The distance to the horizon, also known as the “horizon distance,” is the maximum distance at which objects on the Earth’s surface can be seen before they disappear from view due to the curvature of the planet. The actual distance to the horizon depends on two primary factors: the observer’s height above the ground and the Earth’s radius.

At ground level, the horizon distance is roughly calculated using the formula:

d = √ 2⋅R⋅h + h^{2}

where:

- $d$ is the horizon distance,
- $h$ is the height of the observer above the ground, and
- $R$ is the radius of the Earth (approximately 6,371 kilometers or 3,959 miles).

For example, if an observer is standing at ground level (height $h=0$) on a perfectly flat surface, the horizon distance would be approximately 4.7 kilometers (2.9 miles). If the observer climbs to an elevation of 100 meters (328 feet), the horizon distance increases to about 35.7 kilometers (22.2 miles).

This increase in horizon distance as the observer’s height increases is due to the curvature of the Earth. As the observer’s line of sight rises above the surface, they can see objects that were previously hidden by the Earth’s curvature. The higher the observer’s vantage point, the farther they can see.

It’s important to note that the calculations above assume a clear line of sight without any obstructions such as buildings, trees, or terrain. Additionally, atmospheric conditions can also impact visibility, especially over longer distances.

Understanding the concept of the horizon distance has practical applications, such as in navigation, aviation, and telecommunications. For instance, when sailing or flying, knowing the horizon distance can help pilots and sailors anticipate when objects or landmarks will come into view as they approach.

In summary, the horizon distance is the maximum distance at which objects on the Earth’s surface can be seen before disappearing due to the planet’s curvature. It is influenced by the observer’s height above the ground and the Earth’s radius, and its calculation can be used in various fields to estimate visibility over different distances.