Those long summer days...

Estimate the time difference between the longest amount of daylight in one day and the shortest amount of daylight on one day in seconds over the course of a year if you lived on the Earth's equator with the assumptions below.

Note: this is not the difference between solstices as we are adjusting the earth's rotation axis to be perpendicular to the orbital plane.

Details and assumptions

• The furthest distance from the Sun to Earth is $$d_f = 1.521 \times 10^8 ~\mbox{km}$$.

• The shortest distance from the Sun to Earth is $$d_s = 1.47 \times 10^8~\mbox{km}$$.

• To simplify the problem, assume that the Earth's axis is always perpendicular to the plane of its trajectory around the Sun.

• The Sun always shines on half of the Earth.

• There are 24 hours in a day and 365.25 days in a year.

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