Earth’s orbit is an ellipse with eccentricity 0.016. Thus, earth’s distance from the sun and speed as it moves around the sun varies from day to day. This means that the length of solar day is not constant through the year. Assume that the earth’s spin axis is normal to its orbital plane and find out the length of the shortest and the longest day. A day should be taken from noon to noon. Does this explain variation of length of the day during the year?

From the geometry of the ellipse of eccentricity e and semi-major axis a, the aphelion and perihelion distances are