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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 30 "Gravitational Field Exper
iment" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(plots):\nwith
(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoor
ds has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the p
rotected names norm and trace have been redefined and unprotected\n" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 14 "Two body case." 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "g:=1*(1/sqrt(x^2+y^2)+4/sqrt((2-x
)^2+y^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,&*&\"\"\"F'*$-%%s
qrtG6#,&*$)%\"xG\"\"#F'F'*$)%\"yGF0F'F'F'!\"\"F'*&\"\"%F',*F6F'*&F6F'F
/F'F4F-F'F1F'#F4F0F'" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 63 "Two Dim
ensional Gravitational Potential for three body problem." }}{PARA 256 
"" 0 "" {TEXT -1 46 "Unit mass at (0,0) and (1,1). Mass 4 at (2,0)." }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "f:=1*(1/sqrt(x^2+y^2)+4/sqrt((2-x)
^2+y^2))+1/sqrt((1-x)^2+(1-y)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"fG,(*&\"\"\"F'*$-%%sqrtG6#,&*$)%\"xG\"\"#F'F'*$)%\"yGF0F'F'F'!\"\"F
'*&\"\"%F',*F6F'*&F6F'F/F'F4F-F'F1F'#F4F0F'*&F'F'*$-F*6#,,F0F'*&F0F'F/
F'F4F-F'*&F0F'F3F'F4F1F'F'F4F'" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 
72 "After you execute this worksheet (including the with(plots) line a
bove)," }}{PARA 256 "" 0 "" {TEXT -1 60 "below will be the level curve
s of f for the values 2 and 10." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 258 87 "You can add other comma separated values
 for f between 2 and 10 to see more level sets." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 33 "What happens in between
 2 and 10?" }{TEXT 256 59 " \nAre there values when the level sets cha
nge their shape? " }}{PARA 0 "" 0 "" {TEXT 259 36 "If so can you find \+
them? Accurately?" }}{PARA 0 "" 0 "" {TEXT 260 49 "What happens to the
 level sets of the function g?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "c
ontourplot(f,x=-4..5,y=-4..4,grid=[100,100],contours=[2,10],coloring=[
red,blue],thickness=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "4 5 1" 2 }
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