Discrete Universe.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 8.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[    167801,       3258]
NotebookOptionsPosition[    165251,       3204]
NotebookOutlinePosition[    165782,       3223]
CellTagsIndexPosition[    165739,       3220]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData["\[AliasDelimiter]"], "Input",
 CellChangeTimes->{
  3.756689917464726*^9},ExpressionUUID->"a12fbfd2-1fb6-4d02-86f1-\
6e5903a024e5"],

Cell["", "Section",ExpressionUUID->"a8b193a2-d35e-4225-b8b6-61c01341e96b"],

Cell[CellGroupData[{

Cell["Energy Conservation in Discrete Universe", "Title",
 CellChangeTimes->{{3.569721556307778*^9, 3.569721569598296*^9}, {
   3.5749652323854218`*^9, 3.574965237024982*^9}, {3.5763585373524313`*^9, 
   3.576358550756617*^9}, 
   3.7566918432177763`*^9},ExpressionUUID->"3ef80519-7412-442c-a71a-\
653fa43f8339"],

Cell[CellGroupData[{

Cell["Introduction", "Section",
 CellChangeTimes->{{3.569721618115736*^9, 
  3.5697216266560698`*^9}},ExpressionUUID->"44306c87-f959-405a-86b9-\
78df6cb38e2c"],

Cell[TextData[{
 "This model is an agent-based universe in which each agent reacts to each \
other according to the Newton\[CloseCurlyQuote]s law of universal \
gravitation. Everything is discrete, including time. \n\nThe questions that \
we are trying to answer are: \n1) How does the initial velocity of one planet \
affect its trajectory around the sun?  How about mass? Location?\n2) By \
calculating the gravitational potential (also known as Newtonian potential) \
energy and the kinetic energy, we will investigate whether the total energy \
can be conserved in a discrete universe. \n\nTheoretical Framework:\nFirst, \
because of the complexity of simulating the entire solar system, we only \
included the sun and one planet in our model.  The sun is set to be initially \
located at the origin. The position (",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubscriptBox["x", "p"], ","}], TraditionalForm]],ExpressionUUID->
  "79cfeb15-465e-47de-9599-8c5468e4e4c2"],
 " ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["y", "p"], TraditionalForm]],ExpressionUUID->
  "a847210e-56ad-42b1-a6ca-eed81960148c"],
 "), the initial velocities (",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubscriptBox["x", "v"], ","}], TraditionalForm]],ExpressionUUID->
  "27e0bb5a-c7a6-4281-8014-ba7748891e6f"],
 " ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["y", "v"], TraditionalForm]],ExpressionUUID->
  "0b977f76-04ca-49ab-b716-d7eb3c29dffe"],
 "), and the mass of the planet will be manipulated. Each agent will interact \
with each other according to Newton\[CloseCurlyQuote]s law of universal \
gravitation:\nF=G ",
 Cell[BoxData[
  FormBox[
   FractionBox[
    RowBox[{
     SubscriptBox["m", "1"], 
     SubscriptBox["m", "2"]}], 
    SuperscriptBox["r", "2"]], TraditionalForm]],ExpressionUUID->
  "4692f014-f579-4209-8232-7e17dea7ec22"],
 "\nwhere:\nF is the force between the masses,\nG is the gravitational \
constant,\n",
 Cell[BoxData[
  FormBox[
   SubscriptBox["m", "1"], TraditionalForm]],ExpressionUUID->
  "f56aeb44-1c52-4ca2-b41d-e446dbe08ed1"],
 "is the first mass,\n",
 Cell[BoxData[{
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{
      SubscriptBox["m", "2"], "is", " ", "the", " ", "second", " ", "mass"}], 
     ",", "and"}], " "}], TraditionalForm], "\[IndentingNewLine]", 
  FormBox[
   RowBox[{
   "r", " ", "is", " ", "the", " ", "distance", " ", "between", " ", "the", 
    " ", "centers", " ", "of", " ", "the", " ", 
    RowBox[{"masses", "."}]}], TraditionalForm]}],ExpressionUUID->
  "61d115be-1d96-4587-86be-feab2303c155"],
 "\nIn this equation, r is calculated as the square-root of (x",
 Cell[BoxData[
  FormBox[
   SubscriptBox["", "p1"], TraditionalForm]],ExpressionUUID->
  "c33b95b5-4963-482d-a8b4-558f18b2cae0"],
 "-",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "p2"], TraditionalForm]],ExpressionUUID->
  "ceaf6ee8-104c-4177-ab77-54b20b22da22"],
 ")^2 + (y",
 Cell[BoxData[
  FormBox[
   SubscriptBox["", "p1"], TraditionalForm]],ExpressionUUID->
  "c5b4fec5-32d5-4aea-8765-3e742a353fa9"],
 "-",
 Cell[BoxData[
  FormBox[
   SubscriptBox["y", "p2"], TraditionalForm]],ExpressionUUID->
  "0e1e2612-448f-4dc1-a499-e4474dc70097"],
 ")^2\n\nAfter that, we will apply the Newton\[CloseCurlyQuote]s law of \
motion: F=ma to derive the acceleration vector of each sun. Since we have the \
