eqtime: Equation of time
In insol: Solar Radiation

Description Usage Arguments Value Author(s) References Examples

Computes the equation of time for a given Julian Day.

1	eqtime(jd)

`jd`	Julian Day.

Equation of time in minutes.

Javier G. Corripio

https://www.esrl.noaa.gov/gmd/grad/solcalc/calcdetails.html

Meeus, J. 1999. Astronomical Algorithms. Willmann-Bell, Richmond, Virginia, USA.

Reda, I. and Andreas, A. 2003. Solar Position Algorithm for Solar Radiation Applications. 55 pp.; NREL Report No. TP-560-34302, Revised January 2008. https://www.nrel.gov/docs/fy08osti/34302.pdf

# plot the equation of time for 2013 at daily intervals
jdays = seq(ISOdate(2013,1,1),ISOdate(2013,12,31),by='day')
jd = JD(jdays)
plot(eqtime(jd))
abline(h=0,col=8)

# Analema
plot(eqtime(jd),declination(jd))

# Analema from Greenwich Observatory
latGwch = 51.4791
x = 180+eqtime(jd)*15/60
y = 90-latGwch+declination(jd)
plot(x,y,ylim=c(0,90),xlab=expression(paste('Azimuth (',degree,')')),
	ylab=expression(paste('Elevation (',degree,')')))

## Add the solstices and equinoxes (nearest day, see Meeus ch. 26 for more precision)
decl = declination(jd)
wintersolstice = which(decl==min(decl))
summersolstice = which(decl==max(decl))
## spring equinox: when declination becomes zero in the first part of the year
springeqx = uniroot(declination,jd[c(1,180)])$root
springeqx = daydoy(JD(springeqx,inv=TRUE))
autumeqx = uniroot(declination,jd[c(180,360)])$root
autumeqx = daydoy(JD(autumeqx,inv=TRUE))
nodeseqx = c(springeqx,summersolstice,autumeqx,wintersolstice)
points(x[nodeseqx],y[nodeseqx],pch=19,col=3)
abline(h=c(90-latGwch,90-latGwch+max(decl),90-latGwch+min(decl)),col=8)