The Hardest Part of a Sundial is the Sun
Turns out that when the sun is at its highest point isn’t actually noon. At least not 98.9% of the year
Instead, the sun will appear at the highest point in the sky anywhere from 11:46am to 12:16pm, a surprisingly large discrepancy
The reason: the Earth orbit isn’t circular and the Earth had a tilt
The Earth’s orbit has a small eccentricity, but this is enough for the Earth’s orbit to be close enough to an oval instead of a circle that it will have an effect. Because of eccentric orbit of the Earth and Kepler’s Laws, there are parts in the orbit where the Earth speeds up or slows down as it is closer or further from the sun. As a result, the Earth can be either ahead or behind where it might be expected if the orbit was perfectly circular. This is the effect of eccentricity
The tilt of the Earth relative to the plane of the solar system ranges but is about 23.4 degrees. This is what causes seasons but also has an impact on the length of a day. Because of the tilt in the Earth’s orbit, the sun’s apparent position and motion along the ecliptic will vary when viewed from the Equatorial plane. This is the effect of obliquity
Combined together, the sum of the change caused by the eccentricity and obliquity form the Equation of Time (or at least form the largest contributing factors)
Equation of Time = (Where the Sun is) - (Where the Sun Should Be)
This is the simplest form of the Equation of Time. Everything is always changing. The eccentricity of the Earth changes over time, by about 2 degrees, as well as the obliquity, so the exact amount of time difference varies every year
This is a non-trivial problem but this is best discussion for learning about the components of the Equation of Time:
Provides much information and images on the EQUATION OF TIME. What it is. Its Components, How to calculate it. How it used in astronomy . H
