1. What is the NOAA Sunrise Equation?

The NOAA (National Oceanic and Atmospheric Administration) sunrise equation calculates the time of sunrise based on latitude and solar declination. It provides an approximate time when the sun's upper limb appears on the horizon.

2. How Does the Calculator Work?

The calculator uses the NOAA sunrise equation:

Where:

• \( T \) — Sunrise time in hours (local solar time)
• \( lat \) — Latitude in degrees (-90 to 90)
• \( dec \) — Solar declination in degrees (-23.5 to 23.5)

Explanation: The equation calculates the hour angle of sunrise and converts it to local solar time. The 15 comes from 360° divided by 24 hours.

3. Importance of Sunrise Calculation

Details: Sunrise calculations are important for agriculture, photography, aviation, marine navigation, and various outdoor activities. They also have cultural and religious significance in many societies.

4. Using the Calculator

Tips: Enter latitude in degrees (-90 to 90), positive for north, negative for south. Enter solar declination in degrees (-23.5 to 23.5), which varies throughout the year.

5. Frequently Asked Questions (FAQ)

Q1: Why is the result different from my local sunrise time?
A: This calculates solar time. Local sunrise depends on time zone, daylight saving, and atmospheric refraction which this simple equation doesn't account for.

Q2: 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 between ±23.5° throughout the year.

Q3: Can I use this for sunset calculation?
A: Sunset time would be 24 minus the sunrise time in this simplified model (12 + hour_angle/15).

Q4: Why does the equation fail near the poles?
A: Near the poles during summer/winter, the sun may not set/rise at all, making the equation invalid as the arccos argument goes outside [-1,1].

Q5: How accurate is this calculation?
A: This is a simplified model. For precise times, atmospheric refraction, elevation, and the sun's finite size should be considered.