It’s common knowledge that the length of a day (time from sunrise to sunset) varies over the year and with one’s location on the earth. Given only the following, can you derive an approximate equation for the length of a day (in hours) of any specific location on the earth, on any given day of the year?

1) The inclination of the earth’s rotational axis is 23.45 degrees

2) The length of a day is exactly 24 hours

3) The length of a year is exactly 365 days

4) Location on earth is given by the latitude

You are allowed to ignore secondary (but real!) effects such as the earth’s non-circular orbit, the sun being a disc, refraction of sunlight by the atmosphere, etc. To allow easier comparison of different solutions, let’s also assume that North Latitude is positive, and that the Winter Solstice in the Northern Hemisphere is “day 0” (Hint: therefore also day 365!) of the year.

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Posted by cogap on 2024-11-02 08:05:58