Question

investigation plan: 1. measure the distance between the foci - the sun and the other point inside the ellipse. record in the first column below. 2. measure the length of the major axis - the longest diameter of the ellipse. record in the second column below. 3. calculate the eccentricity (\out of roundness\) using the equation below and write your answer in the third column. eccentricity = \\(\frac{distance\\ between\\ foci}{length\\ of\\ the\\ major\\ axis}\\) 4. continue steps one through three for the remaining ellipses. observations: | ellipse | distance between foci (mm) | length of major axis (mm) | show your work here | eccentricity | |---|---|---|---|---| | 1 | | | | | | 2 | | | | | | 3 | | | | | | 4 | | | | | | 5 | | | | | | 6 | | | | | application: 1. what would happen to the shape of the ellipse if the foci were farther apart? 2. what is the relationship between the eccentricity of an ellipse and how nearly round the ellipse appears to be? 3. of the six ellipses, which one do you think is closest to the earths eccentricity?

Explanation:

Step1: Measure distances

Use a ruler to measure the distance between foci and length of major - axis for each ellipse and record in the first two columns of the table.

Step2: Calculate eccentricity

For each row in the table, use the formula $Eccentricity=\frac{distance\ between\ foci}{length\ of\ the\ major\ axis}$ to calculate the eccentricity. Write the calculation process in the "Show your work here" column and the result in the "Eccentricity" column.

Step3: Analyze shape - focus relationship

If the foci are farther apart while the length of the major axis remains the same, the eccentricity increases, and the ellipse becomes more elongated.

Step4: Understand eccentricity - roundness relationship

The closer the eccentricity is to 0, the more nearly round the ellipse appears. As the eccentricity approaches 1, the ellipse becomes more elongated.

Step5: Estimate Earth - like eccentricity

The Earth's orbit has an eccentricity of about 0.0167. Compare the calculated eccentricities of the six ellipses to this value to determine which one is closest.

Answer:

1. The ellipse would become more elongated.
2. The closer the eccentricity is to 0, the more nearly round the ellipse appears; as it approaches 1, the ellipse becomes more elongated.
3. Compare the calculated eccentricities of the six ellipses to 0.0167 to determine which one is closest. (Since no actual measurements and calculations are done for the six ellipses in the table, a specific ellipse number cannot be given.)