Difficulty level: Middle or High School

Class time: 30 minutes or less

In this lesson, students will analyze data from solar magnetogram images collected over 25 years at the National Solar Observatory Vacuum Telescope at Kitt Peak, AZ. Students use the data and graph constructed in the lesson "Aphelion and Perihelion Pt. 2" to determine the eccentricity of the earth's orbit.

You should be able to answer the following when you have completed this exercise:

1. What is the eccentricity of the earth's orbit?
2. Determine the degree of error in your estimate of the eccentricity.

Going Further: after completing this lesson, find out how the shape of the earth's orbit may be responsible for changes in our planet's climate. Do a search on the internet for the Milankovitch Theory.

In 1601, Johannes Kepler determined that the orbits of the planets were elliptical in shape, rather than circular as was previously thought. An ellipse is a flattened circle, like an oval or egg in shape and can be defined mathematically as the ratio of the distance between the foci and the major axis. Eccentricity is a measure of how circular the orbit of a planet or satellite is. For a perfectly circular orbit the eccentricity is zero; elliptical orbits have eccentricities between zero and one.

From the graph your students constructed in the lesson, "Determining Aphelion and Perihelion 2" estimate the maximum and minimum sizes of the sun in pixels.

Eccentricity is equal to the ratio of D - d to D + d where D is the largest diameter and d is the smallest diameter.

For the projected trend line on the graph below:

D = 430 pixels; d = 417.5 pixels
D - d = 12.5 pixels; and, D + d = 847.5 pixels

Ratio of D - d to D + d is 1:67.8

The accepted eccentricity for earth's orbit is 1:60.

Have your students construct graphs like the one below for as many consecutive years as possible and compare their calculations of eccentricity. Why is there variation from one year to the next for this calculation?