Declination(in degrees) for any given day

Declination angle \(\delta\)

• Def: The declination \(\delta\) is the angular distance of the sun’s rays north (orsouth) of the equator.
• it is the angle between a line extending from the centre ofthe sun to the centre of the earth and the projection of this line upon the earth’s equitorial plane.
• This is the direct consequence of the tilt and it would vary between 23.5⁰ on June 22^nd to 23.5⁰ on December 22^nd.

——–

• The declination in degrees for any given day may be calculated from the approximate equation of Cooper(1969) \(\delta(in degrees)=23.45sin(\frac{360}{365})(284+n)\)
  where n is the day of the year (i.e., n=1 means January 1^st and n=365 means December 31^st)

#Assigning day number to dates
days<-seq( as.Date("2017-03-22"), as.Date("2018-03-21"), by="+1 day")
ndays<-length(seq( as.Date("2017-03-22"), as.Date("2018-03-21"), by="+1 day"))
ndays

## [1] 365

delta<-0

for (i in 1:ndays){
        delta[i]<-23.45*sin((360/365)*(pi/180)*(280+i))        
}

plot(days,delta,type="l",main="Variation of Sun's Declination",xlab="Time of the year",ylab = "Declination(delta) in degrees")

max(delta)

## [1] 23.44978