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Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style["target escape velocity", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`level$$], "first", "level"}, { "first", "second", "third"}}, { Hold[ Style["geometry", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`conehght$$], 5, "head height \!\(\*SubscriptBox[\(h\), \(1\)]\)"}, 3, 10, 0.1}, {{ Hold[$CellContext`bodyhght$$], 20, "body height \!\(\*SubscriptBox[\(h\), \(2\)]\)"}, 5, 30, 1}, {{ Hold[$CellContext`bodyradius$$], 1, "body radius \!\(\*SubscriptBox[\(r\), \(2\)]\)"}, 1, 3, 0.1}, { Hold[ Style["specification", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`M0$$], 500, "initial mass \!\(\*SubscriptBox[\(M\), \(0\)]\)"}, 100, 1000, 1}, {{ Hold[$CellContext`MF$$], 60, "final mass \!\(\*SubscriptBox[\(M\), \(F\)]\)"}, 10, 90, 1}, { Hold[ Style["performance", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`ve$$], 4500, "exhaust velocity \!\(\*SubscriptBox[\(v\), \(e\)]\)"}, 1000, 5000, 100}, {{ Hold[$CellContext`m$$], 2, "mass flow rate m"}, 1, 20, 1}, {{ Hold[$CellContext`uplimits$$], 180, "acceleration limits \!\(\*SubscriptBox[\(a\), \(l\)]\)"}, 150, 200, 1}, { Hold[ Style["launch", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`view$$], "front", "view point"}, { "front", "side"}}, {{ Hold[$CellContext`option$$], "ground", "view option"}, { "ground", "earth"}}, {{ Hold[$CellContext`showtime$$], 200, "time maximum \!\(\*SubscriptBox[\(t\), \(max\)]\)"}, {100, 200, 500, 1000}}, {{ Hold[$CellContext`time$$], 0, "flight time t"}, 0, Dynamic[$CellContext`showtime$$], 1}}, Typeset`size$$ = { 348., {200., 205.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`level$36213$$ = 0, $CellContext`conehght$36214$$ = 0, $CellContext`bodyhght$36215$$ = 0, $CellContext`bodyradius$36216$$ = 0, $CellContext`M0$36217$$ = 0, $CellContext`MF$36218$$ = 0, $CellContext`ve$36219$$ = 0, $CellContext`m$36220$$ = 0, $CellContext`uplimits$36221$$ = 0, $CellContext`view$36222$$ = False, $CellContext`option$36223$$ = False, $CellContext`showtime$36224$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`bodyhght$$ = 20, $CellContext`bodyradius$$ = 1, $CellContext`conehght$$ = 5, $CellContext`level$$ = "first", $CellContext`m$$ = 2, $CellContext`M0$$ = 500, $CellContext`MF$$ = 60, $CellContext`option$$ = "ground", $CellContext`showtime$$ = 200, $CellContext`time$$ = 0, $CellContext`uplimits$$ = 180, $CellContext`ve$$ = 4500, $CellContext`view$$ = "front"}, "ControllerVariables" :> { Hold[$CellContext`level$$, $CellContext`level$36213$$, 0], Hold[$CellContext`conehght$$, $CellContext`conehght$36214$$, 0], Hold[$CellContext`bodyhght$$, $CellContext`bodyhght$36215$$, 0], Hold[$CellContext`bodyradius$$, $CellContext`bodyradius$36216$$, 0], Hold[$CellContext`M0$$, $CellContext`M0$36217$$, 0], Hold[$CellContext`MF$$, $CellContext`MF$36218$$, 0], Hold[$CellContext`ve$$, $CellContext`ve$36219$$, 0], Hold[$CellContext`m$$, $CellContext`m$36220$$, 0], Hold[$CellContext`uplimits$$, $CellContext`uplimits$36221$$, 0], Hold[$CellContext`view$$, $CellContext`view$36222$$, False], Hold[$CellContext`option$$, $CellContext`option$36223$$, False], Hold[$CellContext`showtime$$, $CellContext`showtime$36224$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`EV = If[$CellContext`level$$ == "first", $CellContext`firstEV, If[$CellContext`level$$ == "second", $CellContext`secondEV, $CellContext`thirdEV]]; \ $CellContext`sol = FindRoot[$CellContext`EV == $CellContext`ve$$ Log[E, $CellContext`Rneed], {$CellContext`Rneed, 1}]; $CellContext`Rneed = Part[ Part[$CellContext`sol, 1], 2]; $CellContext`Rgive = N[$CellContext`M0$$/$CellContext`MF$$]; $CellContext`parameters = \ $CellContext`rocketdynamics[$CellContext`time$$, $CellContext`ve$$, \ $CellContext`M0$$, $CellContext`MF$$, $CellContext`m$$]; \ $CellContext`equationplot = Plot[ Tooltip[$CellContext`ve$$ Log[E, $CellContext`MR], "rocket equation"], {$CellContext`MR, 1, 50}, PlotLabel -> Row[{"rocket equation ", Style["V", Italic], " = ", Style[ Subscript["v", "e"], Italic], " ln\!\(\*FractionBox[SubscriptBox[\(M\), \(0\)], \(M\)]\)"}], FrameLabel -> { Row[{"mass ratio ", Style["R", Italic], " = ", Subscript[ Style["M", Italic], 0], "/", Style["M", Italic]}], Row[{"velocity ", Style["V", Italic], "(m/s)"}]}, PlotStyle -> Directive[Blue, Thick], PlotRange -> {{1, 50}, {0, 21000}}, AxesOrigin -> {0.1, 0}, Frame -> True, ImageSize -> $CellContext`imagesize, ImagePadding -> $CellContext`imagepadding, Epilog -> {Thick, Dotted, Orange, PointSize[Large], Tooltip[ Line[{{1, $CellContext`EV}, {$CellContext`Rneed, \ $CellContext`EV}}], Row[{$CellContext`level$$, " escape velocity = ", $CellContext`EV, "m/s"}]], Tooltip[ Line[{{$CellContext`Rneed, 0}, {$CellContext`Rneed, $CellContext`EV}}], Row[{"required mass ratio = ", NumberForm[$CellContext`Rneed, {3, 2}]}]], Tooltip[ Point[{$CellContext`Rneed, $CellContext`EV}], "cross point"], Dashed, Black, Tooltip[ Line[{{$CellContext`Rgive, 0}, {$CellContext`Rgive, 21000}}], Row[{"designed mass ratio = ", NumberForm[$CellContext`Rgive, {3, 2}]}]], Blue, Tooltip[ Point[{ Part[$CellContext`parameters, 4], Part[$CellContext`parameters, 6]}], Row[{"velocity = ", Part[$CellContext`parameters, 6]}]]}]; $CellContext`functionplot = Plot[{ Tooltip[( 1/$CellContext`scale) $CellContext`acceleration[$CellContext`t, \ $CellContext`ve$$, $CellContext`M0$$, $CellContext`m$$], "acceleration curve"], Tooltip[ $CellContext`velocity[$CellContext`t, $CellContext`ve$$, \ $CellContext`M0$$, $CellContext`m$$], "velocity curve"], Tooltip[$CellContext`scale $CellContext`altitude[$CellContext`t, \ $CellContext`ve$$, $CellContext`M0$$, $CellContext`m$$], "altitude curve"]}, {$CellContext`t, 0, Part[$CellContext`parameters, 2]}, PlotRange -> {{0, Part[$CellContext`parameters, 2] + 100}, { 0, 2.1 10^4}}, PlotStyle -> { Directive[Red, Thick], Directive[Blue, Thick], Directive[Green, Thick]}, PlotLabel -> Row[{"dynamic parameters"}], ImageSize -> $CellContext`imagesize, ImagePadding -> $CellContext`imagepadding, Frame -> True, FrameLabel -> {"flight time t (s)", Column[{ Row[{"acceleration ", Style["a", Italic], " (", Style["m", Italic], "/", Style["s", Italic], ") \[Times] \!\(\*SuperscriptBox[\(10\), \(-2\)]\)"}], Row[{"velocity ", Style["V", Italic], " (", Style["m", Italic], "/", Style["s", Italic], ")"}], Row[{"altitude ", Style["S", Italic], " (", Style["m", Italic], ")\[Times] \!