Why Can You See 100 Miles Out to Sea When the Earth is Round?

The idea that the Earth is round and yet we can still see objects far beyond the horizon is often puzzling. The apparent contradiction is resolved through a combination of basic trigonometry, atmospheric refraction, and careful observation. Let’s explore how this visual phenomenon can be explained and why it is not a contradiction.

Understanding the Basics

When we look out at the horizon, it often seems impossible to see beyond 100 miles, given that Earth is a sphere. However, this is possible because of the curvature of the Earth and atmospheric refraction.

Atmospheric Refraction

Atmospheric refraction can bend light, allowing us to see objects that are slightly beyond the horizon. This happens because the air near the Earth's surface is denser than the air above it, causing light to bend slightly. This effect is not just theoretical but can be observed and quantified.

Visual Experiments

Let’s look at some actual visual experiments to illustrate how this works.

Example 1: Looking from San Bernardino

From an elevation of 3304 meters on San Bernardino, you can see a point 200 kilometers away on Thirst. At first glance, this might seem impossible since the Earth's curvature would block such a distant view. However, when you take into account refraction, it becomes clear that the light is being bent, allowing you to see beyond the horizon.

Applying the formula and considering 8/7 Earth radius refraction:

6371 * (8/7) 7281.143 km (rounded to 7280 km)

This means from 3.3 km up, the observer can see to the horizon at 7280 km and to the other side of the triangle at 7283.3 km, making the distance to the other side 219 km beyond Thirst.

Example 2: Looking from Cayambe and Yr Wyddfa

Results from these elevations are equally astounding. From Cayambe at 5790 meters and Yr Wyddfa at 1085 meters, you can see distant points and even beyond the horizon. These experiments demonstrate that the Earth is not blocking the view but bending the light, allowing us to see much farther.

Photographic Evidence

Photographic evidence is perhaps the most compelling way to understand this phenomenon. Let's consider some specific examples:

View from Two Hills

From 849 meters up on one hill looking at a mountain 1003 meters up and from 802 meters up on Cadair Idris, which is even farther away, you can see these distant points and even beyond the horizon. The order of appearance in the photographs does not necessarily match the order of height, but rather the visual distance and atmospheric refraction.

View from Rainier

Looking from 4392 meters up on Rainier, you can see Jefferson, Hood, Adams, and North Sister in a specific order that doesn’t match their actual elevation but rather the visual distance. This is further confirmed by the calculations:

3201 meters and 3158 meters with a 43-meter difference 3286 meters asl (above sea level), 164 km away, 1.0 degree down 3027 meters asl, 242 km away, 1.2 degrees down 3106 meters asl, 306 km away, 1.4 degrees down

Using trigonometry, the peaks are calculated as:

2.862631 km down from Rainier 5.068066 km down from Rainier 7.476246 km down from Rainier

This places sea level under each peak:

1756.631 meters down from Rainier 3703.066 meters down from Rainier 6190.246 meters down from Rainier

The reciprocal of 0.065 is 15.126, and when divided by 12.742, it is 1.187 or 19/16. This means 65 mm times the square of the distance in km matches the Earth’s curvature with 19R/16 refraction.

Conclusion

While the Earth being round seems to block distant views, atmospheric refraction, combined with careful observation and calculation, explains why we can see far beyond the expected horizon. These phenomena are not contradictions but rather manifestations of the complex interplay between the Earth's curvature and atmospheric conditions.

Key Takeaways

Atmospheric refraction allows light to bend, enabling us to see objects slightly beyond the horizon. Visual experiments and photographic evidence support the phenomenon. Subtle differences in elevation and distance explain the observed order of appearance in visual and photographic observations. Understanding Earth curvature and refraction can resolve the seeming impossibility of seeing 100 miles out to sea when the Earth is round.

By recognizing these factors, we can better appreciate the beauty and complexity of our natural world.