initial velocity (v",
 Cell[BoxData[
  FormBox[
   SubscriptBox["", "0"], TraditionalForm]],ExpressionUUID->
  "f09b6150-0c50-44d0-981c-440aeb9f1f81"],
 "), we can obtain the velocity (",
 Cell[BoxData[
  FormBox[
   SubscriptBox["v", "t"], TraditionalForm]],ExpressionUUID->
  "5bf0b18e-d24d-41cb-b594-e1236b460970"],
 ") after each unit of time (potentially every second) using the equation \
vt=v",
 Cell[BoxData[
  FormBox[
   SubscriptBox["", "0"], TraditionalForm]],ExpressionUUID->
  "49a59de4-8012-4e91-ae19-7f503fcf04bc"],
 " + at. The suns will move accordingly to their velocity vectors (",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubscriptBox["x", "v"], ","}], TraditionalForm]],ExpressionUUID->
  "16cf7d5a-861a-464e-bdf5-28aa6a32a4f1"],
 " ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["y", "v"], TraditionalForm]],ExpressionUUID->
  "3593927c-5941-4b5d-b3cf-6befce18c14d"],
 ") and arrive at new positions. Since our universe is discreet, we can only \
report the positions of all the suns discreetly at each given time. \n\nAt \
each given time and velocity, we can calculate the total energy of each sun \
using the gravitational potential energy formula and kinetic energy formula: \
\n U= -m ",
 Cell[BoxData[
  FormBox[
   RowBox[{"\[Sum]", "G"}], TraditionalForm]],ExpressionUUID->
  "e6e37acd-7dfd-45de-9866-7eb8fde7947b"],
 " ",
 Cell[BoxData[
  FormBox[
   FractionBox["M", "r"], TraditionalForm]],ExpressionUUID->
  "672b990b-8333-468e-b6fc-6d0066fd8c3d"],
 "\t     ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubscriptBox["E", 
     RowBox[{"k", " "}]], "=", "  ", 
    FractionBox["1", "2"]}], TraditionalForm]],ExpressionUUID->
  "9475c498-dfd9-4e4b-87e9-76d5c4338441"],
 "m",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["v", "2"], TraditionalForm]],ExpressionUUID->
  "2fffef41-53ad-4bcb-bdfc-79c3f2597555"],
 "\nThe total energy of the entire universe is then calculated and presented \
in a graph. "
}], "Text",
 CellChangeTimes->{{3.56972165624826*^9, 3.56972171154564*^9}, {
   3.569721755752033*^9, 3.569721772704761*^9}, 3.569878058729706*^9, {
   3.5749651978020363`*^9, 3.5749652269380693`*^9}, {3.576350309639492*^9, 
   3.5763503103248796`*^9}, {3.576350365675055*^9, 3.576350374492063*^9}, {
   3.576350410459478*^9, 3.576350572970331*^9}, {3.576350617530933*^9, 
   3.5763506420529737`*^9}, {3.5763506722917557`*^9, 3.576350885279457*^9}, {
   3.576350956398929*^9, 3.576351016326586*^9}, {3.5763511196310053`*^9, 
   3.5763512667884083`*^9}, 3.5763515075156803`*^9, {3.5763516103135433`*^9, 
   3.57635170593198*^9}, {3.576351765512122*^9, 3.576351783288178*^9}, {
   3.576351911586285*^9, 3.5763519187672863`*^9}, {3.576354312299696*^9, 
   3.5763543315265408`*^9}, {3.576354392566289*^9, 3.576354971516087*^9}, {
   3.576355010907436*^9, 3.576355023746984*^9}, {3.576355057258902*^9, 
   3.5763552489464703`*^9}, {3.5764518773011093`*^9, 3.576451889099065*^9}, {
   3.756670355920734*^9, 
   3.756670399258507*^9}},ExpressionUUID->"5f4276fe-6a81-4129-948f-\
3d66d4f0b83e"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Functions", "Section",
 CellChangeTimes->{{3.569721863255413*^9, 
  3.569721865438335*^9}},ExpressionUUID->"55e11d3b-89c1-42f7-8b23-\
3f4ae359e0fc"],

Cell["Below are all the functions required for the model. ", "Text",
 CellChangeTimes->{{3.569721883912477*^9, 3.569721901000572*^9}, {
  3.5697221580446787`*^9, 3.569722263457993*^9}, {3.569722298836804*^9, 
  3.569722307891799*^9}, {3.7566704037800407`*^9, 
  3.75667042518504*^9}},ExpressionUUID->"f1c47c8d-ce42-4414-9513-\
6b05987871e6"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"G", "=", 
   RowBox[{"0.01296", "*", "6.674", "*", 
    RowBox[{"10", "^", 
     RowBox[{"(", 
      RowBox[{"-", "11"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"dsquare", "[", 
    RowBox[{"x1_", ",", "x2_", ",", "y1_", ",", "y2_"}], "]"}], ":=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"x1", "-", "x2"}], ")"}], "^", "2"}], " ", "+", " ", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"y1", "-", "y2"}], ")"}], "^", "2"}]}]}], " ", 
  RowBox[{"(*", 
   RowBox[{
   "function", " ", "to", " ", "calculate", " ", "distance", " ", "between", 
    " ", "2", " ", "agents"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"AB", "[", 
