1. What is the Hour Angle?

The hour angle at any instant is the angle through which the earth has to turn to bring the meridian of the observer directly in line with the sun's rays. It is measured in radians and represents the sun's position relative to the local meridian.

2. How Does the Calculator Work?

The calculator uses the hour angle formula:

Where:

• \( \omega \) — Hour angle (radians)
• \( ST \) — Solar Time (seconds)

Explanation: The formula converts solar time from seconds to hours, adjusts for the 12-hour reference, and converts degrees to radians (15 degrees per hour × 0.0175 rad/degree).

3. Importance of Hour Angle Calculation

Details: Accurate hour angle calculation is crucial for solar tracking systems, astronomical observations, and determining the sun's position for various applications including solar energy systems and navigation.

4. Using the Calculator

Tips: Enter solar time in seconds. The value must be valid (solar time > 0). The calculator will compute the hour angle in radians.

5. Frequently Asked Questions (FAQ)

Q1: What is solar time?
A: Solar Time is a calculation of the passage of time based on the position of the Sun in the sky. It is taken in a 24-hour format. For example, 6PM is 18:00 hours.

Q2: Why convert to radians?
A: Radians are the standard unit for angular measurements in mathematical calculations and many scientific applications.

Q3: What does the hour angle represent?
A: The hour angle represents how far the sun is from the local meridian, with negative values indicating before solar noon and positive values after solar noon.

Q4: How is this different from local apparent time?
A: Solar time is based on the actual position of the sun, while local apparent time accounts for the equation of time and longitude correction.

Q5: What are typical hour angle values?
A: Hour angle ranges from -π to π radians (-180° to 180°), with 0 at solar noon, negative values in the morning, and positive values in the afternoon.