<p>This is a consequence of geometry: consider a cross section of the Earth through the poles, so that it can represented as a circle. Given a place at latitude <span class="math-container">$\lambda$</span>, the horizon is equal to the <a href="https://en.wikipedia.org/wiki/Tangent" rel="nofollow noreferrer">tangent</a> of the circle at that point. The tangent of a circle makes a 90 degree angle with the 'line from the place through the Earth's center', so the angle between Polaris and the horizon (Polaris' altitude) is the same angle as between the equator and the 'line from the place through the Earth's center'.</p>
<p>I've drawn Polaris quite close to Earth; the reason this works for <em>all</em> places is that in fact it's very far away (compared to the Earth's size), but always in the same direction (straight up North).</p>
<p><a href="https://i.sstatic.net/o1XSL.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/o1XSLm.jpg" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-11-01T20:35:16.263Z
2021-11-01T20:35:16.263Z
Glorfindel
<p>How to prove geometrically that the altitude of Polaris is equal to the latitude?</p>
<p>I have seen in handouts that the altitude of the pole star gives the latitude of that place.</p>

<coordinate><positional-astronomy><pole>
Altitude of Polaris is latitude
Particle king
# Altitude of Polaris is latitude

(Asked by: username_0 on 2021-11-01)

How to prove geometrically that the altitude of Polaris is equal to the latitude?

I have seen in handouts that the altitude of the pole star gives the latitude of that place.

**Tags:** coordinate, positional-astronomy, pole


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## 1 answers

### Answer by username_1 on 2021-11-01. Score: 4 | Accepted answer

This is a consequence of geometry: consider a cross section of the Earth through the poles, so that it can represented as a circle. Given a place at latitude $\lambda$, the horizon is equal to the [tangent](https://en.wikipedia.org/wiki/Tangent) of the circle at that point. The tangent of a circle makes a 90 degree angle with the 'line from the place through the Earth's center', so the angle between Polaris and the horizon (Polaris' altitude) is the same angle as between the equator and the 'line from the place through the Earth's center'.

I've drawn Polaris quite close to Earth; the reason this works for *all* places is that in fact it's very far away (compared to the Earth's size), but always in the same direction (straight up North).

[![enter image description here](https://i.sstatic.net/o1XSLm.jpg)](https://i.sstatic.net/o1XSL.jpg)


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