Yesterday I climbed Cime du Cherion and to my surprise
[I saw Corsica](http://grulicueva.homenet.org/~mdione/PhotoShow/?f=trips%2F2016%2FGr%C3%A9oli%C3%A8res-les-Neiges%2F2016-04-14T11.22.43.jpg)[^0].
Then a friend of mine pointed me to
[an article](http://m.nicematin.com/nice/pourquoi-voit-on-si-bien-la-corse-depuis-la-cote-dazur.1955539.html)
explaining that if you manage to see the island from the coast is because a
mirage in a dry air layer 1000m high due to the Föhn's effect.
It's notable that the
[French Wikipedia article](https://fr.wikipedia.org/wiki/Effet_de_foehn) about
this effect is way more complete than the English one.

Punta Minuta (2556m) is one of the highest points in Corsica close to the
northwestern coast. Cime du Cherion is 1778m. The distance between them is[^1]:

    surface_distance= 225.11km

[Earth's mean radius](https://en.wikipedia.org/wiki/Earth)[^2] is:

    km_per_radian= 6371km

which is also by definition the length of a radian on
[the theoretical surface of the Earth](https://en.wikipedia.org/wiki/Figure_of_the_Earth)[^3].
Those two mountains are then separated by an angle of:

    alpha= 225.11km/6371km= 0.035333 radians.

or a little more than 2°[^4]. According to
[this](https://en.wikipedia.org/wiki/Circular_segment), the sagitta is then:

    sagitta= km_per_radian*(1-math.cos (alpha/2))= 0.994215km, or 994.215m.

This means that is *is* possible to see the last 1.5km of Punta Minuta from Cime
du Cherion and almost anything above around 1000m, which is quite a lot of
Corsica, but definitely not what I saw.

In conclusion, we were both right, but him more than me :) And yes, I'm ignoring
there is an angle between both points; if we take that in account and assume that
Cime du Cherion is at 0°, then the projection of Punta Minuta over the secant
that passes through those points is:

    projection= math.sin (0.035333)/0.035333*2556m= 2555.46m

A little over half a meter :) Doesn't really change much in the calculations.

Last, a graph showing the height of the sagitta in function of the distance,
quite surprising!

![](/images/sagitta-vs-distance-on-Earth-surface.png)

[^0]: Name in corsican :)

[^1]: Measured with [marble](https://marble.kde.org/).

[^2]: From the same page, polar radius is 6356.8km and equatorial is 6378.1km.
      We're measuring points between 42°20' and 43°50'N, so using the median is not
      that crazy.

[^3]: Don't go there.

[^4]: Another fun fact: 1° is about 111km.