1. What is the NOAA Sunrise Formula?

The NOAA (National Oceanic and Atmospheric Administration) sunrise formula calculates the time of sunrise based on latitude and solar declination. It provides an accurate estimate of sunrise times for astronomical and navigational purposes.

2. How Does the Calculator Work?

The calculator uses the NOAA solar time formula:

Where:

• \( lat \) — Latitude in degrees
• \( decl \) — Solar declination in degrees
• \( \arccos \) — Inverse cosine function
• \( \tan \) — Tangent function

Explanation: The formula calculates the hour angle of sunrise and converts it to local solar time, with 12 representing solar noon.

3. Importance of Sunrise Calculation

Details: Accurate sunrise calculations are essential for astronomy, navigation, agriculture, photography, and various outdoor activities. They help in planning daily schedules and understanding seasonal variations.

4. Using the Calculator

Tips: Enter latitude in degrees (-90 to +90), solar declination in degrees (-23.5 to +23.5). Positive values for northern hemisphere, negative for southern hemisphere.

5. Frequently Asked Questions (FAQ)

Q1: What is solar declination?
A: Solar declination is the angle between the rays of the sun and the plane of the Earth's equator, varying throughout the year due to Earth's axial tilt.

Q2: Why does the formula return "No sunrise"?
A: This occurs during polar day (24-hour daylight) or polar night (24-hour darkness) when the sun doesn't rise or set for extended periods.

Q3: How accurate is this calculation?
A: The formula provides theoretical sunrise times. Actual sunrise may vary due to atmospheric refraction, elevation, and local topography.

Q4: What is the 1/15 factor in the formula?
A: This converts degrees to hours (15 degrees of longitude per hour of time difference).

Q5: Can this calculate sunset times?
A: Sunset can be calculated as 12 + (1/15) × acos(-tan(lat)tan(decl)), which is symmetric to the sunrise formula.