\(\*SuperscriptBox[\(10\), \(2\)]\)"}]}]}, Epilog -> {Thick, Dotted, PointSize[Large], Red, Tooltip[ Line[{{0, (1/$CellContext`scale) $CellContext`uplimits$$}, { Part[$CellContext`parameters, 2] + 100, (1/$CellContext`scale) $CellContext`uplimits$$}}], Row[{"acceleration limits ", $CellContext`uplimits$$, "(m/\!\(\*SuperscriptBox[\(s\), \(2\)]\))"}]], Dashed, Black, Tooltip[ Line[{{ Part[$CellContext`parameters, 2], 0}, { Part[$CellContext`parameters, 2], 2.1 10^4}}], Row[{"burn out at ", NumberForm[ Part[$CellContext`parameters, 2], {5, 1}], "(s)"}]], Red, Tooltip[ Point[{ Part[$CellContext`parameters, 1], (1/$CellContext`scale) Part[$CellContext`parameters, 5]}], Row[{"acceleration = ", Part[$CellContext`parameters, 5], "(m/\!\(\*SuperscriptBox[\(s\), \(2\)]\))"}]], Blue, Tooltip[ Point[{ Part[$CellContext`parameters, 1], Part[$CellContext`parameters, 6]}], Row[{"velocity = ", Part[$CellContext`parameters, 6], "(m/s)"}]], Green, Tooltip[ Point[{ Part[$CellContext`parameters, 1], $CellContext`scale Part[$CellContext`parameters, 7]}], Row[{"altitude = ", 0.001 Part[$CellContext`parameters, 7], "(km)"}]]}]; $CellContext`rocketplot = \ $CellContext`rocketmodel[$CellContext`scale Part[$CellContext`parameters, 7], $CellContext`conehght$$, $CellContext`bodyhght$$, \ $CellContext`bodyradius$$, If[$CellContext`view$$ == "front", Front, {10, 10, 10}]]; $CellContext`r = 6378.7; $CellContext`h = 0.001 Part[$CellContext`parameters, 7]; $CellContext`earth = Graphics3D[{ Opacity[0.5], Tooltip[ Sphere[{0, 0, 0}, $CellContext`r], Row[{"earth radius = ", $CellContext`r, "(km)"}]], PointSize[Large], Opacity[1], Red, Tooltip[ Point[{0, 0, $CellContext`r + $CellContext`h}], Row[{"rocket altitude = ", $CellContext`h, "(km)"}]], Yellow, Tooltip[ Point[{0, 0, $CellContext`r}], "launch site"]}, Boxed -> False, SphericalRegion -> True, Background -> Black, ImageSize -> {340, 400}]; If[$CellContext`option$$ == "ground", Grid[{{ Column[{$CellContext`equationplot, $CellContext`functionplot}], \ $CellContext`rocketplot}}], $CellContext`earth]), "Specifications" :> { Style[ "target escape velocity", Bold], {{$CellContext`level$$, "first", "level"}, { "first", "second", "third"}, ControlType -> Setter, ImageSize -> Tiny}, Delimiter, Style[ "geometry", Bold], {{$CellContext`conehght$$, 5, "head height \!\(\*SubscriptBox[\(h\), \(1\)]\)"}, 3, 10, 0.1, Appearance -> "Labeled", ImageSize -> Tiny}, {{$CellContext`bodyhght$$, 20, "body height \!\(\*SubscriptBox[\(h\), \(2\)]\)"}, 5, 30, 1, Appearance -> "Labeled", ImageSize -> Tiny}, {{$CellContext`bodyradius$$, 1, "body radius \!\(\*SubscriptBox[\(r\), \(2\)]\)"}, 1, 3, 0.1, Appearance -> "Labeled", ImageSize -> Tiny}, Delimiter, Style[ "specification", Bold], {{$CellContext`M0$$, 500, "initial mass \!\(\*SubscriptBox[\(M\), \(0\)]\)"}, 100, 1000, 1, Appearance -> "Labeled", ImageSize -> Tiny}, {{$CellContext`MF$$, 60, "final mass \!\(\*SubscriptBox[\(M\), \(F\)]\)"}, 10, 90, 1, Appearance -> "Labeled", ImageSize -> Tiny}, Delimiter, Style[ "performance", Bold], {{$CellContext`ve$$, 4500, "exhaust velocity \!\(\*SubscriptBox[\(v\), \(e\)]\)"}, 1000, 5000, 100, Appearance -> "Labeled", ImageSize -> Tiny}, {{$CellContext`m$$, 2, "mass flow rate m"}, 1, 20, 1, Appearance -> "Labeled", ImageSize -> Tiny}, {{$CellContext`uplimits$$, 180, "acceleration limits \!\(\*SubscriptBox[\(a\), \(l\)]\)"}, 150, 200, 1, Appearance -> "Labeled", ImageSize -> Tiny}, Delimiter, Style[ "launch", Bold], {{$CellContext`view$$, "front", "view point"}, { "front", "side"}, ControlType -> Setter, ImageSize -> Tiny}, {{$CellContext`option$$, "ground", "view option"}, { "ground", "earth"}, ControlType -> Setter, ImageSize -> Tiny}, {{$CellContext`showtime$$, 200, "time maximum \!\(\*SubscriptBox[\(t\), \(max\)]\)"}, {100, 200, 500, 1000}, ControlType -> Setter, ImageSize -> Tiny}, {{$CellContext`time$$, 0, "flight time t"}, 0, Dynamic[$CellContext`showtime$$], 1, Appearance -> "Labeled", ImageSize -> Tiny, ControlType -> Trigger}}, "Options" :> { ControlPlacement -> Left, TrackedSymbols :> Manipulate, SynchronousUpdating -> False, SynchronousInitialization -> False, AutorunSequencing -> {2, 3, 4, 13}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{607., {227., 232.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({{$CellContext`EV = 7830., $CellContext`firstEV = 7830., $CellContext`secondEV = 11200., $CellContext`thirdEV = 16600., $CellContext`sol = { 16.38602064160383 -> 5.697343422671991}, $CellContext`Rneed = 5.697343422671991, $CellContext`Rgive = 8.333333333333334, $CellContext`parameters = { 0, 220., 500, 1., 18., 0., 0.}, $CellContext`rocketdynamics[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`ve, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`M, Blank[]], Pattern[$CellContext`m, Blank[]]] := Module[{$CellContext`burntime}, $CellContext`burntime = N[($CellContext`M0/$CellContext`m) ( 1 - $CellContext`M/$CellContext`M0)]; If[$CellContext`t <= $CellContext`burntime, {$CellContext`t, \ $CellContext`burntime, $CellContext`mass[$CellContext`t, $CellContext`M0, \ $CellContext`m], $CellContext`massratio[$CellContext`t, $CellContext`M0, \ $CellContext`m], $CellContext`acceleration[$CellContext`t, $CellContext`ve, \ $CellContext`M0, $CellContext`m], $CellContext`velocity[$CellContext`t, $CellContext`ve, \ $CellContext`M0, $CellContext`m], $CellContext`altitude[$CellContext`t, $CellContext`ve, \ $CellContext`M0, $CellContext`m]}, {$CellContext`burntime, \ $CellContext`burntime, $CellContext`mass[$CellContext`burntime, $CellContext`M0, \ $CellContext`m], $CellContext`massratio[$CellContext`burntime, $CellContext`M0, \ $CellContext`m], $CellContext`acceleration[$CellContext`burntime, \ $CellContext`ve, $CellContext`M0, $CellContext`m], $CellContext`velocity[$CellContext`burntime, $CellContext`ve, \ $CellContext`M0, $CellContext`m], $CellContext`altitude[$CellContext`burntime, $CellContext`ve, \ $CellContext`M0, $CellContext`m]}]], $CellContext`mass[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := $CellContext`M0 - $CellContext`m $CellContext`t, \ $CellContext`massratio[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := N[$CellContext`M0/$CellContext`mass[$CellContext`t, $CellContext`M0, \ $CellContext`m]], $CellContext`acceleration[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`ve, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := N[($CellContext`m $CellContext`ve)/($CellContext`M0 - $CellContext`m \ $CellContext`t)], $CellContext`velocity[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`ve, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := N[$CellContext`ve