    RowBox[{"a1_", ",", "a2_", ",", "b1_", ",", "b2_"}], "]"}], ":=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"a2", "-", "a1"}], ",", 
     RowBox[{"b2", "-", "b1"}]}], "}"}]}], 
  RowBox[{"(*", 
   RowBox[{
   "calculate", " ", "direction", " ", "vector", " ", "between", " ", "point",
     " ", "A", " ", "and", " ", "point", " ", "B"}], 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"F", "[", 
    RowBox[{
    "m1_", ",", "m2_", ",", "xa_", ",", "xb_", ",", "ya_", ",", "yb_"}], 
    "]"}], ":=", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"G", "*", "m1", "*", "m2"}], ")"}], "/", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"Sqrt", "[", 
         RowBox[{"dsquare", "[", 
          RowBox[{"xa", ",", "xb", ",", "ya", ",", "yb"}], "]"}], "]"}], 
        ")"}], "^", "3"}]}], ")"}], 
    RowBox[{"AB", "[", 
     RowBox[{"xa", ",", "xb", ",", "ya", ",", "yb"}], "]"}]}]}], 
  RowBox[{"(*", 
   RowBox[{
   "calculate", " ", "the", " ", "force", " ", "vector", " ", "between", " ", 
    "2", " ", "agents"}], "*)"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Force", "[", "result_", "]"}], ":=", 
   RowBox[{"(", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"t", "=", "24"}], ";", 
     RowBox[{"(*", 
      RowBox[{"delta", " ", "t"}], "*)"}], "\[IndentingNewLine]", 
     RowBox[{"Big", "=", 
      RowBox[{"Quiet", "[", 
       RowBox[{"Table", "[", 
        RowBox[{
         RowBox[{"F", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "3", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "j", "]"}], "]"}], "[", 
            RowBox[{"[", "3", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "1", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "j", "]"}], "]"}], "[", 
            RowBox[{"[", "1", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "2", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "j", "]"}], "]"}], "[", 
            RowBox[{"[", "2", "]"}], "]"}]}], "]"}], ",", 
         RowBox[{"{", 
          RowBox[{"i", ",", " ", "1", ",", "2"}], "}"}], ",", " ", 
         RowBox[{"{", 
          RowBox[{"j", ",", "1", ",", " ", "2"}], "}"}]}], "]"}], "]"}]}], 
     ";", 
     RowBox[{"(*", 
      RowBox[{
      "Matrix", " ", "of", " ", "forces", " ", "of", " ", "the", " ", 
       "entire", " ", "system"}], "*)"}], "\[IndentingNewLine]", 
     RowBox[{"new", "=", 
      RowBox[{"ReplacePart", "[", 
       RowBox[{"Big", ",", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"i_", ",", "i_"}], "}"}], "\[Rule]", " ", 
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}]}], ";", 
     RowBox[{"(*", 
      RowBox[{
       RowBox[{
       "In", " ", "order", " ", "to", " ", "solve", " ", "the", " ", 
        "indeterminate", " ", "problems", " ", "caused", " ", "by", " ", 
        "r"}], "=", 
       RowBox[{
       "0", " ", "when", " ", "calculating", " ", "force", " ", "of", " ", 
        "the", " ", "planet", " ", "on", " ", "itself"}]}], "*)"}], 
     "\[IndentingNewLine]", 
     RowBox[{"allforce", "=", 
      RowBox[{"Table", "[", " ", 
       RowBox[{
        RowBox[{"Sum", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"new", "[", 
            RowBox[{"[", "i", "]"}], "]"}], "[", 
           RowBox[{"[", "j", "]"}], "]"}], ",", 
          RowBox[{"{", 
           RowBox[{"j", ",", "1", ",", "2"}], "}"}]}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     RowBox[{"(*", 
      RowBox[{
      "the", " ", "total", " ", "vector", " ", "force", " ", "of", " ", "the",
        " ", "entire", " ", "system", " ", "on", " ", "each", " ", 
       "individual", " ", "planet"}], "*)"}], "\[IndentingNewLine]", 
     RowBox[{"accel", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"allforce", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "/", 
         RowBox[{
          RowBox[{"result", "[", 
           RowBox[{"[", "i", "]"}], "]"}], "[", 
          RowBox[{"[", "3", "]"}], "]"}]}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     RowBox[{"(*", 
      RowBox[{"Matrix", " ", "of", " ", "acceleration", " ", "vectors"}], 
      "*)"}], "\[IndentingNewLine]", 
     RowBox[{"velocity", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "4", "]"}], "]"}], "+", 
           RowBox[{
            RowBox[{
             RowBox[{"accel", "[", 
              RowBox[{"[", "i", "]"}], "]"}], "[", 
             RowBox[{"[", "1", "]"}], "]"}], "*", "t"}]}], ",", 
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "5", "]"}], "]"}], "+", 
