Ellipses and Eccentricity** Eccentricity** ** - you will see this on the Lab Practical in JUNE! Objective: To compare the shape of the earth’s orbit (eccentricity) with the orbits of other planets and with a circle.
Focus 1
Focus 2
d
L
d = distance between foci
L = Length of major axis
Procedure: 1. Cut a piece of string about 22 cm in length and tie the ends together to form a loop. 2. On a plain sheet of white paper, lightly draw a straight line down the middle of the paper (lengthwise). 3. Near the center of this line, draw two (2) dots 3 cm apart. 4. Place the paper on a piece of cardboard and put a thumbtack in each dot (focus). 5. Loop the string around the thumbtacks and draw the ellipse by placing your pencil inside the loop as shown below. 6. Label this ellipse #1
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7. Measure the distance between the foci (thumbtacks) and record this on your report sheet under “d”. 8. Measure the length of the major axis “L” and record this on the report sheet. 9. Remove only one (1) of the tacks and slide it away from the other by an additional 2.0 cm and using a different color pencil, draw a second ellipse. Label this ellipse #2 and measure and record “d” and “L”. 10. Again remove the same tack as in step 9 and slide it away by another 2.0 cm. Label this ellipse #3 and measure and record “d” and “L”. 11. Again remove the same tack as in step 9 and slide it away by another 2.0 cm. Label this ellipse #4 and measure and record “d” and “L”. 12. Place a dot in the exact center of the first (original) two (2) foci. Using only one (1) thumbtack, loop the string around the tack so that when it is extended with your pencil it touches ellipse #1. This will be the radius of the circle you will draw. 13. Write the formula for eccentricity (E) found on your Earth Science Reference Tables in the box below:
14. Calculate the eccentricity for each of the five figures you drew. You must show all your work!!! Ellipse #1 d= L= E= Ellipse #2 d= L= E=
Show All Work Here
Ellipse #3 d= L= E=
Show All Work Here
Ellipse #4 d= L= E=
Show All Work Here
Circle d= L= E=
Show All Work Here
Ellipse & Eccentricity Lab
Show All Work Here
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Questions and Conclusions: 1. Which change takes place in the eccentricity of the ellipses when you increase the distance? [Answer in complete sentences]
2. What is the minimum eccentricity that an ellipse can have? 3. What is the name of the geometric figure which has the minimum eccentricity?
4. Which of the 4 ellipses you drew, not including the circle, was the most eccentric? 5. Which of the 4 ellipses you drew, not including the circle, was the least eccentric? 6. How does the numerical value of “E” change as the shape of the ellipse approaches a straight line? [Answer in complete sentences]
7. Where is the sun located on a diagram of Earth’s orbit? [Answer in complete
sentences]
8. Using your Earth Science Reference Tables, compare the eccentricity of Earth’s orbit with the eccentricity of ellipse #1. [Answer in complete sentences]
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9. Referring to the “Solar System Data” chart in your Earth Science Reference Tables, the planets are listed in order by their distance from the sun. Is there a direct relationship between the eccentricity of its orbit and the distance a planet is from the sun? Explain your answer:
10. List the planets in order of increasing eccentricity of their orbits:
Least eccentric:
Most eccentric:
11. Describe the true shape of Earth’s orbit based on your knowledge of eccentricity. [Answer in complete sentences]
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12. The Earth reaches its greatest orbital speed when it is A) farthest from the Moon B) closest to the Moon C) farthest from the Sun D) closest to the Sun
13. The diagram below shows a planet's orbit around the Sun. At which location is the planet's orbital velocity greatest?
A) D B) C C) B D) A
14. According to the Earth Science Reference Tables, what is the approximate eccentricity of the ellipse shown below?
A) 0.25
B) 4.0
C) 2.0
D) 0.50
15. What is the eccentricity of an orbit having a major axis length of 100 million miles and a focal distance of 10 million miles? A) 1
Ellipse & Eccentricity Lab
B) 0.01
C) 10
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D) 0.1
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16. According to the Earth Science Reference Tables, which of the following takes the longest time to make one complete spin on its axis? A) Uranus
B) Mercury
C) Earth
D) Jupiter
17. The actual shape of the Earth's orbit around the Sun is best described as A) a slightly eccentric ellipse B) an oblate spheroid C) a perfect circle D) a very eccentric ellipse 18. According to the Earth Science Reference Tables, which planet has a diameter most similar to the Earth's? A) Saturn
B) Venus
C) Jupiter
D) Mars
19. Planet A has a greater mean distance from the Sun than planet B. On the basis of this fact, which further comparison can be correctly made between the two planets? A) Planet A's day is longer. B) Planet A's revolution period is longer. C) Planet A is larger. D) Planet A's speed of rotation is greater. 20. Other than Jupiter, identify one Jovian (GAS GIANT) planet in our solar system.
