Seeing Corsica from France

Yesterday I climbed Cime du Cherion and to my surprise I saw Corsica¹. Then a friend of mine pointed me to an article 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 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 is²:

surface_distance= 225.11km

Earth's mean radius³ is:

km_per_radian= 6371km

which is also by definition the length of a radian on the theoretical surface of the Earth⁴. Those two mountains are then separated by an angle of:

alpha= 225.11km/6371km= 0.035333 radians.

or a little more than 2°⁵. According to this, 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!