Sun Declination

The declination of the sun varies between the Tropics of Cancer and Capricorn depending on the time of year. This is a measured fact. This is the approximate formula for the declination of the sun:

S_dec ~= 23.45° x sine( 360°/365 x (d - 81) ) Where: d is the day of the year.

So, for December 2024 solstice:

January: 31
February: 29 → total 60
March: 31 → total 91
April: 30 → total 121
May: 31 → total 152
June: 30 → total 182
July: 31 → total 213
August: 31 → total 244
September: 30 → total 274
October: 31 → total 305
November: 30 → total 335
December: 21 days → total 356

Applying the formula:

S_dec = 23.45° x sine( 360°/365 x (d - 81) )
S_dec = 23.45° x sine( 360°/365 x (356 - 81) )
S_dec = 23.45° x sine( 0.98630137° x (275) )
S_dec = 23.45° x sine( 271.23287671° )
S_dec = 23.45° x -0.9997685
S_dec = -23.44457137°

For December 15, 2024: −23.37°