Loudoun County Public Schools



Name __________________________________________ Date ______________ Block ____________ Lab Activity—Drawing Planetary Orbits Earth Science Purpose: to demonstrate Kepler’s First Law of Planetary Motion by calculating the eccentricity of ellipses.Objectives: Upon completion of this laboratory exercise, students will be able to:Define the words: eccentricity, ellipse, and fociCalculate the eccentricity of an ellipseDescribe how the eccentricity changes as the distance between foci changesExplain Kepler’s First Law of Planetary MotionDescribe how Earth’s orbit compares to any given orbitDescribe the shape of an ellipse with an eccentricity of 0.00 or 1.00Give an example of a celestial object with a highly eccentric orbitDescribe Earth’s orbital shapeProcedure: Tie a piece of string into a loop of approximately 10 centimeters Place a piece of white paper on the cardboard square (may secure with a small piece of tape)In the center of the piece of paper, place the two pushpins approximately 2.0 cm apart.Mark one of the holes “F1” for focus 1 and the other “F2” for focus 2.Take the loop of string and place it over the two pushpins.Using one hand, place a finger on top of each pushpin.Using the other hand, take a colored pencil put it inside the looped string and stretch it out as far as it goesSlowly move the pencil around the two pushpins keeping the string tight at all times. Only move your fingers that are on top of the pushpins when necessary.Length of major axisUse the ruler to draw a line that runs from the outside of the ellipse through the two foci as shown below.F1F2Foci distance Measure the distance of the length of the major axis to the nearest tenth of a centimeter and record your results in the data table below.Ellipse NumberDistance between Foci (cm)Length of the Major Axis (cm)1. F1 - F22.02. F1 - F35.03. F1 - F47.04. F1 - F59.0Return one of the pushpins to the focus marked “F1” and this time place the second pushpin approximately 5.0 cm away and mark it “F3”. Repeat steps 5-8 using a different colored pencil.Measure the distance of the major axis to the nearest tenth of a centimeter and record your results in the data table above.Repeat procedure with “F4” marked 7.0 cm away and “F5” marked 9.0 cm. On pg. 706 in the Earth Science Book to look up and record the formula used to calculate the eccentricity of an ellipse below. Record the eccentricity formula in this space:Using the formula and your data, calculate the eccentricity of each of the ellipses. Record your results to the nearest thousandth (3 decimal places). Show all work!Ellipse # 1Ellipse # 2Ellipse # 3Ellipse # 4Questions:1. Describe the relationship between the distance between the foci and the eccentricity of the ellipse. ___________________________________________________________________________________________________________A. What is the maximum value that an eccentricity can be? ___________________B. What shape would this be? ___________________C. What is the minimum value an eccentricity can be? ___________________D. What shape would this be? ___________________E. If there were only one pushpin used, what would be the shape of the ellipse? ___________________F. What would its eccentricity be? 2. Which of the four ellipses you drew do you believe is the most similar in eccentricity to the Earth’s orbit? ___________ Why? ______________________________________________________________________3. Using the data below, calculate the eccentricity of Earth’s orbit to the nearest thousandth. (3 decimal places)Length of Major Axis299,000,000 kmDistance Between Foci 5,083,000 km_______________ = Earth’s Eccentricity 4. Compare the eccentricity of Earth’s orbit with the eccentricity of the ellipses you drew: Which is more round—ellipse #1-4 or Earth’s Orbit?___________________ How can you tell?______________________________________________________5. ___________________________ Compared to the other planets in our solar system (Pluto is not included), which planet has an eccentricity most similar to one of the ellipses you drew?6. ___________________________ In step #4 of the Procedure, you labeled one foci “F1” and the other “F2”. If you were to draw the Earth’s orbit, what celestial object would be one of the foci? 7. The diagram below represents an object’s orbit around the Sun. Draw an ‘X’ where the other foci would be located. ................
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