This procedure calculates the number of days in a given date and it applies it to the computation of the solar declination angle, δ

1. Day number in the year and Solar Declination Angle.xmcd
This procedure calculates the number of days in a given date and it applies it to the
computation of the solar declination angle, δ,
ORIGIN 1

days 31 28 31 30 31 30 31 31 30 31 30 31
( )
T

N N1 0

Ni daysi 1
 Ni 1



i 2 12


for
N
return

N
T
0 31 59 90 120 151 181 212 243 273 304 334
( )

n is the day number in the year for a given date: D Month day

( ) NMonth day


Example: Calculate the day number in the year for June 1
Month 6
 day 1

n D Month day

( ) 152


An application of this day number in the year is in the calculation of The solar
declination angle, δ,
δ n
( ) 23.45° sin 360°
284 n

( )
365







δ n
( ) 22.0°

The solar declination has a maximum value of +23.45o on June 21 and a minimum
value of –23.45o on December 21.
Month 6
 day 21

n D Month day

( ) 172

 δmax δ n
( ) 23.45°

 QED
Month 12
 day 21

n D Month day

( ) 355

 δmax δ n
( ) 23.45
 °

 QED
Q.E.D. or QED is an initialism of the Latin phrase "quod erat demonstrandum",
literally meaning "what was to be shown"
Julio C. Banks page 1 of 1