Log[E, $CellContext`M0/$CellContext`mass[$CellContext`t, \ $CellContext`M0, $CellContext`m]]], $CellContext`altitude[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`ve, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := N[($CellContext`ve ($CellContext`M0/$CellContext`m)) ( 1 - ($CellContext`mass[$CellContext`t, $CellContext`M0, \ $CellContext`m]/$CellContext`M0) ( Log[E, $CellContext`M0/$CellContext`mass[$CellContext`t, \ $CellContext`M0, $CellContext`m]] + 1))], $CellContext`equationplot = Graphics[{{{}, {}, { Hue[0.67, 0.6, 0.6], Directive[ RGBColor[0, 0, 1], Thickness[Large]], Tooltip[ Line[CompressedData[" 1:eJwV1Ps/1PkDxfFJ5FpuoWRLaqdUJiS3mj7HbYx1CUkXXSkUckkUyVglX0WS 2tokYcd9TaGdairX3DIGa1u3pWWpHtrcL5HZ9/eH83g9nv/AWesZ6HpSgkaj hZL9v/IRgQqLaCPU3en8sTtnQih/Z9udN5gjVIKfovy2OmcI6Wv8v4scoUZb H/pfzD2GlDZho9nUCBVpUPCbml8QNPUY10KGR6kBpw4L03+jods3LDvw5zj1 zeektrZjEhKeVpuFqE9QBZyO5l8WbmD4etopmtsEdSI0PzSmPRk8M4d6reYJ anZFNI5GpMD0VkH83ppJqj65m1eccxu2rNPStY+nqQDVRO6L+/eRq2VpsvfL NBVn7tF/wSUNcuMrffq3zFDJ94sVfKQeQPiw/o04Z4Zy6PZ7MuaTDvfZjXGm 6bPU4COR3bHrGThZOCSZnzBHecw4pYo1shCrclIi0UtM1ZovZdTxcnDR/AaP zRVT7woqWCZzOQjzfHZE8qOY8uhUU5GzyYVRR1wP04QGaV/znoE/ckHX7TIr E9Dwet+Tp0/G8yBfHzuWVbsIVeMVRQ9UC9Eu0+4V07MYnhl3q97MFqNV65N5 78JiyFSPaLho8iDUFysztSVRceFQV6IJD3X7dctnPCWheE5uWXgwD89zo7SC Pkji9P625Sv7eUhn09uPjEthqWKltOarx/CND2ftlJWB4pRcaax7CU7MfFA8 sVEGu8997WIGlOCo78GOa7YyOJhrXdsZWwJ3NtO/64oM1Ef0VF7xSmAtszgl QkIW26p7vQxlS6Edn9TDn5OFYnvbp6VlpXh39ZfQ7f/KYzjVRR1fy8C62pbJ aFPE77u+t8+y4aNj2Hzm2agiuO8DdCLc+TDWbeHqyCjh8oXzQ/DhoyHJdL6I roTYj4LS9Hg+xg5I51R7KWGjb0F6egMfliPZ86M9SuD6HHpWZ/8Mf2v15Ti0 KqOntWn+ktVzrA1zX1j0QhVJgfd5fksFcH6ZLnOrURX7dNr/2aAlAEdySGV9 tyq8X6Lx3SYB+lLCN7C+qaLiTsyMCluAjOK7zgnUcowvPbNsNkaA1R87M1Wq lyMo30Hj9rgAmoeO2q5rUsP6HbMfEoQvsdzSN9m6VwPHU+1N33u/Rn+i1Jka wSok/moftEKqAhvGa/VXf14DxqpgeqJFJV5eWW82IamDwD+lWFtcq/B7S370 zJd1mH3j31+5vRrc/Cq+ryQdldaZAUvUauBtlalxfnIDJocqtBhtNSja3re9 vFsXFqcinfWj36C4lMcK/bwZdIXCJoUttXg4zoqq7dRDalxzCqOyFnavA7lx o1ux42Bd9P6DdWCORdpSYn04ZV9i7husQ9NAplBuwgBnP0WERx2vx/PvVHdf /2aI+k1X/Tp765Fu7O15eHIb1no5q/F3N6D3tkTgwKLt4JsrZE1XNmDgkVPX VVljZG8d8uAyGtGXGNUZITZG39499XlJjTArn2xdJ2eK1acvv3Mba8T/Wp2P aC02g9fBY8eT7d/iwU0PO4NpM3yRPv9J8PAtlv1UrDcvNofUz2cbMqbfIuzi YLb69A4E7Zjalcdqws5cb7UhCSYSNhfdsL/XhBrOnX/aZHfhXs0rh5ShJtiY 5bGVxLvglhWcZ8QQQjntR9cYSaAlR1Pl+HkhIuV1fsjkAMxIfmPECyFsXe4F u3wFVruMbDw6J4Sledltj0sW0GGFOZTtaib/YhmbOGuB+FKT4OrIZhy+ERqg GW2JVXu0stcJmhE1p7G2ec4SynevrHk01Qwx85akSpgVjLsZrtYaIvDWlQwU f7VCkm4hq9VIhEMXrJPOhVnDMbvmCX+3CCYhEUZ35q3x+anjiK6/CKEW8XI2 HBsMV+a+8rkqQiFHOn/VnA0S3t07sDNDBFWvzSxHDgthttz+xOcinCsrL+DO sxAhdeyv1FYRzP7Ss0gKs0VpoKMM96MIW/KpNtFX4k2Jb+gSLdAcrGTsCGPD QDy959qKFpjUfIqjzbPhLn8+z1W/BYbXiy4rEW+Lv3JhLzFjT9CP2sRGpjft 9hPT309GgTjXIOvjYWL1b7RzHOKfEx7rniKeMtLwon1jo+iP8Lxo4tJsK4q2 wEb+UH5OITHPbwlTifh406XwYuJCw3pzbeIrg862T4izy52MQaxV8mXwN+Jb 3Qf0OMQNZRr0KuKQ5UGraGI21nspZ3cQn+kyXKlELODUne0mPp05qa5NPNgS ZdVL7KkfqQLimWX9fw8QuzjEyXKI3SZ+WjtC7KBqJ51M/OxXjI4RszvlpTKI q9KGyieJ4XuTVk7cqKp/bI5451a3hWZiYVrL1gVi0yn1+V7i6APBYppBC4xe dsx+Ie61U2xeTKx/OW1aTDwWUJC+hPg/s5xvfQ== "]], "rocket equation"]}}}, { AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesOrigin -> {0.1, 0}, Epilog -> { Thickness[Large], Dashing[{0, Small}], RGBColor[1, 0.5, 0], PointSize[Large], Tooltip[ Line[{{1, 7830.}, {5.697343422671991, 7830.}}], Row[{"first", " escape velocity = ", 7830., "m/s"}]], Tooltip[ Line[{{5.697343422671991, 0}, {5.697343422671991, 7830.}}], Row[{"required mass ratio = ", NumberForm[5.697343422671991, {3, 2}]}]], Tooltip[ Point[{5.697343422671991, 7830.}], "cross point"], Dashing[{Small, Small}], GrayLevel[0], Tooltip[ Line[{{8.333333333333334, 0}, {8.333333333333334, 21000}}], Row[{"designed mass ratio = ", NumberForm[8.333333333333334, {3, 2}]}]], RGBColor[0, 0, 1], Tooltip[ Point[{1., 0.}], Row[{"velocity = ", 0.}]]}, Frame -> True, FrameLabel -> { Row[{"mass ratio ", Style["R", Italic], " = ", Subscript[ Style["M", Italic], 0], "/", Style["M", Italic]}], Row[{"velocity ", Style["V", Italic], "(m/s)"}]}, ImagePadding -> {{80, 5}, {35, 30}}, ImageSize -> {230, 200}, PlotLabel -> Row[{"rocket equation ", Style["V", Italic], " = ", Style[ Subscript["v", "e"], Italic], " ln\!\(\*FractionBox[SubscriptBox[\(M\), \(0\)], \(M\)]\)"}], PlotRange -> {{1, 50}, {0, 21000}}, PlotRangeClipping -> True, PlotRangePadding -> {Automatic, Automatic}}], Attributes[Subscript] = {NHoldRest}, Subscript[$CellContext`X, Pattern[$CellContext`j, Blank[]]][ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`t, Blank[]]] := ($CellContext`x - \ $CellContext`\[Mu][$CellContext`p1, $CellContext`j, $CellContext`t])/Sqrt[ 2 $CellContext`\[Mu][2, $CellContext`j, $CellContext`t]], Subscript[$CellContext`c, Pattern[$CellContext`j, Blank[]]][ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`t, Blank[]]] := ((1/3) Exp[-Subscript[$CellContext`X, $CellContext`j][$CellContext`x, \ $CellContext`t]^2]) ((1 + $CellContext`\[Mu][3, $CellContext`j, Part[ Delete[{1, 2, 3}, $CellContext`j], 1], Part[ Delete[{1, 2, 3}, $CellContext`j], 2], $CellContext`t] (( 8 Subscript[$CellContext`X, $CellContext`j][$CellContext`x, \ $CellContext`t]^3 - 12 Subscript[$CellContext`X, $CellContext`j][$CellContext`x, \ $CellContext`t])/( 6 (2 $CellContext`\[Mu][ 2, $CellContext`j, $CellContext`t])^1.5)))/ Sqrt[(2 Pi) $CellContext`\[Mu][ 2, $CellContext`j, $CellContext`t]]), Subscript[$CellContext`g, 1][ Pattern[$CellContext`x, Blank[]]] = $CellContext`x, Subscript[$CellContext`g, 2][ Pattern[$CellContext`x, Blank[]]] = 2^($CellContext`x/2), Subscript[$CellContext`g, 3][ Pattern[$CellContext`x, Blank[]]] = 2^(2^(-1 + $CellContext`x/2)), Subscript[$CellContext`g, 4][ Pattern[$CellContext`x, Blank[]]] = 2^(2^(-1 + 2^(-1 + $CellContext`x/2))), Subscript[$CellContext`g, 5][ Pattern[$CellContext`x, Blank[]]] = 2^(2^(-1 + 2^(-1 + 2^(-1 + $CellContext`x/2)))), Subscript[$CellContext`g, 6][ Pattern[$CellContext`x, Blank[]]] = 2^(2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + $CellContext`x/2))))), Subscript[$CellContext`g, 7][ Pattern[$CellContext`x, Blank[]]] = 2^(2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + $CellContext`x/2)))))), Subscript[$CellContext`g, 8][ Pattern[$CellContext`x, Blank[]]] = 2^(2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + $CellContext`x/2))))))), Subscript[$CellContext`g, 9][ Pattern[$CellContext`x, Blank[]]] = 2^(2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + $CellContext`x/2)))))))), Subscript[$CellContext`g, 