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How long is the day at any latitude and tilt?

The hours of daylight at any latitude, on any day of the year, for any axial tilt.

°

North is positive and south is negative. London is about 51.5. From −90 to 90°.

°

Earth’s is 23.44°. With no tilt there are no seasons. From 0 to 90°.

Day 172 is 21 June and day 355 is 21 December. From 1 to 366.

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Daylight

12 h

At latitude 0°, on a planet tilted 23.44°, the Sun is above the horizon for 12 h on day 172 of the year.

Latitude where the Sun is overhead
23.4°
Latitude of the polar circles
66.56°
The Sun stays up all day
no
The Sun stays down all day
no

Try an example

How it is worked out

g = 357.529 + 0.98560028*dq = 280.459 + 0.98564736*dL = q + 1.915*sin(g) + 0.020*sin(2*g)decl = asin(sin(tilt)*sin(L))H0 = acos(-tan(lat)*tan(decl))day = 2*H0/15

Where the numbers come from

Keep in mind

Geometric: the Sun’s centre at the horizon. Refraction (+0.83°) plus the Sun’s half-disc add ~5-8 min at mid-latitudes; true sunrise/sunset need those corrections.

Address
https://clipwright.studio/tools/day-length-by-latitude?latitude_deg=0&tilt_deg=23.44&day_of_year=172

Anyone who opens this address sees the same answer.

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