Bild:Zeitgleichung.png
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| Description |
equation of time; also: the equation of time without the ecliptic and as if the earth was turning around the sun on a circle. |
|---|---|
| Source |
[1] and other sources on the net. created with GNU R, see source below |
| Date |
13 jan 2007 |
| Author | |
| Permission |
Thomas Steiner put it under the CC-by-SA 2.5. |
   |
This file is licensed under the Creative Commons Attribution ShareAlike 2.5 License. In short: you are free to share and make derivative works of the file under the conditions that you appropriately attribute it, and that you distribute it only under a license identical to this one. Official license |
R-source:
#formulas, equations and notation from http://homeweb2.unifr.ch/hungerbu/pub/sonnenuhr/sundial.ps # and by the paper of C. Blatter (http://dz-srv1.sub.uni-goettingen.de/sub/digbib/loader?did=D241775) epsilon=23.45*2*pi/360 alpha =78.5 *2*pi/360 kappa =0.016722 mu<-function(t,epsilon,alpha,kappa) { zaehl= -sin(delta(t,kappa))+tan(epsilon/2)^2*sin(2*(t-alpha)+delta(t,kappa)) nenn = cos(delta(t,kappa))+tan(epsilon/2)^2*cos(2*(t-alpha)+delta(t,kappa)) return( atan(zaehl/nenn) ) } # approximation by Blatter psi<-function(t) { return(t+delta(t)) } delta<-function(t,kappa) { return( 2*sin(t)*kappa+5/4*sin(2*t)*kappa^2 ) } png(filename="Zeitgleichung.png", width=1024, height=768, pointsize=12) par(bg="whitesmoke") time=seq(-0.6,2*pi+0.4,length=365+(0.6+0.4)/(2*pi)*365) da<-paste("1.",as.character(seq(1,12,by=2)),".07",sep="") da<-as.Date(c(da,"1.1.08"),"%d.%m.%y") #umrechungsfaktor: 24h=2*pi plot(time,mu(time,epsilon,alpha,kappa)*24*60/(2*pi),type="l",col="red",xlab="Tag",ylab="Zeitgleichung in Minuten",main="Zeitgleichung: wahre Ortszeit - mittlere Ortszeit",cex.main=1.5,lwd=3,xaxt="n",xaxs="i",xlim=range(time)) lines(time,mu(time,epsilon=0,alpha,kappa)*24*60/(2*pi),lwd=2,col="navy",lty="dotdash") lines(time,mu(time,epsilon,alpha,kappa=0)*24*60/(2*pi),lwd=2,col="purple",lty="dashed") #grid abline(h=c(-15,-10,-5,5,10,15),lty="dotted",col="grey") abline(h=0,lty="solid",col="grey33") tage=cumsum(c(0,31,28,31,30,31,30,31,31,30,31,30,31))/365-3/365 abline(v=tage*2*pi,lty="dotted",col="grey") axis(1,at=seq(0,2*pi,length=7)-3*2*pi/365,labels=as.character(da,"1. %b")) legend(x=5.5,y=-10.9,legend=c("Zeitgleichung","ohne Ekliptik","auf Kreisbahn"),col=c("red","navy","purple"),lwd=c(3,2,2),lty=c("solid","dotdash","dashed")) dev.off()
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