The distance to the horizon depends on the viewer's point of view. Since the earth is a sphere, height is important.
The distance of the horizon: How far away it is
The distance to the horizon depends on the observer's height above sea level. The reason for this is the spherical shape of the earth.
- The surface of the Earth is curved. When you are on the surface of the Earth, this curvature blocks your view of points further away. The higher you are, the further you can see beyond this curvature.
- From an elevated vantage point, the line of sight is further away before it touches the earth's surface. You have a wider angle of view, which increases the distance to the horizon.
- The distance can be easily calculated using the Pythagorean theorem. For the calculation, you need the equator radius, which is approximately 6378 kilometers, and the observer's eye height, which you can generally set at 2 meters at sea level. The altitude can be added to the 2 meters.
How the distance of the horizon is calculated
To illustrate the calculation, you can draw the situation. First, draw a circle with a compass. On the edge of the circle, draw a little man. Now draw a straight line from the man (h) to the center of the circle and a straight line (e) from the man's head to the edge of the circle. Draw a straight line (r) between end point of straight line e and the center. This creates a right-angled triangle, where the right angle between the end point of e and r is located.
- You now know the Earth’s radius r With a value of 6378 kilometers and h as the viewer’s viewing height with 2 meters. The distance to the horizon as e is still unknown to you.
- About the unknown e The Pythagorean theorem helps to calculate a^2 + b^2 = c^2. Applied to our data, the formula is (r+h)^2=r^2+e^2. You know e but not, which is why you need to change the formula.
- Algebra will help you here. You want to find the unknown e alone on one side and therefore take r on the other side: (r+h)^2-r^2=e^2.
- To get concrete numbers, you need the root sign√. The formula is now √((r+h)^2-r^2)=e.
- Now the numbers are inserted √((6378000+2)^2-6378000^2)=e. Since you want to calculate in meters, you have to use the 6378 kilometersAdd three more 0s. The conversion has already taken place in the formula.
- The final result is then 5050. This means that at a height of 2 meters above sea level, you will see the horizon at a distance of approximately 5000 metersi.e. 5 Kilometersee.
- Assuming you are 262 meters above sea level and add your viewing height of 2 meters, the calculation is: √((6378000+264)^2-6378000^2)=e. e is then equal to 58031. So you see the horizon at a distance of 58 kilometers.
- Of course, a clear view is always a prerequisite. If the view is blocked by houses, there is a high mountain in the field of vision or visibility is restricted by fog or something similar, this value is of course not correct.
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