1. What is Effective Radius with Refraction?

The effective radius accounts for atmospheric refraction when calculating Earth's curvature. Refraction makes the Earth appear less curved than it actually is by bending light rays.

2. How Does the Calculator Work?

The calculator uses the effective radius formula:

Where:

• \( r \) — Actual Earth radius (6,371,000 m typically)
• \( k \) — Refraction coefficient (typically 0.13-0.25)
• \( effective\_r \) — Apparent radius accounting for refraction

Explanation: Atmospheric refraction effectively increases the apparent radius of the Earth, making distant objects more visible than pure geometry would predict.

3. Importance of Refraction in Curvature Calculations

Details: Refraction is crucial for accurate visibility calculations, horizon distance estimates, and understanding optical phenomena like looming or mirages.

4. Using the Calculator

Tips: Enter Earth's radius in meters and refraction coefficient (typically 0.13 for standard conditions). The coefficient ranges from 0 (no refraction) to nearly 1 (extreme refraction).

5. Frequently Asked Questions (FAQ)

Q1: What's a typical value for Earth's radius?
A: The mean radius is approximately 6,371,000 meters (6,371 km).

Q2: How does refraction coefficient vary?
A: The coefficient typically ranges from 0.13 (standard conditions) to 0.25 (strong refraction). It can be negative in unusual temperature inversion conditions.

Q3: Why is refraction important for horizon calculations?
A: Refraction extends the visible horizon by about 8-15% compared to geometric calculations.

Q4: How does this affect satellite and surveying calculations?
A: Refraction must be accounted for in precise geodetic measurements and satellite observations.

Q5: Can refraction make objects appear above the horizon?
A: Yes, under strong refraction conditions (high k values), objects geometrically below the horizon can become visible.