A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2017 Jul 22, 17:10 -0700
Ron Jones, you wrote:
"I think Kepler's second law accounts for the Equation of Time see attached."
It accounts for about half of it. The other half is just geometry due to the inclination of the Earth's axis. Imagine this: if the Earth had no tilt, then the varying speed of the Earth's motion (Kepler II) would be the only effect to consider. In that case, a graph of the equation of time, graphed over the course of a year, would be a simple annual sinusoidal curve (and the analemma would be an ellipse). On the other hand, if the Earth's orbit were perfectly circular, but tilted 23.5° as it is now, then the equation of time would be a semi-annual sinusoidal curve (and the analemma would be a symmetrical figure-eight). Since we have both an eccentric orbit and also an axial tilt, the two effects combine yielding a mixed sinusoid with two greater maximum/minimum points and two lesser max/min points every year (and the analemma ends up as an asymmetrical figure-eight-like shape). So it's really both factors and in about equal measure. But when it comes to explaining things to introductory students, I usually explain the Kepler II portion of it and only mention that there's "more to it". I find that the varying orbital speed is familiar to many people, and they can visualize its effect on the Sun's daily motion without much trouble.