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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

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Mathcad day number in the year and solar declination angle

  • 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