10][ Pattern[$CellContext`x, Blank[]]] = 2^(2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + $CellContext`x/2))))))))), Subscript[$CellContext`g, 11][ Pattern[$CellContext`x, Blank[]]] := 1.9887117734139532`, Subscript[$CellContext`g, 12][ Pattern[$CellContext`x, Blank[]]] := 1.992190882947057, Subscript[$CellContext`g, 13][ Pattern[$CellContext`x, Blank[]]] := 1.994594450712101, Subscript[$CellContext`g, 14][ Pattern[$CellContext`x, Blank[]]] := 1.9962566662658583`, Subscript[$CellContext`g, 15][ Pattern[$CellContext`x, Blank[]]] := Sqrt[2]^( Sqrt[2]^( Sqrt[2]^( Sqrt[2]^( Sqrt[2]^( 2^(2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + 2^(-1 + $CellContext`x/2)))))))))))))), Subscript[C, $CellContext`A0] = 1, Subscript[C, $CellContext`B0] = 4, Subscript[D, $CellContext`AS] = 0.0010064496000000002`, Subscript[D, $CellContext`BS] = 0.0005032248000000001, Subscript[$CellContext`v, 1] = 1/50, Subscript[$CellContext`v, 2] = (-3)/100, Subscript[$CellContext`v, 3] = 1/25, $CellContext`\[Mu][$CellContext`p1, 1, Pattern[$CellContext`t, Blank[]]] := (2 Subscript[$CellContext`v, 1] - Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 3]) ((1 - Exp[((-3) $CellContext`ke) $CellContext`t])/( 9 $CellContext`ke)) + (Subscript[$CellContext`v, 1] + Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 3]) ($CellContext`t/ 3), $CellContext`\[Mu][$CellContext`p1, 2, Pattern[$CellContext`t, Blank[]]] := (2 Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 1] - Subscript[$CellContext`v, 3]) ((1 - Exp[((-3) $CellContext`ke) $CellContext`t])/( 9 $CellContext`ke)) + (Subscript[$CellContext`v, 1] + Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 3]) ($CellContext`t/ 3), $CellContext`\[Mu][$CellContext`p1, 3, Pattern[$CellContext`t, Blank[]]] := (2 Subscript[$CellContext`v, 3] - Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 1]) ((1 - Exp[((-3) $CellContext`ke) $CellContext`t])/( 9 $CellContext`ke)) + (Subscript[$CellContext`v, 1] + Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 3]) ($CellContext`t/ 3), $CellContext`\[Mu][2, 1, Pattern[$CellContext`t, Blank[]]] := (-(2 Subscript[$CellContext`v, 1] - Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 3])^2) ( Exp[((-6.) $CellContext`ke) $CellContext`t]/( 81 $CellContext`ke^2)) - (( 2 (2 Subscript[$CellContext`v, 1]^2 - Subscript[$CellContext`v, 2]^2 - Subscript[$CellContext`v, 3]^2 - 2 (Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 3] - (2 Subscript[$CellContext`v, 2]) Subscript[$CellContext`v, 3]))) $CellContext`t) ( Exp[((-3) $CellContext`ke) $CellContext`t]/( 27 $CellContext`ke)) + ( 8 (Subscript[$CellContext`v, 1]^2 + Subscript[$CellContext`v, 2]^2 + Subscript[$CellContext`v, 3]^2 - ( Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 3] + Subscript[$CellContext`v, 2] Subscript[$CellContext`v, 3]))) ( Exp[((-3.) $CellContext`ke) $CellContext`t]/( 81 $CellContext`ke^2)) + ((-4) Subscript[$CellContext`v, 1]^2 - 7 Subscript[$CellContext`v, 2]^2 - 7 Subscript[$CellContext`v, 3]^2 + (4 Subscript[$CellContext`v, 1]) Subscript[$CellContext`v, 2] + (4 Subscript[$CellContext`v, 1]) Subscript[$CellContext`v, 3] + (10 Subscript[$CellContext`v, 2]) Subscript[$CellContext`v, 3])/( 81. $CellContext`ke^2) + ((54 $CellContext`Diff) $CellContext`ke + 4 (Subscript[$CellContext`v, 1]^2 + Subscript[$CellContext`v, 2]^2 + Subscript[$CellContext`v, 3]^2 - Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 3] - Subscript[$CellContext`v, 2] Subscript[$CellContext`v, 3])) ($CellContext`t/( 27. $CellContext`ke)), $CellContext`\[Mu][2, 2, Pattern[$CellContext`t, Blank[]]] := (-(2 Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 1] - Subscript[$CellContext`v, 3])^2) ( Exp[((-6.) $CellContext`ke) $CellContext`t]/( 81 $CellContext`ke^2)) - (( 2 (2 Subscript[$CellContext`v, 2]^2 - Subscript[$CellContext`v, 1]^2 - Subscript[$CellContext`v, 3]^2 - 2 (Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 2] Subscript[$CellContext`v, 3] - (2 Subscript[$CellContext`v, 1]) Subscript[$CellContext`v, 3]))) $CellContext`t) ( Exp[((-3) $CellContext`ke) $CellContext`t]/( 27 $CellContext`ke)) + ( 8 (Subscript[$CellContext`v, 1]^2 + Subscript[$CellContext`v, 2]^2 + Subscript[$CellContext`v, 3]^2 - ( Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 3] + Subscript[$CellContext`v, 2] Subscript[$CellContext`v, 3]))) ( Exp[((-3.) $CellContext`ke) $CellContext`t]/( 81 $CellContext`ke^2)) + ((-4) Subscript[$CellContext`v, 2]^2 - 7 Subscript[$CellContext`v, 1]^2 - 7 Subscript[$CellContext`v, 3]^2 + (4 Subscript[$CellContext`v, 1]) Subscript[$CellContext`v, 2] + (4 Subscript[$CellContext`v, 2]) Subscript[$CellContext`v, 3] + (10 Subscript[$CellContext`v, 1]) Subscript[$CellContext`v, 3])/( 81. $CellContext`ke^2) + ((54 $CellContext`Diff) $CellContext`ke + 4 (Subscript[$CellContext`v, 1]^2 + Subscript[$CellContext`v, 2]^2 + Subscript[$CellContext`v, 3]^2 - Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 3] - Subscript[$CellContext`v, 2] Subscript[$CellContext`v, 3])) ($CellContext`t/( 27. $CellContext`ke)), $CellContext`\[Mu][2, 3, Pattern[$CellContext`t, Blank[]]] := (-(2 Subscript[$CellContext`v, 3] - Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 1])^2) ( Exp[((-6.) $CellContext`ke) $CellContext`t]/( 81 $CellContext`ke^2)) - (( 2 (2 Subscript[$CellContext`v, 3]^2 - Subscript[$CellContext`v, 2]^2 - Subscript[$CellContext`v, 1]^2 - 2 (Subscript[$CellContext`v, 3] Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 3] - (2 Subscript[$CellContext`v, 2]) Subscript[$CellContext`v, 1]))) $CellContext`t) ( Exp[((-3) $CellContext`ke) $CellContext`t]/( 27 $CellContext`ke)) + ( 8 (Subscript[$CellContext`v, 1]^2 + Subscript[$CellContext`v, 2]^2 + Subscript[$CellContext`v, 3]^2 - ( Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 2] + Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 3] + Subscript[$CellContext`v, 2] Subscript[$CellContext`v, 3]))) ( Exp[((-3.) $CellContext`ke) $CellContext`t]/( 81 $CellContext`ke^2)) + ((-4) Subscript[$CellContext`v, 3]^2 - 7 Subscript[$CellContext`v, 2]^2 - 7 Subscript[$CellContext`v, 1]^2 + (4 Subscript[$CellContext`v, 3]) Subscript[$CellContext`v, 2] + (4 Subscript[$CellContext`v, 1]) Subscript[$CellContext`v, 3] + (10 Subscript[$CellContext`v, 2]) Subscript[$CellContext`v, 1])/( 81. $CellContext`ke^2) + ((54 $CellContext`Diff) $CellContext`ke + 4 (Subscript[$CellContext`v, 1]^2 + Subscript[$CellContext`v, 2]^2 + Subscript[$CellContext`v, 3]^2 - Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 