Calculate Extraterrestrial Radiation Falling on a Horizontal Surface

Explanation: Extraterrestrial radiation on a horizontal surface is the total solar irradiance received from the Sun without the interference of Earth's atmosphere. This question involves calculating the solar irradiance for a given day of the year at a specific latitude. To solve this, we utilize an equation that accounts for the Earth's eccentricity and its position relative to the Sun over the course of the year.

The formula given here is related to identifying the correct modulation of the solar constant (H₀) due to the Earth's elliptical orbit around the Sun. The solar constant is approximately 1.37 kW/m². The equations provided all start with the solar constant, following a correction factor that includes a cosine function with a factor representing the day of the year (N) and an adjustment to the angle to account for the eccentricity of Earth's orbit.

In the context of this problem, we need to determine which formula correctly represents this modulation. It is known that Earth is closest to the Sun (perihelion) around January 3rd, and that's when the solar irradiance is slightly more than the average due to Earth's elliptical orbit. The expression '1 + 0.034 × cos(360 × (N+10)/365)' corresponds to this understanding as it reflects an increase in solar radiation around this time.

If we consider that March 5th is the 64th day of the year, we plug N=64 into our formula to get the factor by which to multiply the solar constant to get the extraterrestrial radiation for that location and time.