Sun Earth Angles

The angle between the earth- sun line and the earth"s equatorial plane is known as the angle of declination. This varies with the date; and the orbital velocity of the earth traveling around the elliptic plane also varies slightly.

The two angles that completely describe the sun position are the solar altitude b, measured from 0° to 90° above the horizon, and the solar azimuth f, measured from 0° to 180° from the south with positive sign eastwards and negative sign westwards. To determine these two angles from data on Latitude, date and time, the following calculation is carried out:

Instead of being expressed in time units, true solar time can be expressed in angular terms related to the earth"s rotation as the hour angle, H, where

H = 0.25 X

Where

H: hour angle
X: Number of minutes from true solar time noon

Since in one minute the earth rotates 0.25°. Values a.m. are +ve and p.m. +ve. Then,

sin b = cos L cos d cos H + sin L sin d

and

sin f = (cos d sin H) / cos b

L: Latitude, degrees
d: declination, degrees (northern hemisphere =+ve, southern hemisphere = -ve)

Values of b and f may be available from tables in publications or graphical techniques for finding them are also available.