## Changes to day length at solstices vs. equinoxes

Probably dumb question. I am trying to understand why the change in day length from day to day is greatest at the equinoxes and least at the solstices. This effect is greater at higher latitudes (N or S). I'm assuming it has to do with the tilt of the earth's axis relative to the incident sun rays, which is greatest at the solstices (when the sun "stands still"), but I'm too stoopid to work out the geometry to my satisfaction.

I know that the change in day length can be described by a sine wave curve, which demonstrates this effect, but I'm trying to understand why that is the case. For example, the contribution to the equation of time from the earth's orbital speed variation can also be shown as a sine wave curve, but the explanation is given by Kepler's First and Second Laws, Newtonian dynamics, etc. You can go beyond just saying "it's a sine wave curve" and look at the underlying geometry/physics.

I've looked at a lot of animations explaining the mechanism of seasonal change in day length, but I haven't found anything that particularly focuses on this aspect (why the rate of change is greatest at the equinoxes and least at the solstices). Does anyone have a reference to a relatively simple explanation (trig OK, calc gonna be a challenge), animation preferred if possible?
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 Recognitions: Homework Help Welcome to PF; Just to be clear - "change in day length" from what? Anyway, such effects are due to the combination of the Earth orientation at different times of the year and the rotation of the Earth. You should be able to see it by sketing out the positions at the specified times.

## Changes to day length at solstices vs. equinoxes

 Quote by Simon Bridge Welcome to PF; Just to be clear - "change in day length" from what? Anyway, such effects are due to the combination of the Earth orientation at different times of the year and the rotation of the Earth. You should be able to see it by sketing out the positions at the specified times.
Thanks for your reply. I was referring to the change in the length of daylight from day to day at the equinoxes (maximum change) and the solstices (minimal change). I think I need to improve my sketching tools/ability!
 Recognitions: Science Advisor A simple way to see it is to look at it as a math problem. In elementary calculus you learn that the derivative of a function = 0 at local min or max. The solstices are local min and max, so the rate of change (derivative) = 0.

Recognitions:
Homework Help
 Quote by AstroDoug Thanks for your reply. I was referring to the change in the length of daylight from day to day at the equinoxes (maximum change) and the solstices (minimal change).
In that case... what mathman said.