Day Length and the Equation of Time
Daylight length follows a sine curve almost perfectly — almost. This explores the extra wobble caused by Earth's tilted, elliptical orbit.
Where this idea comes from
Start here — these are the sources that inspired this exploration.
Introduction
A plain sinusoidal model gets you close to real daylight-length data, but not exact. The gap comes from two effects layered on top of each other: Earth's axis is tilted, and its orbit is elliptical, so it moves faster in January than in July. This combination, called the equation of time, is why the earliest sunset of the year in the northern hemisphere falls well before the winter solstice, and the latest sunrise falls well after it. Fit a plain sine curve to daylight-length data for one location, then look at where it misses, and see if you can explain the gap using the equation of time rather than just latitude.
Guiding Questions
- Fit a plain sinusoidal model to a year of daylight-length data for one location. Where are the residuals largest?
- Look up the equation of time for your location. How does it explain the gap between your sinusoidal model and the real data?
- Why does the earliest sunset of the year fall before the winter solstice, not on it? Use your model plus the equation of time to explain the date.
- Would adding a second, smaller sinusoidal term improve the fit more than a single sine curve does? Test it.