Question

If the Earth were perfectly flat with no mountains, valleys, etc., how far away should you be able to see? Is this distance possible anywhere in our world?

Answer 1

If the Earth were perfectly flat with no mountains, valleys, or any other obstacles, the distance you could see would be determined by the curvature of the Earth. The curvature of the Earth can be approximated by the formula for the Earth's radius, which is approximately 6,371 kilometers (3,959 miles). This means that for every kilometer or mile you move away from a point, the Earth's surface will drop by about 8 centimeters or 5 inches respectively.

To calculate the maximum visible distance, you can use the formula for the horizon distance, which is derived from the Pythagorean theorem. The formula is:

$d=\sqrt{2Rh}$

Where:

• $d$ is the maximum visible distance,
• $R$ is the radius of the Earth, and
• $h$ is the height of the observer above the Earth's surface.

If you assume an average eye height of about 1.7 meters (5.6 feet) for a standing person, you can calculate the maximum visible distance using this formula. Plugging in the values:

$d=\sqrt{2\times 6,371\times 1.7}$

The result of this calculation is approximately 83 kilometers (51.6 miles). This means that in ideal conditions, without any obstacles, you would be able to see objects up to 83 kilometers (51.6 miles) away.

However, it's important to note that in reality, various factors like atmospheric conditions, the presence of objects in the line of sight, and the height of the observer can affect visibility. So, in practice, it may not always be possible to see the maximum visible distance.

Furthermore, it's worth mentioning that there are no perfectly flat areas on Earth without any variations. Even in the most open and flat terrains, there will always be minor variations due to factors like wind, water flow, and geological processes.