Understanding Earth's Curvature: Measurement and Impact on Distances

Q: If eyesight level is the same as sea level, how much would the Earth drop in curvature over 1 mile?

When standing at sea level, the "drop" due to Earth's curvature over a certain distance can be approximated by the formula: drop (in feet) ≈ 8 inches × (distance in miles)². For 1 mile, the drop would be roughly 8 inches (or about 0.67 feet). This means that over a 1-mile horizontal distance, the Earth's surface curves away enough that the surface drops about 8 inches relative to a straight line tangent to the Earth's surface at the observer's eye level. This is a simple approximation useful for understanding how much the Earth curves over short distances.

Q: So if eyesihht level is the same as sea level, how much does the Earth curve over 100 miles

To calculate how much the Earth's surface curves over a distance of 100 miles at sea level (assuming eye level is at sea level), we can determine the 'sagitta' or the height of the curve drop over that distance. The Earth's radius (R) is approximately 3,959 miles. For a chord length (distance along the surface) of 100 miles, we can find the height of the curvature (h) using the formula: h = R - √(R² - d²) where d is half the distance (the radius of the chord from the midpoint), so d = 100 / 2 = 50 miles. Calculating: h = 3959 - √(3959² - 50²) = 3959 - √(15,677,681 - 2,500) = 3959 - √(15,675,181) ≈ 3959 - 3958.37 = 0.63 miles So over 100 miles, the Earth's surface curves downward by approximately 0.63 miles (about 3,322 feet or 1,013 meters). This curvature means that if you looked straight across 100 miles at sea level, the Earth would drop away by around 0.63 miles due to curvature.

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Understanding Earth's Curvature: Measurement and Impact on Distances

Learning Corner · Accepted Answer

The Earth's curvature can be understood through the geometric principles of a sphere. The Earth is not a perfect sphere but is approximated as an oblate spheroid, which means it is slightly flattened at the poles and bulges at the equator. For our calculations and explanations, we often consider it as a sphere with a radius of approximately 6,371 kilometers (or about 3,959 miles).

To determine how far the Earth’s curvature affects visibility or the distance to the horizon, we can use a basic formula that relates distance and height:

Distance to Horizon (D) = √(Height x 2 x Radius)

For example, if you are standing at a height of 1.8 meters (about 6 feet), the distance to the horizon would be calculated as follows:

Radius of Earth (R) = 6,371,000 meters
Height (H) = 1.8 meters
Distance (D) = √(1.8 x 2 x 6,371,000) ≈ √(22,671,000) ≈ 4,769 meters, or about 4.77 kilometers (2.97 miles)

This means that from a height of 1.8 meters, you could see approximately 4.77 kilometers to the horizon before the curvature of the Earth obstructs your line of sight.

In summary, the curvature of the Earth impacts distances, particularly in navigation and visibility. This principle is crucial for various fields, including aviation, sailing, and geology, where understanding the layout of the Earth is essential.

Understanding Earth's Curvature: Measurement and Impact on Distances

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If eyesight level is the same as sea level, how much would the Earth drop in curvature over 1 mile?

So if eyesihht level is the same as sea level, how much does the Earth curve over 100 miles