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Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`xkezd$$], 3, Subscript["x", 0]}, -4, 4, 0.01}, {{ Hold[$CellContext`ykezd$$], 0.1, Subscript["y", 0]}, -4, 4, 0.01}, {{ Hold[$CellContext`vxkezd$$], 0.1, Subscript["x'", 0]}, -4, 4, 0.01}, {{ Hold[$CellContext`vykezd$$], 0.6, Subscript["y'", 0]}, -4, 4, 0.01}, {{ Hold[$CellContext`showforce$$], False, "show gravity force"}, { True, False}}, {{ Hold[$CellContext`showvelocity$$], False, "show velocity"}, { True, False}}, {{ Hold[$CellContext`p$$], 0, "go!"}, 0, DirectedInfinity[1]}}, Typeset`size$$ = {488., {240., 248.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`xkezd$1373$$ = 0, $CellContext`ykezd$1374$$ = 0, $CellContext`vxkezd$1375$$ = 0, $CellContext`vykezd$1376$$ = 0, $CellContext`showforce$1377$$ = False, $CellContext`showvelocity$1378$$ = False, $CellContext`p$1379$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`p$$ = 0, $CellContext`showforce$$ = False, $CellContext`showvelocity$$ = False, $CellContext`vxkezd$$ = 0.1, $CellContext`vykezd$$ = 0.6, $CellContext`xkezd$$ = 3, $CellContext`ykezd$$ = 0.1}, "ControllerVariables" :> { Hold[$CellContext`xkezd$$, $CellContext`xkezd$1373$$, 0], Hold[$CellContext`ykezd$$, $CellContext`ykezd$1374$$, 0], Hold[$CellContext`vxkezd$$, $CellContext`vxkezd$1375$$, 0], Hold[$CellContext`vykezd$$, $CellContext`vykezd$1376$$, 0], Hold[$CellContext`showforce$$, $CellContext`showforce$1377$$, False], Hold[$CellContext`showvelocity$$, $CellContext`showvelocity$1378$$, False], Hold[$CellContext`p$$, $CellContext`p$1379$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`eqns$, $CellContext`soln$, $CellContext`x$, \ $CellContext`y$}, $CellContext`G = 1.; $CellContext`m = 2.; $CellContext`Rstar = Sqrt[$CellContext`m/20]; $CellContext`k = 100; $CellContext`r0 = ($CellContext`xkezd$$^2 + \ $CellContext`ykezd$$^2)^ Rational[ 1, 2]; $CellContext`v0 = ($CellContext`vxkezd$$^2 + \ $CellContext`vykezd$$^2)^ Rational[1, 2]; $CellContext`Et = $CellContext`v0^2/ 2 - $CellContext`G $CellContext`m/$CellContext`r0; $CellContext`J = \ $CellContext`xkezd$$ $CellContext`vykezd$$ - $CellContext`ykezd$$ \ $CellContext`vxkezd$$; $CellContext`se = $CellContext`J^2/($CellContext`G \ $CellContext`m); $CellContext`ex = (1 + 2 $CellContext`Et $CellContext`J^2/($CellContext`G^2 \ $CellContext`m^2))^ Rational[ 1, 2]; $CellContext`lambdax = (-$CellContext`m) \ ($CellContext`xkezd$$/$CellContext`r0) + $CellContext`vykezd$$ $CellContext`J; \ $CellContext`lambday = (-$CellContext`m) \ ($CellContext`ykezd$$/$CellContext`r0) - $CellContext`vxkezd$$ $CellContext`J; \ $CellContext`theta0 = Pi + ArcTan[$CellContext`lambdax, $CellContext`lambday]; \ $CellContext`angle0 = ArcTan[$CellContext`xkezd$$/$CellContext`r0, \ $CellContext`ykezd$$/$CellContext`r0]; $CellContext`eqns$ = { Derivative[ 2][$CellContext`x$][$CellContext`t] + $CellContext`G \ ($CellContext`m \ $CellContext`x$[$CellContext`t]/($CellContext`x$[$CellContext`t]^2 + \ $CellContext`y$[$CellContext`t]^2)^(3/2)) HeavisideTheta[ Sqrt[$CellContext`x$[$CellContext`t]^2 + \ $CellContext`y$[$CellContext`t]^2] - $CellContext`Rstar - 0.1] + $CellContext`k HeavisideTheta[$CellContext`Rstar + 0.1 - Sqrt[$CellContext`x$[$CellContext`t]^2 + \ $CellContext`y$[$CellContext`t]^2]] Sqrt[Derivative[1][$CellContext`x$][$CellContext`t]^2 + Derivative[1][$CellContext`y$][$CellContext`t]^2] Derivative[1][$CellContext`x$][$CellContext`t] == 0, Derivative[ 2][$CellContext`y$][$CellContext`t] + $CellContext`G \ ($CellContext`m \ $CellContext`y$[$CellContext`t]/($CellContext`x$[$CellContext`t]^2 + \ $CellContext`y$[$CellContext`t]^2)^(3/2)) HeavisideTheta[ Sqrt[$CellContext`x$[$CellContext`t]^2 + \ $CellContext`y$[$CellContext`t]^2] - $CellContext`Rstar - 0.1] + $CellContext`k HeavisideTheta[$CellContext`Rstar + 0.1 - Sqrt[$CellContext`x$[$CellContext`t]^2 + \ $CellContext`y$[$CellContext`t]^2]] Sqrt[Derivative[1][$CellContext`x$][$CellContext`t]^2 + Derivative[1][$CellContext`y$][$CellContext`t]^2] Derivative[1][$CellContext`y$][$CellContext`t] == 0, Derivative[1][$CellContext`x$][ 0] == $CellContext`vxkezd$$, $CellContext`x$[ 0] == $CellContext`xkezd$$, Derivative[1][$CellContext`y$][ 0] == $CellContext`vykezd$$, $CellContext`y$[ 0] == $CellContext`ykezd$$}; $CellContext`soln$ = NDSolve[$CellContext`eqns$, { $CellContext`x$[$CellContext`t], $CellContext`y$[$CellContext`t], Derivative[1][$CellContext`x$][$CellContext`t], Derivative[ 1][$CellContext`y$][$CellContext`t]}, {$CellContext`t, \ $CellContext`p$$, $CellContext`p$$ + 1}]; With[{$CellContext`pont$ = Part[ Evaluate[ ReplaceAll[ ReplaceAll[{ $CellContext`x$[$CellContext`t], $CellContext`y$[$CellContext`t]}, $CellContext`soln$], \ {$CellContext`t -> $CellContext`p$$}]], 1], $CellContext`seb$ = Part[ Evaluate[ ReplaceAll[ ReplaceAll[{ Derivative[1][$CellContext`x$][$CellContext`t], Derivative[ 1][$CellContext`y$][$CellContext`t]}, $CellContext`soln$], \ {$CellContext`t -> $CellContext`p$$}]], 1]}, Show[{ If[$CellContext`ex < 1, PolarPlot[$CellContext`se/(1 - $CellContext`ex Cos[$CellContext`u - $CellContext`theta0]), {$CellContext`u, 0, 2 Pi}, PlotRange -> 5, Axes -> True, GridLines -> Automatic], PolarPlot[$CellContext`se/(1 - $CellContext`ex Cos[$CellContext`u - $CellContext`theta0]), {$CellContext`u, \ $CellContext`theta0 + ArcCos[1/$CellContext`ex], 2 Pi + $CellContext`theta0 - ArcCos[1/$CellContext`ex]}, PlotRange -> 5, Axes -> True, GridLines -> Automatic]], Graphics[{ RGBColor[1., 0, 0], If[ EuclideanDistance[{0, 0}, $CellContext`pont$] < $CellContext`Rstar + 0.1, Text[ Style["Planet falls into star...", 16], {-3, 3.5}], Point[{0, 0}]], RGBColor[1, 0.71, 0], Disk[{0, 0}, $CellContext`Rstar], Darker[Green, 0.4], Disk[$CellContext`pont$, 0.1], If[$CellContext`showforce$$, { RGBColor[1, 0.47, 0], Arrowheads[Small], Arrow[{{ Part[$CellContext`pont$, 1], Part[$CellContext`pont$, 2]}, { Part[$CellContext`pont$, 1] - 3 $CellContext`m Part[$CellContext`pont$, 1]/ EuclideanDistance[{0, 0}, $CellContext`pont$]^3, Part[$CellContext`pont$, 2] - 3 $CellContext`m Part[$CellContext`pont$, 2]/ EuclideanDistance[{0, 0}, $CellContext`pont$]^3}}], Text[ Style[$CellContext`F, Medium], { Part[$CellContext`pont$, 1] - 3.1 $CellContext`m Part[$CellContext`pont$, 1]/ EuclideanDistance[{0, 0}, $CellContext`pont$]^3, Part[$CellContext`pont$, 2] - 3.1 $CellContext`m Part[$CellContext`pont$, 2]/ EuclideanDistance[{0, 0}, $CellContext`pont$]^3}]}, Point[{0, 0}]], If[$CellContext`showvelocity$$, { ColorData["HTML", "SlateBlue"], Arrowheads[Small], Arrow[{$CellContext`pont$, { Part[$CellContext`pont$, 1] + Part[$CellContext`seb$, 1], Part[$CellContext`pont$, 2] + Part[$CellContext`seb$, 2]}}], Text[ Style[$CellContext`v, Medium], { Part[$CellContext`pont$, 1] + 1.2 Part[$CellContext`seb$, 1], Part[$CellContext`pont$, 2] + 1.2 Part[$CellContext`seb$, 2]}]}, Point[{0, 0}]]}]}, ImageSize -> {390, 390}]]], "Specifications" :> { Style[ "initial position and velocity:", Bold, "Label"], {{$CellContext`xkezd$$, 3, Subscript["x", 0]}, -4, 4, 0.01, Appearance -> "Labeled", ImageSize -> Tiny}, {{$CellContext`ykezd$$, 0.1, Subscript["y", 0]}, -4, 4, 0.01, Appearance -> "Labeled", ImageSize -> Tiny}, {{$CellContext`vxkezd$$, 0.1, Subscript["x'", 0]}, -4, 4, 0.01, Appearance -> "Labeled", ImageSize -> Tiny}, {{$CellContext`vykezd$$, 0.6, Subscript["y'", 0]}, -4, 4, 0.01, Appearance -> "Labeled", ImageSize -> Tiny}, Delimiter, {{$CellContext`showforce$$, False, "show gravity force"}, { True, False}}, {{$CellContext`showvelocity$$, False, "show velocity"}, {True, False}}, {{$CellContext`p$$, 0, "go!"}, 0, DirectedInfinity[1], ControlType -> Trigger}}, 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Kepleri seadused moodustavad hea mudeli arvutamaks planeetide, mis ei \ erine\nliialt nendest piirangutest, orbiite." }], "Text", CellChangeTimes->{{3.630755968756037*^9, 3.6307559912113214`*^9}, { 3.630756179893113*^9, 3.630756209838826*^9}, {3.6307562796038165`*^9, 3.6307563221202483`*^9}, {3.630756424810122*^9, 3.6307564379498734`*^9}, { 3.6307564809233313`*^9, 3.6307564860096226`*^9}}], Cell["\<\ Peaaegu sajand hiljem t\[OTilde]estas Isaac Newton, et Kepleri seadused \ kehtivad kindlatel ideaalsetel tingimustel, mis piisavalt hea \ l\[ADoubleDot]hendusega esinevad P\[ADoubleDot]ikeses\[UDoubleDot]steemis, ja \ tulenevad Newtoni kolmest seadusest ja gravitatsiooniseadusest. Kuna \ planeetidel on mass ja massist tulenev liikumise perturbatsioon, kehtivad \ Kepleri seadused ainult ligikaudselt ja ei kirjelda t\[ADoubleDot]pselt P\ \[ADoubleDot]ikeses\[UDoubleDot]steemi sisemist liikumist.\ \>", "Text", CellChangeTimes->{{3.6307566024932847`*^9, 3.6307566233844795`*^9}}] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Miks kasutatakse mudeleid", FontFamily->"Arial"]], "Section", CellChangeTimes->{{3.62994524665625*^9, 3.62994525453125*^9}, { 3.62994604709375*^9, 3.6299460715*^9}, 3.62994610928125*^9, { 3.629946241375*^9, 3.629946247203125*^9}, {3.62997133659375*^9, 3.629971353578125*^9}}, FontSize->24], Cell[TextData[StyleBox["Modelleerimist rakendatakse siis, kui originaali \ vahetu uurimine on liiga kulukas, \nliiga raske v\[OTilde]i eetiliselt \ lubamatu. 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