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Question of Théo and Sarah (01.31.2023): How far away is the horizon when looking at
the sea?
R:
Here is a table containing different heights in relation to sea level, to give you an idea:
You are lying on the sand and look at the sea at 20 cm from the ground  1.60 km 
A standing adult, estimating his eyes at 1.70 m tall  4,65 km 
The tallest man in the world, Robert Wadlow 2.72m, estimating his eyes at 2.55m tall  5.70 km 
Depuis le pont du navire de Blackbeard, on his frigate the Queen Anne's Revenge, at 6 m high  8.74 km 
From the lookout of the frigate Hermione at 50 m high or from the top of a lighthouse.  25.24 km 
From the top of the spire of the Notre Dame de Paris cathedral, 96 m high  34.97 km 
On top of the Eiffel Tower, 300 m high  61.83 km 
On top of the Burj Khalifa Tower to Dubaï, 828 m high / 163 floors  102.72 km 
On top of the Mont Blanc, 4 808 m high  247.54 km 
On top of the Everest, 8 848 m high  335.77 km 
from an aircraft at an altitude of 10,000 m  356.96 km 
Try the horizon calculator
Enter the height you want in meters, and observe the result.
Formula:
where d = distance, R = radius of the earth or 6371.009 km, h = height of the point of view towards the horizon.
We use km for d and R and meters for h, so it must be divided by 1000.
The right questions!
« And if I use binoculars, can I see further? »
Paradoxically, no! This does not change anything because considering an object on the water and because of the curvature of the earth, it is not possible to see behind the horizon. Hence the use of the radius of the earth in the formula.
« What about atmospheric disturbances and other natural elements that interfere with the view? »
Indeed, there are many factors that can vary the distance to the visible horizon, such as:
 the relief of the waves,
 the refraction of the electromagnetic waves according to the nature of the atmosphere, which causes a kind of lifting of the horizon, which moves away the limit. This can reproduce the effect of mirage as if the earth was "less" round.
 the curvature of the earth,
 the temperature,
 thehumidity,
« I read that the earth was not round, so the radius R is not the right one? »
Indeed, the earth is not round, it has rather an elliptic shape, very light of course.
The equatorial radius of the Earth is 6,378.137 km, the polar radius is 6,356.752 km, the radius from the bottom of the Arctic Ocean is 6,352.8 km, the radius from the summit of Chimborazo is 6,384.415 km, the bottom of the Arctic Ocean is a delta of about 32 km.
The formula therefore takes into account the average radius, i.e. 6,371.009 km, which is the unit of length used in fields such as astronomy and geology.
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