2] - Subscript[$CellContext`v, 1] Subscript[$CellContext`v, 3] - Subscript[$CellContext`v, 2] Subscript[$CellContext`v, 3])) ($CellContext`t/( 27. $CellContext`ke)), $CellContext`\[Mu][3, Pattern[$CellContext`j, Blank[]], Pattern[$CellContext`l, Blank[]], Pattern[$CellContext`m, Blank[]], Pattern[$CellContext`t, Blank[]]] := ((-2) (2 Subscript[$CellContext`v, $CellContext`j] - Subscript[$CellContext`v, $CellContext`l] - Subscript[$CellContext`v, $CellContext`m])^3) ( Exp[((-9) $CellContext`ke) $CellContext`t]/( 729 $CellContext`ke^3)) - (( 2 (2 Subscript[$CellContext`v, $CellContext`j] - Subscript[$CellContext`v, $CellContext`l] - Subscript[$CellContext`v, $CellContext`m])) (((-4) Subscript[$CellContext`v, $CellContext`j]^2 + (4 Subscript[$CellContext`v, $CellContext`j]) Subscript[$CellContext`v, $CellContext`l] - 4 Subscript[$CellContext`v, $CellContext`l]^2 + (4 Subscript[$CellContext`v, $CellContext`j]) Subscript[$CellContext`v, $CellContext`m] - 4 Subscript[$CellContext`v, $CellContext`m]^2 + (4 Subscript[$CellContext`v, $CellContext`m]) Subscript[$CellContext`v, $CellContext`l]) + (( 3 $CellContext`ke) $CellContext`t) ( 2 Subscript[$CellContext`v, $CellContext`j]^2 - (2 Subscript[$CellContext`v, $CellContext`j]) Subscript[$CellContext`v, $CellContext`l] - Subscript[$CellContext`v, $CellContext`l]^2 - (2 Subscript[$CellContext`v, $CellContext`j]) Subscript[$CellContext`v, $CellContext`m] - Subscript[$CellContext`v, $CellContext`m]^2 + (4 Subscript[$CellContext`v, $CellContext`m]) Subscript[$CellContext`v, $CellContext`l]))) ( Exp[((-6) $CellContext`ke) $CellContext`t]/( 243 $CellContext`ke^3)) - (( 2 Subscript[$CellContext`v, $CellContext`j] - Subscript[$CellContext`v, $CellContext`l] - Subscript[$CellContext`v, $CellContext`m]) (((-2) Subscript[$CellContext`v, $CellContext`j]^2 + (2 Subscript[$CellContext`v, $CellContext`j]) Subscript[$CellContext`v, $CellContext`l] + 16 Subscript[$CellContext`v, $CellContext`l]^2 + (2 Subscript[$CellContext`v, $CellContext`j]) Subscript[$CellContext`v, $CellContext`m] + 16 Subscript[$CellContext`v, $CellContext`m]^2 - (34 Subscript[$CellContext`v, $CellContext`m]) Subscript[$CellContext`v, $CellContext`l]) + (( 36 $CellContext`ke) $CellContext`t) (- Subscript[$CellContext`v, $CellContext`j]^2 + Subscript[$CellContext`v, $CellContext`j] Subscript[$CellContext`v, $CellContext`l] - Subscript[$CellContext`v, $CellContext`l] Subscript[$CellContext`v, $CellContext`m] + Subscript[$CellContext`v, $CellContext`j] Subscript[$CellContext`v, $CellContext`m]) + (( 9 $CellContext`ke^2) $CellContext`t^2) ( Subscript[$CellContext`v, $CellContext`j]^2 - Subscript[$CellContext`v, $CellContext`j] Subscript[$CellContext`v, $CellContext`l] + Subscript[$CellContext`v, $CellContext`l]^2 - Subscript[$CellContext`v, $CellContext`j] Subscript[$CellContext`v, $CellContext`m] + Subscript[$CellContext`v, $CellContext`m]^2 - Subscript[$CellContext`v, $CellContext`m] Subscript[$CellContext`v, $CellContext`l]))) ( Exp[((-3) $CellContext`ke) $CellContext`t]/( 243 $CellContext`ke^3)) + ( 2 (2 Subscript[$CellContext`v, $CellContext`j] - Subscript[$CellContext`v, $CellContext`l] - Subscript[$CellContext`v, $CellContext`m])) ((((-11) Subscript[$CellContext`v, $CellContext`j]^2 + (11 Subscript[$CellContext`v, $CellContext`j]) Subscript[$CellContext`v, $CellContext`l] + 13 Subscript[$CellContext`v, $CellContext`l]^2 + (11 Subscript[$CellContext`v, $CellContext`j]) Subscript[$CellContext`v, $CellContext`m] + 13 Subscript[$CellContext`v, $CellContext`m]^2 - (37 Subscript[$CellContext`v, $CellContext`m]) Subscript[$CellContext`v, $CellContext`l]) + (( 9 $CellContext`ke) $CellContext`t) ( Subscript[$CellContext`v, $CellContext`j]^2 - Subscript[$CellContext`v, $CellContext`j] 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$CellContext`body, $CellContext`wings, $CellContext`nozzle, \ $CellContext`ground}, $CellContext`cone[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`\[Phi], Blank[]], Pattern[$CellContext`\[Theta], Blank[]], Pattern[$CellContext`h1, Blank[]]] := $CellContext`p + {($CellContext`r Cos[$CellContext`\[Phi]]) ($CellContext`\[Theta]/ Pi), ($CellContext`r Sin[$CellContext`\[Phi]]) ($CellContext`\[Theta]/Pi), ( 1 - $CellContext`\[Theta]/ Pi) $CellContext`h1}; $CellContext`head[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h1, Blank[]]] := ParametricPlot3D[{ $CellContext`cone[{ 0, 0, $CellContext`p}, $CellContext`r, $CellContext`\[Phi], \ $CellContext`\[Theta], $CellContext`h1]}, {$CellContext`\[Phi], 0, 2 Pi}, {$CellContext`\[Theta], 0, Pi}, Boxed -> True, Mesh -> None, Axes -> True]; $CellContext`headplus[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h1, Blank[]]] := Graphics3D[{ Cylinder[{{0, 0, $CellContext`p}, { 0, 0, 1.5 $CellContext`h1 + $CellContext`p}}, 0.1 $CellContext`r]}]; $CellContext`body[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h2, Blank[]]] := Graphics3D[{ Cylinder[{{0, 0, $CellContext`p}, { 0, 0, -$CellContext`h2 + $CellContext`p}}, $CellContext`r]}, BaseStyle -> { Opacity[1], EdgeForm[]}, Lighting -> Automatic, Boxed -> False, Axes -> False, Background -> LightBlue, ImageSize -> {110, 400}, ViewPoint -> $CellContext`view]; $CellContext`wings[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h2, Blank[]]] := Graphics3D[{ Polygon[{{0, 0, (-0.5) $CellContext`h2 + $CellContext`p}, { 0, 2 $CellContext`r, (-0.7) $CellContext`h2 + \ $CellContext`p}, {0, 2 $CellContext`r, -$CellContext`h2 + $CellContext`p}, { 0, 0, (-0.8) $CellContext`h2 + $CellContext`p}}], Polygon[{{0, 0, (-0.5) $CellContext`h2 + $CellContext`p}, { 0, (-2) $CellContext`r, (-0.7) $CellContext`h2 + \ $CellContext`p}, { 0, (-2) $CellContext`r, -$CellContext`h2 + $CellContext`p}, { 0, 0, (-0.8) $CellContext`h2 + $CellContext`p}}], Polygon[{{0, 0, (-0.5) $CellContext`h2 + $CellContext`p}, { 2 $CellContext`r, 0, (-0.7) $CellContext`h2 + $CellContext`p}, { 2 $CellContext`r, 0, -$CellContext`h2 + $CellContext`p}, { 0, 0, (-0.8) $CellContext`h2 + $CellContext`p}}], Polygon[{{ 0, 0, (-0.5) $CellContext`h2 + $CellContext`p}, {(-2) \ $CellContext`r, 0, (-0.7) $CellContext`h2 + $CellContext`p}, {(-2) \ $CellContext`r, 0, -$CellContext`h2 + $CellContext`p}, { 0, 0, (-0.8) $CellContext`h2 + $CellContext`p}}]}]; \ $CellContext`quadraticsurface[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`t, Blank[]]] := $CellContext`p + {$CellContext`r Cos[$CellContext`t], $CellContext`r Sin[$CellContext`t], -$CellContext`r^2}; $CellContext`nozzle[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h2, Blank[]]] := ParametricPlot3D[ $CellContext`quadraticsurface[{ 0, 0, -$CellContext`h2 + 0.2 $CellContext`r + $CellContext`p}, $CellContext`rad, \ $CellContext`t], {$CellContext`t, 0, 2 Pi}, {$CellContext`rad, 0, 1}, Mesh -> None]; $CellContext`ground[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h2, Blank[]]] := Graphics3D[{Green, Opacity[0.5], Polygon[{{(-10) $CellContext`r, (-10) $CellContext`r, \ -($CellContext`h2 + 1)}, {(-10) $CellContext`r, 10 $CellContext`r, -($CellContext`h2 + 1)}, { 10 $CellContext`r, 10 $CellContext`r, -($CellContext`h2 + 1)}, { 10 $CellContext`r, (-10) $CellContext`r, -($CellContext`h2 + 1)}}]}]; Show[ $CellContext`body[$CellContext`position, $CellContext`radius, \ $CellContext`height2], $CellContext`head[$CellContext`position, $CellContext`radius, \ $CellContext`height1], $CellContext`headplus[$CellContext`position, \ $CellContext`radius, $CellContext`height1], $CellContext`nozzle[$CellContext`position, $CellContext`radius, \ $CellContext`height2], $CellContext`ground[$CellContext`position, $CellContext`radius, \ $CellContext`height2], $CellContext`wings[$CellContext`position, $CellContext`radius, \ $CellContext`height2]]], $CellContext`r = 6378.7, $CellContext`quadraticsurface[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`t, Blank[]]] := $CellContext`p + {$CellContext`r Cos[$CellContext`t], $CellContext`r Sin[$CellContext`t], -$CellContext`r^2}, $CellContext`h = 0., $CellContext`earth = Graphics3D[{ Opacity[0.5], Tooltip[ Sphere[{0, 0, 0}, 6378.7], Row[{"earth radius = ", 6378.7, "(km)"}]], PointSize[Large], Opacity[1], RGBColor[1, 0, 0], Tooltip[ Point[{0, 0, 6378.7}], Row[{"rocket altitude = ", 0., "(km)"}]], RGBColor[1, 1, 0], Tooltip[ Point[{0, 0, 6378.7}], "launch site"]}, Boxed -> False, SphericalRegion -> True, Background -> GrayLevel[0], ImageSize -> {340, 400}]}; {$CellContext`imagesize = {230, 200}; $CellContext`imagepadding = {{80, 5}, {35, 30}}; $CellContext`scale = 0.01; $CellContext`firstEV = 7.83 10^3; $CellContext`secondEV = 11.2 10^3; $CellContext`thirdEV = 16.6 10^3; $CellContext`mass[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := $CellContext`M0 - $CellContext`m $CellContext`t; \ $CellContext`massratio[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := N[$CellContext`M0/$CellContext`mass[$CellContext`t, \ $CellContext`M0, $CellContext`m]]; $CellContext`acceleration[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`ve, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := N[$CellContext`m ($CellContext`ve/($CellContext`M0 - $CellContext`m \ $CellContext`t))]; $CellContext`velocity[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`ve, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := N[$CellContext`ve Log[E, $CellContext`M0/$CellContext`mass[$CellContext`t, \ $CellContext`M0, $CellContext`m]]]; $CellContext`altitude[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`ve, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`m, Blank[]]] := N[($CellContext`ve ($CellContext`M0/$CellContext`m)) ( 1 - ($CellContext`mass[$CellContext`t, $CellContext`M0, \ $CellContext`m]/$CellContext`M0) ( Log[E, $CellContext`M0/$CellContext`mass[$CellContext`t, \ $CellContext`M0, $CellContext`m]] + 1))]; $CellContext`rocketdynamics[ Pattern[$CellContext`t, Blank[]], Pattern[$CellContext`ve, Blank[]], Pattern[$CellContext`M0, Blank[]], Pattern[$CellContext`M, Blank[]], Pattern[$CellContext`m, Blank[]]] := Module[{$CellContext`burntime}, $CellContext`burntime = N[($CellContext`M0/$CellContext`m) ( 1 - $CellContext`M/$CellContext`M0)]; If[$CellContext`t <= $CellContext`burntime, {$CellContext`t, \ $CellContext`burntime, $CellContext`mass[$CellContext`t, $CellContext`M0, \ $CellContext`m], $CellContext`massratio[$CellContext`t, $CellContext`M0, \ $CellContext`m], $CellContext`acceleration[$CellContext`t, $CellContext`ve, \ $CellContext`M0, $CellContext`m], $CellContext`velocity[$CellContext`t, $CellContext`ve, \ $CellContext`M0, $CellContext`m], $CellContext`altitude[$CellContext`t, $CellContext`ve, \ $CellContext`M0, $CellContext`m]}, {$CellContext`burntime, \ $CellContext`burntime, $CellContext`mass[$CellContext`burntime, $CellContext`M0, \ $CellContext`m], $CellContext`massratio[$CellContext`burntime, $CellContext`M0, \ $CellContext`m], $CellContext`acceleration[$CellContext`burntime, \ $CellContext`ve, $CellContext`M0, $CellContext`m], $CellContext`velocity[$CellContext`burntime, $CellContext`ve, \ $CellContext`M0, $CellContext`m], $CellContext`altitude[$CellContext`burntime, $CellContext`ve, \ $CellContext`M0, $CellContext`m]}]]; $CellContext`rocketmodel[ Pattern[$CellContext`position, Blank[]], Pattern[$CellContext`height1, Blank[]], Pattern[$CellContext`height2, Blank[]], Pattern[$CellContext`radius, Blank[]], Pattern[$CellContext`view, Blank[]]] := Module[{$CellContext`cone, $CellContext`head, \ $CellContext`headplus, $CellContext`body, $CellContext`wings, \ $CellContext`nozzle, $CellContext`ground}, $CellContext`cone[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`\[Phi], Blank[]], Pattern[$CellContext`\[Theta], Blank[]], Pattern[$CellContext`h1, Blank[]]] := $CellContext`p + {($CellContext`r Cos[$CellContext`\[Phi]]) ($CellContext`\[Theta]/ Pi), ($CellContext`r Sin[$CellContext`\[Phi]]) ($CellContext`\[Theta]/Pi), ( 1 - $CellContext`\[Theta]/ Pi) $CellContext`h1}; $CellContext`head[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h1, Blank[]]] := ParametricPlot3D[{ $CellContext`cone[{ 0, 0, $CellContext`p}, $CellContext`r, $CellContext`\[Phi], \ $CellContext`\[Theta], $CellContext`h1]}, {$CellContext`\[Phi], 0, 2 Pi}, {$CellContext`\[Theta], 0, Pi}, Boxed -> True, Mesh -> None, Axes -> True]; $CellContext`headplus[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h1, Blank[]]] := Graphics3D[{ Cylinder[{{0, 0, $CellContext`p}, { 0, 0, 1.5 $CellContext`h1 + $CellContext`p}}, 0.1 $CellContext`r]}]; $CellContext`body[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h2, Blank[]]] := Graphics3D[{ Cylinder[{{0, 0, $CellContext`p}, { 0, 0, -$CellContext`h2 + $CellContext`p}}, $CellContext`r]}, BaseStyle -> { Opacity[1], EdgeForm[]}, Lighting -> Automatic, Boxed -> False, Axes -> False, Background -> LightBlue, ImageSize -> {110, 400}, ViewPoint -> $CellContext`view]; $CellContext`wings[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h2, Blank[]]] := Graphics3D[{ Polygon[{{0, 0, (-0.5) $CellContext`h2 + $CellContext`p}, { 0, 2 $CellContext`r, (-0.7) $CellContext`h2 + \ $CellContext`p}, {0, 