Question

eccentricity = \frac{distance between foci}{length of the major axis}

1. 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
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?

created by s. dice
10/05/15 2

Explanation:

Step1: Recall eccentricity formula

The formula for the eccentricity $e$ of an ellipse is $e=\frac{\text{distance between foci}}{\text{length of the major axis}}$.

Step2: Analyze effect of foci distance on shape

If the foci are farther apart while the length of the major - axis remains the same, the value of the eccentricity $e$ increases. An ellipse with a higher eccentricity is more elongated.

Step3: Understand eccentricity - roundness relationship

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

Step4: Know Earth's eccentricity

The Earth's orbit has an eccentricity of approximately $e = 0.0167$. We would need the values of the eccentricities of the six ellipses (which are not given in the problem - statement but would be calculated using the formula $e=\frac{\text{distance between foci}}{\text{length of the major axis}}$) to determine which one is closest to the Earth's eccentricity.

Answer:

1. The ellipse would become more elongated.
2. The closer the eccentricity is to 0, the more nearly round the ellipse appears; as the eccentricity approaches 1, the ellipse becomes more elongated.
3. Cannot be determined without calculating the eccentricities of the six ellipses using the given formula.