Hi, can you explain to me why the day length rate of change varies and why it is greatest at the equinox?

The rate of change of the length of the day is not constant but rather sinusoidal. The main reason for this effect is that the Earth's axis is tipped over about 23.5° from vertical. This produces that the fraction of the 24 hour day that a person in a given location of the earth spends on the lit up portion of the earth changes along the year.

This is a little hard to imagine but a drawing might help. On picture 1 we can see what happens if the Earth's axis were not tilted. The day would be the same length throughout the year, and there would be no solstice or equinox. Now, on picture 2, at the time of the Equinox we can see that the length of the day is equal to the length of the night. At the time of the solstice (in this case is summer), the length of the day is maximum (minimum in winter). The rate of change does the opposite as the length of the day: when the length is maximum the rate of change is minimum and viceversa.

Maria Fernanda Duran Sierra - UC Santa Cruz Graduate Student