           RowBox[{
            RowBox[{
             RowBox[{"accel", "[", 
              RowBox[{"[", "i", "]"}], "]"}], "[", 
             RowBox[{"[", "2", "]"}], "]"}], "*", "t"}]}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     RowBox[{"(*", 
      RowBox[{
      "Matrix", " ", "of", " ", "velocity", " ", "vectors", " ", "after", " ",
        "one", " ", "delta", " ", "t"}], "*)"}], "\[IndentingNewLine]", 
     RowBox[{"displace", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"result", "[", 
               RowBox[{"[", "i", "]"}], "]"}], "[", 
              RowBox[{"[", "4", "]"}], "]"}], "+", 
             RowBox[{
              RowBox[{"velocity", "[", 
               RowBox[{"[", "i", "]"}], "]"}], "[", 
              RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "*", 
           RowBox[{"t", "/", "2"}]}], ",", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"result", "[", 
               RowBox[{"[", "i", "]"}], "]"}], "[", 
              RowBox[{"[", "5", "]"}], "]"}], "+", 
             RowBox[{
              RowBox[{"velocity", "[", 
               RowBox[{"[", "i", "]"}], "]"}], "[", 
              RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "*", 
           RowBox[{"t", "/", "2"}]}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     RowBox[{"(*", 
      RowBox[{
      "Matrix", " ", "of", " ", "displacement", " ", "vectors", " ", "after", 
       " ", "one", " ", "delta", " ", "t"}], "*)"}], "\[IndentingNewLine]", 
     RowBox[{"position", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "1", "]"}], "]"}], "+", 
           RowBox[{
            RowBox[{"displace", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "1", "]"}], "]"}]}], ",", 
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "2", "]"}], "]"}], "+", 
           RowBox[{
            RowBox[{"displace", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "2", "]"}], "]"}]}], ",", 
          RowBox[{
           RowBox[{"result", "[", 
            RowBox[{"[", "i", "]"}], "]"}], "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     RowBox[{"(*", 
      RowBox[{"New", " ", "positions", " ", "of", " ", "each", " ", "agent"}],
       "*)"}], "\[IndentingNewLine]", 
     RowBox[{"final", "=", 
      RowBox[{"Join", "[", 
       RowBox[{"position", ",", "velocity", ",", "2"}], "]"}]}]}], 
    RowBox[{"(*", 
     RowBox[{"New", " ", "system", " ", "after", " ", "delta", " ", "t"}], 
     "*)"}], "\[IndentingNewLine]", ")"}]}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"universe", "[", "duration_", "]"}], ":=", 
   RowBox[{"(", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"full", "=", 
      RowBox[{"Quiet", "[", 
       RowBox[{"Nest", "[", 
        RowBox[{"Force", ",", "init", ",", "duration"}], "]"}], "]"}]}], ";", 
     
     RowBox[{"(*", 
      RowBox[{
      "New", " ", "system", " ", "after", " ", "a", " ", "duration", " ", 
       "chosen", " ", "by", " ", "the", " ", "user"}], "*)"}], 
     "\[IndentingNewLine]", 
     RowBox[{"points", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{"full", "[", 
            RowBox[{"[", "i", "]"}], "]"}], "[", 
           RowBox[{"[", "1", "]"}], "]"}], ",", 
          RowBox[{
           RowBox[{"full", "[", 
            RowBox[{"[", "i", "]"}], "]"}], "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     RowBox[{"(*", 
      RowBox[{
      "New", " ", "positions", " ", "of", " ", "all", " ", "the", " ", 
       "agents", " ", "after", " ", "a", " ", "duration", " ", "chosen", " ", 
       "by", " ", "the", " ", "user"}], "*)"}], "\[IndentingNewLine]", 
     RowBox[{"points1", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"points", "[", 
         RowBox[{"[", "1", "]"}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     RowBox[{"(*", 
      RowBox[{
      "New", " ", "position", " ", "of", " ", "agent", " ", "1", " ", "after",
        " ", "a", " ", "duration"}], "*)"}], "\[IndentingNewLine]", 
     RowBox[{"points2", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"points", "[", 
         RowBox[{"[", "2", "]"}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}]}], ")"}]}], 
  RowBox[{"(*", 
   RowBox[{
   "New", " ", "position", " ", "of", " ", "agent", " ", "2", " ", "after", 
    " ", "a", " ", "duration"}], "*)"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Energy", "[", "result_", "]"}], ":=", 
