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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 268 "eq:=\{\nr*v=R*V, # \+
Conservation of Angular momentum\n1/2*v^2-GM/r=1/2*V^2-GM/R, # Conserv
ation of energy\nV=R*Omega, # Initially rotating with the Earth\nOmega
=2*Pi/86164, # Earth angular velocity\nr=40e6/(2*Pi), # Earth radius\n
GM/r^2=9.81, # Gravity at Earth surface\nR>r\n\};" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#eqG<)2%\"rG%\"RG/*&F'\"\"\"%\"vGF+*&F(F+%\"VGF+/,&*&
\"\"#!\"\"F,F2F+*&%#GMGF+F'F3F3,&*&F2F3F.F2F+*&F5F+F(F3F3/F.*&F(F+%&Om
egaGF+/F;,$*&\"&#3VF3%#PiGF+F+/*&F5F+F'!\"#$\"$\")*FC/F',$*&$\"+++++?F
CF+F@F3F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "sol:=solve(eq,
\{r,v,R,V,GM,Omega\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<(/%&
OmegaG$\"+<N7#H(!#9/%#GMG$\"+YK%e(R\"\"&/%\"RG$\"+j#Re(H!\"#/%\"rG$\"+
Cx>mj!\"$/%\"VG$\"+Z(=+<#!\"'/%\"vG$\"+v;O95!\"&" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 21 "evalf(eval(R-r,sol));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+\"\\>#RB!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 166 "eq2:=\{\n((r+R)/2)^3/T^2=GM/(4*Pi^2), # Kepler's third law\nt
heta=Pi-T/2*Omega, # Impact is T/2 after fall, 180 degrees away, but E
arth rotation must be deducted.\nT>0\n\};" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$eq2G<%/*&,&*&\"\"#!\"\"%\"rG\"\"\"F-*&F*F+%\"RGF-F-
\"\"$%\"TG!\"#,$*(\"\"%F+%#GMGF-%#PiGF2F-2\"\"!F1/%&thetaG,&F7F-*(F*F+
F1F-%&OmegaGF-F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sol2:=s
olve(eval(eq2,sol),\{T,theta\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
%sol2G<$/%&thetaG$\"+2JjfA!\"*/%\"TG$\"+'[P*=C!\"&" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 31 "evalf(eval(theta,sol2)*180/Pi);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"+.Wn%H\"!\"(" }}}{EXCHG {PARA 0 "> " 0 "
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