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256 34 "Model for a spaceship around earth" }{TEXT -1 0 "" }}{PARA 0 "
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0 "> " 0 "" {MPLTEXT 1 0 28 "with(plottools):with(plots):" }}{PARA 7 "
" 1 "" {TEXT -1 98 "Warning, the previous binding of the name arrow ha
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> " 0 "" {MPLTEXT 1 0 101 "text:=textplot(\{[0.2,0.1,` earth`],[1.3,2,
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" {TEXT -1 119 "The gravitational force vector takes the direction fro
m spaceship to earth, i.e., this vector is along the direction of" }}
{PARA 256 "" 0 "" {XPPEDIT 18 0 "MATRIX([[0], [0]])" "6#-%'MATRIXG6#7$
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0 "" {TEXT -1 21 "Scaled by its length " }{XPPEDIT 18 0 "sqrt(x^2+y^2)
" "6#-%%sqrtG6#,&*$%\"xG\"\"#\"\"\"*$%\"yGF)F*" }{TEXT -1 63 ", we hav
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{TEXT -1 41 "  of the gravitational force, yields the " }{TEXT 257 27 
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256 "" 0 "" {XPPEDIT 18 0 "-G*m*M/sqrt(x^2+y^2)^3" "6#,$**%\"GG\"\"\"%
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ewton's second law " }{XPPEDIT 18 0 "m*a=f" "6#/*&%\"mG\"\"\"%\"aGF&%
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{XPPEDIT 18 0 "MATRIX([[d^2*x/dt^2], [d^2*y/dt^2]])" "6#-%'MATRIXG6#7$
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{XPPEDIT 18 0 "m " "6#%\"mG" }{TEXT -1 27 " from both sides and using \+
" }{XPPEDIT 18 0 "G*M" "6#*&%\"GG\"\"\"%\"MGF%" }{TEXT -1 71 " as unit
, we have the simplified model for the trajectory of spaceship:" }}
{PARA 0 "" 0 "" {TEXT -1 20 "                    " }{XPPEDIT 18 0 "MAT
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{XPPEDIT 18 0 "-1/sqrt(x^2+y^2)^3" "6#,$*&\"\"\"F%*$-%%sqrtG6#,&*$%\"x
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}{PARA 0 "" 0 "" {TEXT -1 50 "Suppose at present, the spaceship is at \+
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4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 42 "The trajectory is an ellipse around earth
." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 133 "In-class:   Convert the 2nd order
 IVP-ODE for the satelite to a 4x4 1st order IVP-ODE. Solve the 4x4 sy
stem, and plot the trajectory." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 45 "Homework:   The gravity force magnitude i
s   " }{XPPEDIT 18 0 "G*m*M/(r^s);" "6#**%\"GG\"\"\"%\"mGF%%\"MGF%)%\"
rG%\"sG!\"\"" }{TEXT -1 49 "   for   s = 2.   How would the satelite m
ove if " }{XPPEDIT 18 0 "s;" "6#%\"sG" }{TEXT -1 2 " i" }{TEXT -1 49 "
s different from 2, say,  s=1.5,  2.1,  3,  etc. " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}}{MARK "15 4 5" 44 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 
}{PAGENUMBERS 0 1 2 33 1 1 }