   RowBox[{"(", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"t", "=", "24"}], ";", "\[IndentingNewLine]", 
     RowBox[{"Big", "=", 
      RowBox[{"Quiet", "[", 
       RowBox[{"Table", "[", 
        RowBox[{
         RowBox[{"F", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "3", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "j", "]"}], "]"}], "[", 
            RowBox[{"[", "3", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "1", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "j", "]"}], "]"}], "[", 
            RowBox[{"[", "1", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "2", "]"}], "]"}], ",", 
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "j", "]"}], "]"}], "[", 
            RowBox[{"[", "2", "]"}], "]"}]}], "]"}], ",", 
         RowBox[{"{", 
          RowBox[{"i", ",", " ", "1", ",", "2"}], "}"}], ",", " ", 
         RowBox[{"{", 
          RowBox[{"j", ",", "1", ",", " ", "2"}], "}"}]}], "]"}], "]"}]}], 
     ";", "\[IndentingNewLine]", 
     RowBox[{"new", "=", 
      RowBox[{"ReplacePart", "[", 
       RowBox[{"Big", ",", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"i_", ",", "i_"}], "}"}], "\[Rule]", " ", 
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"allforce", "=", 
      RowBox[{"Table", "[", " ", 
       RowBox[{
        RowBox[{"Sum", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"new", "[", 
            RowBox[{"[", "i", "]"}], "]"}], "[", 
           RowBox[{"[", "j", "]"}], "]"}], ",", 
          RowBox[{"{", 
           RowBox[{"j", ",", "1", ",", "2"}], "}"}]}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"accel", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"allforce", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "/", 
         RowBox[{
          RowBox[{"result", "[", 
           RowBox[{"[", "i", "]"}], "]"}], "[", 
          RowBox[{"[", "3", "]"}], "]"}]}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"velocity", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "4", "]"}], "]"}], "+", 
           RowBox[{
            RowBox[{
             RowBox[{"accel", "[", 
              RowBox[{"[", "i", "]"}], "]"}], "[", 
             RowBox[{"[", "1", "]"}], "]"}], "*", "t"}]}], ",", 
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "5", "]"}], "]"}], "+", 
           RowBox[{
            RowBox[{
             RowBox[{"accel", "[", 
              RowBox[{"[", "i", "]"}], "]"}], "[", 
             RowBox[{"[", "2", "]"}], "]"}], "*", "t"}]}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"displace", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"result", "[", 
               RowBox[{"[", "i", "]"}], "]"}], "[", 
              RowBox[{"[", "4", "]"}], "]"}], "+", 
             RowBox[{
              RowBox[{"velocity", "[", 
               RowBox[{"[", "i", "]"}], "]"}], "[", 
              RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "*", 
           RowBox[{"t", "/", "2"}]}], ",", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{
             RowBox[{
              RowBox[{"result", "[", 
               RowBox[{"[", "i", "]"}], "]"}], "[", 
              RowBox[{"[", "5", "]"}], "]"}], "+", 
             RowBox[{
              RowBox[{"velocity", "[", 
               RowBox[{"[", "i", "]"}], "]"}], "[", 
              RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "*", 
           RowBox[{"t", "/", "2"}]}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"position", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "1", "]"}], "]"}], "+", 
           RowBox[{
            RowBox[{"displace", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "1", "]"}], "]"}]}], ",", 
          RowBox[{
           RowBox[{
            RowBox[{"result", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "2", "]"}], "]"}], "+", 
           RowBox[{
            RowBox[{"displace", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "[", 
            RowBox[{"[", "2", "]"}], "]"}]}], ",", 
          RowBox[{
           RowBox[{"result", "[", 
            RowBox[{"[", "i", "]"}], "]"}], "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"final", "=", 
      RowBox[{"Join", "[", 
       RowBox[{"position", ",", "velocity", ",", "2"}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"potential", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"-", 
          RowBox[{
           RowBox[{"final", "[", 
