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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 48 "Example 14.4-1. Estimati
on of the Solar Constant" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 90 "The solar constant is the radiant heat flux entering th
e earth's atmosphere from the sun. " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 
"dQ[12]:=sigma*T[1]^4*cos(theta[1])*dA[1]*dA[2]*cos(theta[2])/(Pi*r[12
]^2); " }{TEXT -1 33 "Eqn. 14.4-5 and in the discussion" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>&%#dQG6#\"#7*&*.%&sigmaG\"\"\")&%\"TG6#F+\"\"%
\"\"\"-%$cosG6#&%&thetaGF/F+&%#dAGF/F+&F86#\"\"#F+-F36#&F6F:F+F1*&%#Pi
G\"\"\")&%\"rGF&\"\"#F1!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 32 "dSC:=dQ[12]/cos(theta[2])/dA[2];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$dSCG*&**%&sigmaG\"\"\")&%\"TG6#F(\"\"%\"\"\"-%$cosG6#&%&theta
GF,F(&%#dAGF,F(F.*&%#PiG\"\"\")&%\"rG6#\"#7\"\"#F.!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "SC:=int(dSC/dA[1], A[1]); " }{TEXT 
-1 28 "need to remove dA1 for Maple" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#SCG*&**%&sigmaG\"\"\")&%\"TG6#F(\"\"%\"\"\"-%$cosG6#&%&thetaGF,F(&
%\"AGF,F(F.*&%#PiG\"\"\")&%\"rG6#\"#7\"\"#F.!\"\"" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 35 "A[1]:=Pi*d[1]^2/(4*cos(theta[1])); " }{TEXT 
-1 189 "cos(theta1) can be included because the integral(cos(theta))dA
 is the area of the sun, which is nearly pi*D1^2/4. For simplicity, we
 simply remove it after the integral has been calculated." }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>&%\"AG6#\"\"\",$*&*&%#PiGF')&%\"dGF&\"\"#\"\"
\"F0-%$cosG6#&%&thetaGF&!\"\"#F'\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "SC;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&*&&%\"qG6#%
#b1G\"\"\")&%\"dG6#F*\"\"#\"\"\"F0*$)&%\"rG6#\"#7\"\"#F0!\"\"#F*\"\"%
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sigma:=q[b1]/T[1]^4;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG*&&%\"qG6#%#b1G\"\"\"*$)&%\"
TG6#\"\"\"\"\"%F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "SC
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&*&&%\"qG6#%#b1G\"\"\")&%\"dG6
#F*\"\"#\"\"\"F0*$)&%\"rG6#\"#7\"\"#F0!\"\"#F*\"\"%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Diameter of the sun:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "d[1]:=8.60e5*miles;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>&%\"dG6#\"\"\",$%&milesG$\"$g)\"\"$" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 29 "Distance between dA1 and dA2:" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 20 "r[12]:=9.29e7*miles;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"rG6#\"#7,$%&milesG$\"$H*\"\"&" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 10 "Heat flux:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "q
[b1]:=2.0e7*Btu/hr/ft^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"qG6#%
#b1G,$*&%$BtuG\"\"\"*&%#hrG\"\"\")%#ftG\"\"#F+!\"\"$\"#?\"\"'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "SC;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*&%$BtuG\"\"\"*&%#hrG\"\"\")%#ftG\"\"#F&!\"\"$\"+w&[[
G%!\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Which is reasonably clo
se to the book's answer." }{MPLTEXT 1 0 0 "" }}}}{MARK "10 0 0" 0 }
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