Name______Lab Day A B C D Lab: Modeling Planet Orbits
Objectives: Be able to draw an ellipse and locate the foci and major axis Be able to calculate eccentricity of drawn ellipses Be able to evaluate eccentricity and compare values to solar system observations
Materials: Colored pencils (or markers), two push pins, cardboard surface, tabloid paper (11x17), calculator, loop of dental floss (recycled), ESRT
Background: Briefly state Kepler’s FIRST law of planetary motion. ______
Vocabulary:
Orbit: ______
Ellipse: ______Focus/Foci: ______
Major Axis: ______
Procedure:
1. Fold the paper in half, then in half again as instructed. The folds intersect at the center of the paper. This will be the location of your primary focus. 2. Tape the corners of the paper to the cardboard base. Be sure to flatten the folds as much as possible. 3. Stick a pin in the center of the paper. This is your primary focus. 4. Place your loop of string around the pin. Draw, in RED, your first shape as modeled by your instructor. Use RED. 5. Along the fold line (major axis), place the second pin 1cm from the primary. Place the floss around both pins and draw a BLUE ellipse. 6. Now move the secondary focus 2cm from the first pin (along the major axis) and draw a GREEN ellipse. 7. Move the secondary focus 5cm from the primary and draw an ORANGE ellipse. 8. Move the secondary focus 10cm from the primary and draw a BLACK ellipse.
Using a calculator and your ESRT, complete the eccentricity calculations that follow. Calculations: Follow the directions and record your calculations in the boxes provided. Step 1: Write the formula for Eccentricity (ESRT) Ecc= ______
Step 2: Measure the length of the major axis for the RED ellipse to the nearest tenth of a cm. Plug your values into the equation. Remember to include units. Ecc= ______
Step 3: Solve the math and record the value to the nearest hundredth. Remember, like units cancel out (cm/cm=1).
Ecc=
Eccentricity of BLUE ellipse:
Step 1:
Step 2: (Length to nearest tenth)
Step 3: (Round answer to nearest hundredth) Eccentricity of GREEN ellipse: Step 1:
Step 2:
Step 3:
Eccentricity of ORANGE ellipse:
Step 1:
Step 2:
Step 3:
Follow-up: Eccentricity of BLACK ellipse: Step 1:
Step 2:
Step 3:
1. Your changing the distance between the foci had an effect on the eccentricity. In the space below, sketch a graph showing the relationship between the eccentricity of the ellipse and the distance between the foci.
2. Imagine drawing ellipse after ellipse, each time moving the push pins closer and closer together, until they are both in a single hole at the center of your page. What shape would that ellipse be? ______(look at the RED shape)
What would the eccentricity of that ellipse be? ______. Explain how you know this: ______3. Now imagine drawing ellipse after ellipse again, but this time moving the push pins farther and farther apart. Imagine the string is stretched as tightly as possible between the pins, to the point where the distance between the foci is equal to the length of the major axis. What shape would that ellipse be? ______
What would the eccentricity of that ellipse be? ______. Explain how you know that: ______4. What is the maximum eccentricity that an ellipse can have? ______
a) What is the shape of an ellipse with that eccentricity? ______
3. What is the minimum eccentricity that an ellipse can have? ______
a) What is the shape of an ellipse with that eccentricity? ______
Refer to your ESRT to answer the following questions.
4. Which color ellipse that YOU drew is most similar in eccentricity to the Earth’s path around the sun? ______
5. According to the ESRT, which PLANET’s orbit is closest to being a circle? ______
6. Which PLANET’s orbit is most eccentric? ______
7. In the orbits you drew, what is the name of the location of the sun? ______8. Describe the change in the LOOK or APPEARANCE of the orbits as the distance between the foci increases.
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Calculate the eccentricity of the ellipses below. Show your work (three steps) in the boxes provided.
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