            RowBox[{"[", "i", "]"}], "]"}], "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], "*", "G", "*", 
         RowBox[{
          RowBox[{
           RowBox[{"final", "[", 
            RowBox[{"[", "j", "]"}], "]"}], "[", 
           RowBox[{"[", "3", "]"}], "]"}], "/", 
          RowBox[{"(", 
           RowBox[{"Sqrt", "[", 
            RowBox[{"dsquare", "[", 
             RowBox[{
              RowBox[{
               RowBox[{"final", "[", 
                RowBox[{"[", "i", "]"}], "]"}], "[", 
               RowBox[{"[", "1", "]"}], "]"}], ",", 
              RowBox[{
               RowBox[{"final", "[", 
                RowBox[{"[", "j", "]"}], "]"}], "[", 
               RowBox[{"[", "1", "]"}], "]"}], ",", 
              RowBox[{
               RowBox[{"final", "[", 
                RowBox[{"[", "i", "]"}], "]"}], "[", 
               RowBox[{"[", "2", "]"}], "]"}], ",", 
              RowBox[{
               RowBox[{"final", "[", 
                RowBox[{"[", "j", "]"}], "]"}], "[", 
               RowBox[{"[", "2", "]"}], "]"}]}], "]"}], "]"}], ")"}]}]}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"j", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"kinetic", "=", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{"0.5", "*", 
         RowBox[{
          RowBox[{"final", "[", 
           RowBox[{"[", "i", "]"}], "]"}], "[", 
          RowBox[{"[", "3", "]"}], "]"}], "*", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"Norm", "[", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"final", "[", 
                RowBox[{"[", "i", "]"}], "]"}], "[", 
               RowBox[{"[", "4", "]"}], "]"}], ",", 
              RowBox[{
               RowBox[{"final", "[", 
                RowBox[{"[", "i", "]"}], "]"}], "[", 
               RowBox[{"[", "5", "]"}], "]"}]}], "}"}], "]"}], ")"}], "^", 
          "2"}]}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"potential", "=", 
      RowBox[{"potential", "[", 
       RowBox[{"[", 
        RowBox[{"1", ",", "2"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"kinetic", "=", 
      RowBox[{"Sum", "[", 
       RowBox[{
        RowBox[{"kinetic", "[", 
         RowBox[{"[", "i", "]"}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"totalenergy", "=", 
      RowBox[{"potential", "+", "kinetic"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"final", "=", 
      RowBox[{"Join", "[", 
       RowBox[{"position", ",", "velocity", ",", "2"}], "]"}]}]}], 
    "\[IndentingNewLine]", ")"}]}], 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{"calculate", " ", "the", " ", "potential"}], ",", " ", "kinetic", 
    ",", " ", 
    RowBox[{"and", " ", "total", " ", "energy"}]}], "*)"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"plotenergy", "[", "duration_", "]"}], ":=", 
   RowBox[{"(", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"pot", "=", 
      RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"kin", "=", 
      RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"tol", "=", 
      RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"Do", "[", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{
        RowBox[{"full", "=", 
         RowBox[{"Quiet", "[", 
          RowBox[{"Nest", "[", 
           RowBox[{"Energy", ",", "init", ",", "i"}], "]"}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"pot", "=", 
         RowBox[{"Append", "[", 
          RowBox[{"pot", ",", "potential"}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"kin", "=", 
         RowBox[{"Append", "[", 
          RowBox[{"kin", ",", "kinetic"}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"tol", "=", 
         RowBox[{"Append", "[", 
          RowBox[{"tol", ",", "totalenergy"}], "]"}]}]}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{"{", 
        RowBox[{"i", ",", "1", ",", "duration"}], "}"}]}], "]"}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"plotpot", "=", 
      RowBox[{"ListLinePlot", "[", 
       RowBox[{"pot", ",", 
        RowBox[{"PlotStyle", "\[Rule]", 
         RowBox[{"{", "Blue", "}"}]}], ",", 
        RowBox[{"PlotRange", "\[Rule]", "All"}], ",", 
        RowBox[{"AxesLabel", "\[Rule]", 
         RowBox[{"{", 
          RowBox[{
          "\"\<duration (days)\>\"", ",", 
           "\"\<energy (\!\(\*FractionBox[\(kg*\*SuperscriptBox[\(km\), \
\(2\)]\), SuperscriptBox[\(h\), \(2\)]]\) ~ 0.0772 Joule)\>\""}], "}"}]}]}], 
