<p>I wonder how to calculate the duration of the Sun crossing the line of the horizon on equinox on Pole. For equator I used this formula:</p>
<p><span class="math-container">$t = \frac{2 \times p}{\cos(\phi) \times u}$</span>, where <span class="math-container">$u$</span> - is velocity of the Sun in the sky (<span class="math-container">$15'$</span> per minute), <span class="math-container">$p$</span> is Sun's visual diameter (<span class="math-container">$30'$</span>), <span class="math-container">$\phi$</span> - latitude of observer</p>
<p>On equator everything is easy:</p>
<p><span class="math-container">$\cos(0) = 1$</span></p>
<p>But on Pole:</p>
<p><span class="math-container">$\cos(90) = 0$</span>, but I can't divide by zero.</p>
<p>Is there any other formula?</p>
<p><a href="https://i.sstatic.net/2rg7V.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/2rg7V.png" alt="I used this drawing" /></a></p>

CC BY-SA 4.0
2022-01-23T14:00:11.507Z
Sunrise/set at the poles depends on the Sun's changing declination
Barry Carter
CC BY-SA 4.0
2022-01-23T17:28:29.250Z
The duplicate gives an an answer (32hr 50 min) and explains why.
James K
CC BY-SA 4.0
2022-01-25T11:44:51.037Z
I know that declination of the Sun is zero as it is equinox
ALiCe P.
<the-sun><time><velocity><sunrise><sunset>
How long is the sunrise (or sunset) on North (or South) Pole?
ALiCe P.
# How long is the sunrise (or sunset) on North (or South) Pole?

(Asked by: username_0 on 2022-01-23)

I wonder how to calculate the duration of the Sun crossing the line of the horizon on equinox on Pole. For equator I used this formula:

$t = \frac{2 \times p}{\cos(\phi) \times u}$, where $u$ - is velocity of the Sun in the sky ($15'$ per minute), $p$ is Sun's visual diameter ($30'$), $\phi$ - latitude of observer

On equator everything is easy:

$\cos(0) = 1$

But on Pole:

$\cos(90) = 0$, but I can't divide by zero.

Is there any other formula?

[![I used this drawing](https://i.sstatic.net/2rg7V.png)](https://i.sstatic.net/2rg7V.png)

**Tags:** the-sun, time, velocity, sunrise, sunset

> **Comments:**
> **username_1**: Sunrise/set at the poles depends on the Sun's changing declination  
> **username_2**: The duplicate gives an an answer (32hr 50 min) and explains why.  
> **username_0**: I know that declination of the Sun is zero as it is equinox  

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## 0 answers

