How Can You See Mountaintops from Across the Ocean: Debunking the Myth of Earth’s Curve

The notion that the Earth’s curvature obstructs distant views is a common misconception, especially when it comes to seeing mountaintops from across the ocean. Prime examples of this are visible from Mauritius, where you can see the mountain peaks of Réunion Island despite their considerable distance.

Height of the Peaks

Understanding the visibility of Réunion’s mountaintops from Mauritius requires considering the height of the peaks. The highest peak, Piton des Néiges, rises to an impressive 3000 meters (9800 feet) above sea level. Given this elevation, the peaks can often be seen from a distance, even when the Earth is curved.

Curvature of the Earth

The curvature of the Earth does play a significant role, but it doesn't entirely obscure distant objects. Using the formula for calculating the distance to the horizon, sqrt{2 cdot h}, where h is the height above sea level in meters, we can approximate the distance. For example, a peak at 3000 meters would have a horizon around 77 kilometers (48 miles) away, well within the distance between Mauritius and Réunion.

Atmospheric Refraction

Another factor at play is atmospheric refraction. This is the bending of light due to temperature gradients and pressure differences in the atmosphere. At times, this phenomenon can bend light in a way that allows objects technically beyond the horizon to be visible.

Weather Conditions

Clear weather conditions can significantly enhance visibility, allowing for longer sight lines across the ocean. Ideal weather conditions can often extend the distance one can see beyond the horizon.

Geographical Positioning

The relative positioning of the islands also plays a crucial role. Depending on your location in Mauritius, the line of sight to the peaks can be less obstructed, contributing to the ability to see Réunion's mountains.

Calculations and Real-World Visibility

To understand this better, let's perform a calculation based on real data. The distance from the western tip of Mauritius to Piton de Néiges on Réunion is about 204 km (127 miles).

Assuming an observer is standing on the shore at 10 meters above the ocean surface, and Piton de Néges is a 3069 meter tall mountain, we can use Pythagoras' Theorem to solve for the distance you should be able to see the mountain. The Earth's radius is approximately 6371 km.

1. Distance to the horizon starting point (x1):
x1 sqrt{Rh^2 - R^2} sqrt{(6371.01)^2 - (6371)^2} 11.3 km
2. Distance to the mountain top (x2):
x2 sqrt{Rd^2 - R^2} sqrt{(6374.069)^2 - (6371)^2} 197.8 km
Therefore, the combined distance (x1) (x2) 209.1 km.

Given that the actual distance from Mauritius to Piton de Néges is 204 km, it makes sense that you can see the mountain tops. In reality, you can see even more of the mountain because:

My approximation of the Earth's radius is likely several kilometers off, potentially extending visibility further. Light isn't always traveling in perfectly straight lines. Over long distances, the atmosphere refracts light ever so slightly, which can add an additional distance of visibility.

In conclusion, the combination of the height of the mountains, atmospheric refraction, and favorable weather conditions allows for the visibility of Réunion's peaks from Mauritius, despite the curvature of the Earth.