       "]"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"plotkin", "=", 
      RowBox[{"ListLinePlot", "[", 
       RowBox[{"kin", ",", 
        RowBox[{"PlotStyle", "\[Rule]", 
         RowBox[{"{", "Orange", "}"}]}], ",", 
        RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"plottol", "=", 
      RowBox[{"ListLinePlot", "[", 
       RowBox[{"tol", ",", 
        RowBox[{"PlotStyle", "\[Rule]", 
         RowBox[{"{", "Red", "}"}]}], ",", 
        RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"Show", "[", 
      RowBox[{"plotpot", ",", "plotkin", ",", "plottol", ",", " ", 
       RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]}], 
    "\[IndentingNewLine]", ")"}]}], 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{"plot", " ", "the", " ", "potential"}], ",", " ", "kinetic", ",", 
    " ", 
    RowBox[{"and", " ", "total", " ", "energy"}]}], 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"SetOptions", "[", 
  RowBox[{"$FrontEnd", ",", 
   RowBox[{"DynamicEvaluationTimeout", "\[Rule]", "Infinity"}]}], 
  "]"}]}], "Input",
 InitializationCell->True,
 CellChangeTimes->{
  3.576450418847849*^9, {3.756634129446933*^9, 3.756634138653582*^9}, 
   3.756670033923032*^9},
 CellLabel->"In[28]:=",ExpressionUUID->"d99ccade-ca1a-41d2-aafd-70c81c3cbeb4"]
}, Open  ]],

Cell[CellGroupData[{

Cell["App 1: Trajectory ", "Section",
 CellChangeTimes->{{3.569721966932971*^9, 3.5697219677884197`*^9}, {
  3.576449546234508*^9, 
  3.576449573933477*^9}},ExpressionUUID->"756b34c1-e282-4df5-a0cb-\
d3b138c65bd2"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"init", "=", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"location", ",", "location", ",", "mass", ",", 
         RowBox[{"-", "v"}], ",", "v"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"0", ",", "0", ",", 
         RowBox[{"2", "*", 
          RowBox[{"10", "^", "30"}]}], ",", "0", ",", "0"}], "}"}]}], "}"}]}],
     ";", 
    RowBox[{"(*", 
     RowBox[{
      RowBox[{"location", " ", "in", " ", "km"}], ",", " ", 
      RowBox[{"mass", " ", "in", " ", "kg"}], ",", " ", 
      RowBox[{"v", " ", "in", " ", 
       RowBox[{"km", "/", "h"}]}]}], "*)"}], "\[IndentingNewLine]", 
    RowBox[{"universe", "[", "duration", "]"}], ";", "\[IndentingNewLine]", 
    RowBox[{"planet", "=", 
     RowBox[{"ListPlot", "[", 
      RowBox[{"points1", ",", 
       RowBox[{"PlotRange", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{"-", 
             RowBox[{"10", "^", "9"}]}], ",", 
            RowBox[{"10", "^", "9"}]}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"-", 
             RowBox[{"10", "^", "9"}]}], ",", 
            RowBox[{"10", "^", "9"}]}], "}"}]}], "}"}]}], ",", 
       RowBox[{"PlotStyle", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"Blue", ",", 
          RowBox[{"PointSize", "[", ".02", "]"}]}], "}"}]}], ",", 
       RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"sun", "=", 
     RowBox[{"ListPlot", "[", 
      RowBox[{"points2", ",", 
       RowBox[{"PlotRange", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{"-", 
             RowBox[{"10", "^", "9"}]}], ",", 
            RowBox[{"10", "^", "9"}]}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"-", 
             RowBox[{"10", "^", "9"}]}], ",", 
            RowBox[{"10", "^", "9"}]}], "}"}]}], "}"}]}], ",", 
       RowBox[{"PlotStyle", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"Red", ",", 
          RowBox[{"PointSize", "[", ".08", "]"}]}], "}"}]}], ",", 
       RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"Show", "[", 
     RowBox[{"planet", ",", "sun"}], "]"}]}], ",", "\[IndentingNewLine]", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"location", ",", 
       RowBox[{"14", "*", 
        RowBox[{"10", "^", "7"}]}]}], "}"}], ",", 
     RowBox[{"10", "^", "8"}], ",", 
     RowBox[{"10", "^", "9"}], ",", "100", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"mass", ",", 
       RowBox[{"6", "*", 
        RowBox[{"10", "^", "24"}]}]}], "}"}], ",", 
     RowBox[{"10", "^", "23"}], ",", 
     RowBox[{"2", "*", 
      RowBox[{"10", "^", "28"}]}], ",", 
     RowBox[{"10", "^", "19"}], ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"v", ",", "60000"}], "}"}], ",", "1000", ",", "200000", ",", 