2 $CellContext`r, -$CellContext`h2 + $CellContext`p}, { 0, 0, (-0.8) $CellContext`h2 + $CellContext`p}}], Polygon[{{0, 0, (-0.5) $CellContext`h2 + $CellContext`p}, { 0, (-2) $CellContext`r, (-0.7) $CellContext`h2 + \ $CellContext`p}, { 0, (-2) $CellContext`r, -$CellContext`h2 + $CellContext`p}, \ {0, 0, (-0.8) $CellContext`h2 + $CellContext`p}}], Polygon[{{0, 0, (-0.5) $CellContext`h2 + $CellContext`p}, { 2 $CellContext`r, 0, (-0.7) $CellContext`h2 + $CellContext`p}, { 2 $CellContext`r, 0, -$CellContext`h2 + $CellContext`p}, { 0, 0, (-0.8) $CellContext`h2 + $CellContext`p}}], Polygon[{{ 0, 0, (-0.5) $CellContext`h2 + $CellContext`p}, {(-2) \ $CellContext`r, 0, (-0.7) $CellContext`h2 + $CellContext`p}, {(-2) \ $CellContext`r, 0, -$CellContext`h2 + $CellContext`p}, { 0, 0, (-0.8) $CellContext`h2 + $CellContext`p}}]}]; \ $CellContext`quadraticsurface[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`t, Blank[]]] := $CellContext`p + {$CellContext`r Cos[$CellContext`t], $CellContext`r Sin[$CellContext`t], -$CellContext`r^2}; $CellContext`nozzle[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h2, Blank[]]] := ParametricPlot3D[ $CellContext`quadraticsurface[{ 0, 0, -$CellContext`h2 + 0.2 $CellContext`r + $CellContext`p}, $CellContext`rad, \ $CellContext`t], {$CellContext`t, 0, 2 Pi}, {$CellContext`rad, 0, 1}, Mesh -> None]; $CellContext`ground[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`h2, Blank[]]] := Graphics3D[{Green, Opacity[0.5], Polygon[{{(-10) $CellContext`r, (-10) $CellContext`r, \ -($CellContext`h2 + 1)}, {(-10) $CellContext`r, 10 $CellContext`r, -($CellContext`h2 + 1)}, { 10 $CellContext`r, 10 $CellContext`r, -($CellContext`h2 + 1)}, { 10 $CellContext`r, (-10) $CellContext`r, -($CellContext`h2 + 1)}}]}]; Show[ $CellContext`body[$CellContext`position, $CellContext`radius, \ $CellContext`height2], $CellContext`head[$CellContext`position, $CellContext`radius, \ $CellContext`height1], $CellContext`headplus[$CellContext`position, \ $CellContext`radius, $CellContext`height1], $CellContext`nozzle[$CellContext`position, $CellContext`radius, \ $CellContext`height2], $CellContext`ground[$CellContext`position, $CellContext`radius, \ $CellContext`height2], $CellContext`wings[$CellContext`position, $CellContext`radius, \ $CellContext`height2]]]; Null}}; Typeset`initDone$$ = True), SynchronousInitialization->False, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->481712594], Cell["\<\ The launch of a spacecraft is fundamental to all space activity. As a rocket \ flies it loses mass, because most of its mass is fuel (pure hydrogen and \ oxygen) that provides the propulsive force. \ \>", "ManipulateCaption", CellID->263717364], Cell["\<\ This Demonstration shows the dynamics of an ideal rocket from launch time to \ measured burn-out time, based on Newton's laws and Tsiolkovsky's rocket \ equation. Specify the rocket parameters and launch with the trigger. \ \>", "ManipulateCaption", CellID->693860988], Cell["THINGS TO TRY", "ManipulateCaption", FontSize->10, FontSlant->"Plain", FontColor->RGBColor[ 0.6950942244602121, 0.7903257801174944, 0.29706263828488594`], CellTags->"ControlSuggestions"], Cell[TextData[{ Cell[BoxData[ TooltipBox[ PaneSelectorBox[{False->Cell[TextData[StyleBox["Resize Images", FontFamily->"Verdana"]]], True->Cell[TextData[StyleBox["Resize Images", FontFamily->"Verdana", FontColor->GrayLevel[0.5]]]]}, Dynamic[ CurrentValue["MouseOver"]]], "\"Click inside an image to reveal its orange resize frame.\\nDrag any of \ the orange resize handles to resize the image.\"", LabelStyle->{ FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.35], Background -> GrayLevel[0.98]}]]], StyleBox["\[NonBreakingSpace]\[FilledVerySmallSquare]\[NonBreakingSpace]", FontColor->RGBColor[0.928786, 0.43122, 0.104662]], Cell[BoxData[ TooltipBox[ PaneSelectorBox[{False->Cell[TextData[StyleBox["Gamepad Controls", FontFamily->"Verdana"]]], True->Cell[TextData[StyleBox[ "Gamepad Controls", FontFamily->"Verdana", FontColor->GrayLevel[0.5]]]]}, Dynamic[ CurrentValue["MouseOver"]]], "\"Control this Demonstration with a gamepad or other\\nhuman interface \ device connected to your computer.\"", LabelStyle->{ FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.35], Background -> GrayLevel[0.98]}]]] }], "ManipulateCaption", CellMargins->{{Inherited, Inherited}, {0, 0}}, Deployed->True, FontFamily->"Verdana", CellTags->"ControlSuggestions"], Cell["DETAILS", "DetailsSection"], Cell["\<\ Graphic, top right: Tsiolkovsky's rocket equation, which defines the \ relationship between exhaust velocity and mass ratio\ \>", "DetailNotes", CellID->277789436], Cell["\<\ Graphic, bottom right: rocket dynamic parameters of acceleration, velocity, \ altitude and burn-out time\ \>", "DetailNotes", CellID->77599567], Cell["\<\ Graphic, left: 3D rocket dynamic launch model with altitude function control\ \>", "DetailNotes", CellID->336243608], Cell["\<\ Snapshot 1: ideal rocket specification that surpasses first escape velocity\ \>", "DetailNotes", CellID->748086750], Cell["\<\ Snapshot 2: ideal rocket specification that surpasses second escape velocity\ \>", "DetailNotes", CellID->893742195], Cell["\<\ Snapshot 3: 3D Earth scale model, with the launch site (yellow) and rocket \ altitude (red)\ \>", "DetailNotes", CellID->52159357], Cell[TextData[StyleBox["simplified assumptions: ", FontWeight->"Bold"]], "DetailNotes", CellID->65182283], Cell["1. gravity and aerodynamic drag effects are neglected", "DetailNotes", CellID->26288144], Cell["2. single stage rocket, initial velocity is zero", "DetailNotes", CellID->92558706], Cell["\<\ 3. vertical launch or pitch angle is 90\[Degree]\ \>", "DetailNotes", CellID->108814541], Cell["4. a constant exhaust velocity", "DetailNotes", CellID->41312689], Cell["5. a constant mass flow rate", "DetailNotes", CellID->2277782], Cell[TextData[StyleBox["governing equations: ", FontWeight->"Bold"]], "DetailNotes", CellID->184545377], Cell[TextData[{ "1. Tsiolkovsky's rocket equation or rocket velocity: ", Cell[BoxData[ FormBox[ RowBox[{"V", "=", RowBox[{ SubscriptBox["v", "e"], SubscriptBox["log", "e"], FractionBox[ SubscriptBox["M", "0"], "M"]}]}], TraditionalForm]], "InlineMath"] }], "DetailNotes", CellID->121608588], Cell[TextData[{ "2. mass flow rate: ", Cell[BoxData[ FormBox[ RowBox[{"M", "=", RowBox[{ SubscriptBox["M", "0"], "-", RowBox[{"m", " ", "t"}]}]}], TraditionalForm]], "InlineMath"] }], "DetailNotes", CellID->337993443], Cell[TextData[{ "3. maximum flight time or