1. What is Earth Curvature Calculation?

The Earth curvature calculation determines how much the Earth's surface drops (sagitta) over a given distance, accounting for the planet's spherical shape. This is important for understanding visible distances, surveying, and long-distance observations.

2. How Does the Calculator Work?

The calculator uses the Earth curvature formula:

Where:

• \( R \) — Earth's radius (default 6,371,000 meters)
• \( d \) — Distance along the Earth's surface
• \( \theta \) — Central angle in radians
• sagitta — Vertical drop due to curvature

Explanation: The formula calculates how much the Earth's surface "drops" below a straight line over a given distance.

3. Importance of Sagitta Calculation

Details: Understanding Earth curvature is essential for accurate surveying, determining visibility between points, and correcting for curvature effects in various engineering applications.

4. Using the Calculator

Tips: Enter Earth's radius (default is mean radius) and distance. All values must be positive numbers. For Earth, the mean radius is approximately 6,371,000 meters.

5. Frequently Asked Questions (FAQ)

Q1: Why does the Earth's curvature matter?
A: It affects visibility calculations, satellite communications, and long-distance measurements where the Earth's curvature becomes significant.

Q2: How much does the Earth curve per kilometer?
A: Approximately 7.85 cm per km for the first kilometer, increasing quadratically with distance.

Q3: Does this account for atmospheric refraction?
A: No, this is a pure geometric calculation. Atmospheric refraction can slightly increase visible distances.

Q4: What's the difference between sagitta and horizon drop?
A: Sagitta is the vertical drop at a point, while horizon drop refers to the cumulative effect up to the visible horizon.

Q5: Can I use this for other planets?
A: Yes, just input the appropriate radius for the celestial body you're calculating for.