different means that there has to be something you are different from. Sometimes the thing we are compared to is what is considered normal or standard. It's been said that when you're poor and just a little bit out there, they call you crazy, but when you're rich, they call you eccentric. So how does eccentricity relate to this laboratory? Well, since you asked... The planets travel around the Sun in a path called an orbit. Many people might say that these orbits are circular. Those people would be wrong because the orbits are different. The planets orbits have a special geometric shape called an ellipse. An ellipse can be described by its eccentricity value. Some orbits are slightly eccentric, while others might be more so. An ellipse has two "center points". Each one is called a focus. The Sun is not in the exact middle of the Earth's orbit. Rather, it is found at one of the focal points. OBJECTIVE: Be bold, be daring, and complete this lab on time! You will be able to compare the shape of the Earth's orbit and orbits of other planets with the shape of a circle. DIAGRAM: FORMULA: distance between foci length of major axis VOCABULARY: ellipse: eccentricity: focus (plural is foci): major axis: circle:

2 PROCEDURE: (Check off as you go along.) 1. Cut a piece of string about 22 cm in length and tie the ends together to form a loop. If I like you, I will have this already done for you (although I do enjoy watching some of you spaz out while trying to tie a piece of sting into a loop ) 2. On plain white paper draw a straight line long-ways down the middle of the paper. 3. In the middle of this line, make a tick mark. 4. Make a dot on both sides of the tick mark on the line you drew. Each dot must be 1.5 cm away from the center dot (for a total of 3 cm between the two dots). 5. Placing the paper on a double-piece of cardboard, put a thumbtack in the two last dots you made. (These dots represent the two foci). 6. Loop the string around the thumbtacks and draw the ellipse by placing your pencil inside the loop as shown below. Label this ellipse #1. 7. Measure the distance between the thumbtack holes (foci). This is "d". Record this on your Report Sheet for ellipse #1. 8. Measure the length of the major axis (L) and record this on the Report Sheet for ellipse #1. 9. Move each tack out 1 cm and draw a new ellipse. Label it #2 and measure and record d and L. 10. Move each tack out another 1 cm and draw a new ellipse. Label it #3 and measure and record d and L. 11. Move each tack out another 1 cm and draw another ellipse. Label it #4 and measure and record d and L. 12. Using a drawing compass with a different colored pencil, construct a circle. Place the point of the compass in the center tick mark that you made in step 3.. Extend the compass until the pencil touches ellipse #1 (so it will be about the same radius of ellipse #1) and draw your circle. 13. Label the circle #5 and measure and record d and L. 14. Using the equation from your Earth Science Reference Tables, calculate the eccentricity (e) of each of the five figures. Show all work on your Report Sheet.

3 REPORT SHEET Rounding rules for the Report Sheet: - Round distance between foci to nearest whole cm - Round length of major axis to nearest tenth of a cm - Round eccentricity calculation to nearest thousandths place ELLIPSE # 1 ELLIPSE # 2 ELLIPSE # 3 ELLIPSE # 4 ELLIPSE # 5 (circle)

4 DISCUSSION QUESTIONS: (Answer in Complete Sentences) 1. What change takes place in the eccentricity of the ellipses when you increase the distance between the foci? 2. Which of the four ellipses you drew (not counting the circle) was the most eccentric? 3. Which of the four ellipses you drew (not counting the circle) was the least eccentric? 4. What is the minimum eccentricity an ellipse can have? 5. What is the name of the geometric figure that has the minimum eccentricity?

5 6. How does the numerical value of "e" change as the shape of the ellipse approaches a straight line? 7. Where is the Sun located on a diagram of the Earth's orbit? 8. What was the eccentricity you calculated for Ellipse #1? 9. Which is rounder (less eccentric), the orbit of Earth or your Ellipse #1? 10. List the planets in order of the increasing eccentricity of their orbits. 11. Describe the true shape of the Earth's orbit.

Earth Science Unit 6: Astronomy Period: Date: Elliptical Orbits

Earth Science Unit 6: Astronomy Period: Date: Elliptical Orbits Earth Science Name: Unit 6: Astronomy Period: Date: Lab # 5 Elliptical Orbits Objective: To compare the shape of the earth s orbit (eccentricity) with the orbits of and with a circle. other planets Focus