axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) plot(lambda,lfl_T1,main="Planck's Law for a Blackbody",log="xy",xlab=expression(paste("Wavelength (",mu,"m)")),ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),type="l",col="red",xlim=c(0.01,10),xaxt='n',yaxt='n') lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="blue") legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) line(v=1) ?line line(h=1) ?line abline(h=1) abline(v=1) plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="red", xlim=c(0.01,10), ylim=c(1e5,1e15), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="blue") legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) line(h=1) plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="red", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="blue") legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="red", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="blue") legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^15,label=expression("10"^16)) axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="red", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="blue") legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^16,label=expression("10"^16)) axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="blue", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="red") legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^16,label=expression("10"^16)) axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="blue", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="red") legend(0.1,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^16,label=expression("10"^16)) axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="blue", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="red") legend(1,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^16,label=expression("10"^16)) axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) ?pdf pdf("planck.pdf") plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="blue", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="red") legend(1,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^16,label=expression("10"^16)) axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) dev.off() pdf("planck.pdf") plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="blue", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="red") legend(.65,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^16,label=expression("10"^16)) axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) dev.off() pdf("planck.pdf") plot(lambda,lfl_T1, main="Planck's Law for a Blackbody", log="xy", xlab=expression(paste("Wavelength (",mu,"m)")), ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")), type="l", col="blue", xlim=c(0.01,10), ylim=c(1e6,1e16), xaxt='n', yaxt='n' ) lines(lambda,lfl_T2,col="green") lines(lambda,lfl_T3,col="red") legend(.5,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red")) axis(1,at=0.01,label="0.01") axis(1,at=0.02,label="0.02") axis(1,at=0.05,label="0.05") axis(1,at=0.1,label="0.1") axis(1,at=0.2,label="0.2") axis(1,at=0.5,label="0.5") axis(1,at=1,label="1") axis(1,at=2,label="2") axis(1,at=5,label="5") axis(1,at=10,label="10") axis(2,at=10^16,label=expression("10"^16)) axis(2,at=10^15,label=expression("10"^15)) axis(2,at=10^14,label=expression("10"^14)) axis(2,at=10^13,label=expression("10"^13)) axis(2,at=10^12,label=expression("10"^12)) axis(2,at=10^11,label=expression("10"^11)) axis(2,at=10^10,label=expression("10"^10)) axis(2,at=10^9,label=expression("10"^9)) axis(2,at=10^8,label=expression("10"^8)) axis(2,at=10^7,label=expression("10"^7)) axis(2,at=10^6,label=expression("10"^6)) axis(2,at=10^5,label=expression("10"^5)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^4,label=expression("10"^4)) axis(2,at=10^3,label=expression("10"^3)) axis(2,at=10^2,label=expression("10"^2)) axis(2,at=10^1,label=expression("10"^1)) axis(2,at=1,label=expression("1")) dev.off() 3.828/6.417 4*pi() pi() %pi pi 4*pi 5.965e22 5.965e22/12.5664 sqrt(5.965e22/12.5664) 14959790000000*14959790000000 3.828/12.5664/2.2380/1e26*1e33 1.361e6 / 29979245800 (4.54e-5 * 29979245800)/(5.6704e-5) (4.54e-5 * 29979245800)/(5.6704e-5)^(-4) (4.54e-5 * 29979245800)/(5.6704e-5)^(1/4) 1.568e7^4 (1.568e7)^4 (4.54e-5 * 29979245800) (4.54e-5 * 29979245800)/(5.6704e-5) pow((4.54e-5 * 29979245800)/(5.6704e-5),1/4) power power((4.54e-5 * 29979245800)/(5.6704e-5),1/4) ?power ?exp ?pow power((4.54e-5 * 29979245800)/(5.6704e-5),1/4) (4.54e-5 * 29979245800)/(5.6704e-5) ((4.54e-5 * 29979245800)/(5.6704e-5))^(1/4) 393^4 393.6 - 289.15 0.28979/5800 quit()