Those long summer days...

Classical Mechanics Level 5

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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