# How is the constant “284” derived within the Solar Declination Angle equation?

How is the constant "284" derived within the Solar Declination Angle equation?

The earth's axis results in a day-by-day variation of the angle between the earth-sun line and the earth's equatorial plane called the solar declination $$\delta$$. This angle may be estimated by the following equation [6]: $$\delta = 23.45° \sin\left[\frac{360°}{365}(284+N)\right], \tag{2.1}$$ where $$N =$$ year day, with January 1 $$+ 1$$.

This is to get the correct phase, so that for $$N=81$$ (which is March 21, the March equinox) the result will be $$\delta=0$$, as shown in the graph below.