# The sun's observed position

The angle under which the sun is observed from a point on the earth’s surface is affected by the earth’s daily rotation, the annual rotation of the tilted earth and the latitude of the surface in question.

## Daily Rotation

The solar hour angle Ω expresses the daily rotation of the earth. As the earth rotates 360° within 24 hours, every hour adds another 15° to the sholar hour angle. When the sun is in its highest point in the sky, the solar hour angle is zero. Angles before noon count negative, after noon positive.

As the earth rotates, the angle between the sun and due south, the solar azimuth angle, α, varies from -90° at sunrise (east) to +90° at sunset (west)..

### Declination

The declination angle, δ, is the angular position of the sun at solar noon with respect to the plane of the equator. It varies from -23.45° at winter solstice to +23.45° at summer solstice according to:

As before, n denotes the day in the year with n = 1..365.

### Latitude

For locations other than the equator, the latitude, φ, changes the zenith angle further.

### Zenith Angle

The orientation of an area with respect to the sun is best described by the zenith angle, θ, which is related to latitude, day and time via:

To get the intensity, the peak intensity should be multiplied with the cosine of the zenith angle.

The above equation is only true while the sun can be observed, which allows us to determine the hours of daylight on a horizontal surface as

Obviously, averaged over the year, every location on earth has the same amount of hours of daylight. However, the annual distribution varies by latitude. While cities with higher latitude enjoy more hours of daylight in summer, the peak intensity remains lower due to the larger zenith angle.

## Graphing Intensity and Energy

Applying the formulas above we have put together a few graphs to demonstrate the impact of the latitude on daylight hours, intensity and daily energy. The values for intensity and energy should be seen as maximum values that will only be reached if the sky is very clear.