Measuring the Eccentricity of the Terrestrial Orbit: an experiment in the classroom

Summary

The eccentricity is very small

Most textbooks of physics present the terrestrial orbit by a drawing which shows an ellipse of substantial eccentricity. This suggests a remarkable variation of the distance between Sun and Earth during the year up to a value of about 3:1 and more. Imagine the dramatic variation in size of the radiating area of the Sun seen by the terrestrial inhabitants with all the terrible consequences for temperature. All this is not true. There is no obvious change in size of the solar disc.

In nature the numerical eccentricity of the terrestrial orbit is only ∈ = e/a = 0.01675 (a = major or long axis, b = minor or short axis, e = focal length). This value is so small, that this ellipse cannot be distinguished from a circular orbit in a drawing when using a normal pen (a/b = 1.00014). The deviation would be 1/20 of the width across the line of the pencil. By what procedure would it be possible to measure this small eccentricity using only simple means in the classroom?

Observe the varying size of the solar disc

A first approach could be the idea to take photographs of the Sun throughout the whole year. The angular width of the solar disc varies by about 3% within this period. The focal length f = 50 mm of a normal camera produces an image of the Sun, which is 0.4 mm in diameter on the film. Trying to determine the eccentricity from these pictures better than 10% would mean ability to measure difference of 1μm in size on the film.