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This plot was created using the simple sunrise equation, approximating the sun as a single point and does not take into account effects caused by the atmosphere or the diameter of the Sun. The sunrise equation or sunset equation can be used to derive the time of sunrise or sunset for any solar declination and latitude in terms of local solar ...
The following formulas assume the north-clockwise convention. The solar azimuth angle can be calculated to a good approximation with the following formula, however angles should be interpreted with care because the inverse sine, i.e. x = sin −1 y or x = arcsin y, has multiple solutions, only one of which will be correct.
For a given latitude and a given date, calculate the declination of the Sun using longitude and solar noon time as inputs to the routine; Calculate the sunrise hour angle using the sunrise equation; Calculate the sunrise time, which is the solar noon time minus the sunrise hour angle in degree divided by 15;
The solar zenith angle is the zenith angle of the sun, i.e., the angle between the sun’s rays and the vertical direction.It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane.
(The above formula is related to a reasonably simple and accurate calculation of the Equation of Time, which is described here.) More complicated algorithms [16] [17] correct for changes to the ecliptic longitude by using terms in addition to the 1st-order eccentricity correction above. They also correct the 23.44° obliquity which changes very ...
The cosine of the hour angle (cos(h)) is used to calculate the solar zenith angle. At solar noon, h = 0.000 so cos( h ) = 1 , and before and after solar noon the cos(± h ) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time.
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A plot of hours of daylight as a function of the date for changing latitudes. This plot was created using the simple sunrise equation, approximating the sun as a single point and does not take into account effects caused by the atmosphere or the diameter of the sun. Earth daylight on the June solstice Earth daylight on the December solstice