fuel burn\[Hyphen]out time: ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["t", "max"], "=", RowBox[{ FractionBox[ SubscriptBox["M", "0"], "m"], RowBox[{"(", RowBox[{"1", "-", FractionBox["M", SubscriptBox["M", "0"]]}], ")"}]}]}], TraditionalForm]], "InlineMath"] }], "DetailNotes", CellID->281803685], Cell[TextData[{ "4. rocket altitude: ", Cell[BoxData[ FormBox[ RowBox[{"s", "=", RowBox[{ SubscriptBox["v", "e"], RowBox[{ FractionBox[ SubscriptBox["M", "0"], "m"], "[", RowBox[{"1", "-", RowBox[{ FractionBox["M", SubscriptBox["M", "0"]], RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["log", "e"], FractionBox[ SubscriptBox["M", "0"], "M"]}], "+", "1"}], ")"}]}]}], "]"}]}]}], TraditionalForm]], "InlineMath"] }], "DetailNotes", CellID->375630966], Cell[TextData[{ "5. rocket acceleration: ", Cell[BoxData[ FormBox[ RowBox[{"a", "=", FractionBox[ RowBox[{"m", " ", SubscriptBox["v", "e"]}], RowBox[{ SubscriptBox["M", "0"], "-", RowBox[{"m", " ", "t"}]}]]}], TraditionalForm]], "InlineMath"], ", from ", Cell[BoxData[ FormBox[ RowBox[{"a", "=", FractionBox[ RowBox[{"d", "\[InvisibleSpace]", "V"}], RowBox[{"d", "\[InvisibleSpace]", "t"}]]}], TraditionalForm]], "InlineMath"], " and above governing equations 1 and 2" }], "DetailNotes", CellID->800653703], Cell[TextData[StyleBox["symbols:", FontWeight->"Bold"]], "DetailNotes", CellID->691868879], Cell[TextData[{ Cell[BoxData[ FormBox["V", TraditionalForm]], "InlineMath"], " is the rocket velocity." }], "DetailNotes", CellID->45773628], Cell[TextData[{ Cell[BoxData[ FormBox[ SubscriptBox["v", "e"], TraditionalForm]], "InlineMath"], " is the efficient exhaust velocity, constrained within a range 2500-4500 ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["m", FontSlant->"Plain"], "/", StyleBox["s", FontSlant->"Plain"]}], TraditionalForm]], "InlineMath"], ", using today's liquid\[Hyphen]fueled rocket chemical technology." }], "DetailNotes", CellID->35262624], Cell[TextData[{ Cell[BoxData[ FormBox[ SubscriptBox["M", "0"], TraditionalForm]], "InlineMath"], " is the initial rocket mass." }], "DetailNotes", CellID->213289220], Cell[TextData[{ Cell[BoxData[ FormBox["M", TraditionalForm]], "InlineMath"], " is the current or final rocket mass; ", Cell[BoxData[ FormBox["M", TraditionalForm]], "InlineMath"], " decreases during flight until all the liquid fuel is burned out. " }], "DetailNotes", CellID->745086993], Cell[TextData[{ Cell[BoxData[ FormBox[ SubscriptBox["M", "F"], TraditionalForm]], "InlineMath"], " is the final rocket mass, usually regarded as payload. " }], "DetailNotes", CellID->711047857], Cell[TextData[{ Cell[BoxData[ FormBox["R", TraditionalForm]], "InlineMath"], " is the mass ratio, ", Cell[BoxData[ FormBox[ RowBox[{"R", "=", FractionBox[ SubscriptBox["M", "0"], "M"]}], TraditionalForm]], "InlineMath"], ", which is usually in the range from 3 to 8; 14 is difficult to achieve." }], "DetailNotes", CellID->919875857], Cell[TextData[{ Cell[BoxData[ FormBox["m", TraditionalForm]], "InlineMath"], " is the mass flow rate, which depends on rocket engine design and \ specification; it indicates the rate at which the mass of the rocket is \ decreasing. Also called \"specific impulse\"." }], "DetailNotes", CellID->89679138], Cell[TextData[{ Cell[BoxData[ FormBox["t", TraditionalForm]], "InlineMath"], " is the rocket flight time, ", Cell[BoxData[ FormBox[ SubscriptBox["t", "max"], TraditionalForm]], "InlineMath"], ", which is the fuel burn-out time or the maximum flight time." }], "DetailNotes", CellID->93831264], Cell[TextData[{ Cell[BoxData[ FormBox["a", TraditionalForm]], "InlineMath"], " is the rocket acceleration. It is difficult for the human body to \ withstand high acceleration; 15-20 G is the maximum tolerance limit. (1 G is \ the acceleration due to gravity.)" }], "DetailNotes", CellID->231321746], Cell["References:", "DetailNotes", CellID->555763107], Cell[TextData[{ "J. Peraire, \"", ButtonBox["Variable Mass Systems: The Rocket Equation", BaseStyle->"Hyperlink", ButtonData->{ URL["http://ocw.mit.edu/NR/rdonlyres/Aeronautics-and-Astronautics/16-\ 07Fall-2004/EDABC2D9-6030-4F56-B369-D6CEE666F502/0/d27.pdf"], None}], ",\" MIT OpenCourseWare, 2004." }], "DetailNotes", CellID->507828097], Cell[TextData[{ "M. J. L. Turner, \"Newton's Third Law and the Rocket Equation,\" ", StyleBox["Rocket and Spacecraft Propulsion", FontSlant->"Italic"], ", 2nd ed., New York: Springer, 2005 pp. 14\[Dash]17." }], "DetailNotes", CellID->183421372], Cell[TextData[{ "M. J. L. Turner, \"Launch Vehicle Dynamics,\" ", StyleBox["Rocket and Spacecraft Propulsion", FontSlant->"Italic"], ", 2nd ed., New York: Springer, 2005 pp. 115\[Dash]144." }], "DetailNotes", CellID->3035121], Cell[TextData[{ "M. 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"http://demonstrations.wolfram.com/LaunchingARocket/LaunchingARocket-source.\ nb"], FontWeight->"Bold", FontColor->RGBColor[0.928786, 0.43122, 0.104662]]], "ShowSource", FontSize->10], Cell["PERMANENT CITATION DATA", "CitationSection"], Cell[TextData[{ "\"", ButtonBox["Launching a Rocket", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/LaunchingARocket/"], None}, ButtonNote->"http://demonstrations.wolfram.com/LaunchingARocket/"], "\"", " from ", ButtonBox["The Wolfram Demonstrations Project", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], "\[ParagraphSeparator]\[NonBreakingSpace]", ButtonBox["http://demonstrations.wolfram.com/LaunchingARocket/", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/LaunchingARocket/"], None}, ButtonNote->"http://demonstrations.wolfram.com/LaunchingARocket/"] }], "Citations"], Cell[" ", "AuthorSection"], Cell[TextData[{ "Contributed by: ", ButtonBox["Frederick Wu", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Frederick+Wu"], None}] }], "Author", FontColor->GrayLevel[0.6], CellID->70253165], Cell[TextData[{ "\[Copyright] ", StyleBox[ButtonBox["The Wolfram Demonstrations Project & Contributors", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], FontColor->GrayLevel[0.6]], "\[ThickSpace]\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", StyleBox[ButtonBox["Terms of Use", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/termsofuse.html"], None}, ButtonNote->"http://demonstrations.wolfram.com/termsofuse.html"], FontColor->GrayLevel[0.6]] }], "Text", CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{48, 48}, {20, 50}}, CellFrameColor->GrayLevel[0.45098], FontFamily->"Verdana", FontSize->9, 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