     "1000", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"duration", ",", "1", ",", "1000", ",", "1", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}]}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.576355612302816*^9, 3.576355617547967*^9}, {
  3.576355957811064*^9, 3.576355998589387*^9}, {3.576356049554243*^9, 
  3.576356111000628*^9}, {3.5763561485134974`*^9, 3.5763561689075413`*^9}, {
  3.576356205216567*^9, 3.576356226523017*^9}, {3.576356317545827*^9, 
  3.576356347693606*^9}, {3.576356387389193*^9, 3.576356393349019*^9}},
 CellLabel->"In[40]:=",ExpressionUUID->"ce548c54-d1eb-4d70-bc87-44ef380268c1"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`duration$$ = 40, $CellContext`location$$ = 
    140000000, $CellContext`mass$$ = 
    6000000000000000000000000, $CellContext`v$$ = 88000, Typeset`show$$ = 
    True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`location$$], 140000000}, 100000000, 1000000000, 
      100}, {{
       Hold[$CellContext`mass$$], 6000000000000000000000000}, 
      100000000000000000000000, 20000000000000000000000000000, 
      10000000000000000000}, {{
       Hold[$CellContext`v$$], 60000}, 1000, 200000, 1000}, {
      Hold[$CellContext`duration$$], 1, 1000, 1}}, Typeset`size$$ = {
    540., {163., 171.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = True, $CellContext`location$62754$$ = 
    0, $CellContext`mass$62755$$ = 0, $CellContext`v$62756$$ = 
    0, $CellContext`duration$62757$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`duration$$ = 1, $CellContext`location$$ = 
        140000000, $CellContext`mass$$ = 
        6000000000000000000000000, $CellContext`v$$ = 60000}, 
      "ControllerVariables" :> {
        Hold[$CellContext`location$$, $CellContext`location$62754$$, 0], 
        Hold[$CellContext`mass$$, $CellContext`mass$62755$$, 0], 
        Hold[$CellContext`v$$, $CellContext`v$62756$$, 0], 
        Hold[$CellContext`duration$$, $CellContext`duration$62757$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> ($CellContext`init = {{$CellContext`location$$, \
$CellContext`location$$, $CellContext`mass$$, -$CellContext`v$$, \
$CellContext`v$$}, {
          0, 0, 2 10^30, 0, 
           0}}; $CellContext`universe[$CellContext`duration$$]; \
$CellContext`planet = 
        ListPlot[$CellContext`points1, 
          PlotRange -> {{-10^9, 10^9}, {-10^9, 10^9}}, PlotStyle -> {Blue, 
            PointSize[0.02]}, Axes -> False]; $CellContext`sun = 
        ListPlot[$CellContext`points2, 
          PlotRange -> {{-10^9, 10^9}, {-10^9, 10^9}}, PlotStyle -> {Red, 
            PointSize[0.08]}, Axes -> False]; 
       Show[$CellContext`planet, $CellContext`sun]), 
      "Specifications" :> {{{$CellContext`location$$, 140000000}, 100000000, 
         1000000000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`mass$$, 6000000000000000000000000}, 
         100000000000000000000000, 20000000000000000000000000000, 
         10000000000000000000, Appearance -> 
         "Labeled"}, {{$CellContext`v$$, 60000}, 1000, 200000, 1000, 
         Appearance -> "Labeled"}, {$CellContext`duration$$, 1, 1000, 1, 
         Appearance -> "Labeled"}}, "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{606., {298., 307.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{
  3.576449533082676*^9, 3.5764506496643133`*^9, 3.576451920064817*^9, 
   3.7566704538500767`*^9, 3.7566898767441273`*^9, {3.7566899779591846`*^9, 
   3.756689986831318*^9}, 3.756690154877494*^9, 3.756690191834539*^9, 
   3.756690250314816*^9, 3.756690291735999*^9, 3.756690405907898*^9, 
   3.7566904392615356`*^9},
 CellLabel->"Out[40]=",ExpressionUUID->"2968910d-4c8d-427d-8097-257ea93024bd"]
}, Open  ]],

Cell[BoxData[" "], "Input",
 CellChangeTimes->{
  3.75669022511096*^9},ExpressionUUID->"dd7cfa72-6dd9-447e-bf9a-2db9105e3ae0"]
}, Open  ]],

Cell[CellGroupData[{

Cell["App 2 : Energy Conservation", "Section",
 CellChangeTimes->{{3.576449558143434*^9, 3.576449577865778*^9}, {
  3.5764496080223618`*^9, 
  3.576449634155846*^9}},ExpressionUUID->"8555bebd-9f10-4fda-8251-\
454dff0d6578"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"init", "=", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"location", ",", "location", ",", "mass", ",", 
         RowBox[{"-", "v"}], ",", "v"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"0", ",", "0", ",", 
         RowBox[{"2", "*", 
          RowBox[{"10", "^", "30"}]}], ",", "0", ",", "0"}], "}"}]}], "}"}]}],
     ";", "\[IndentingNewLine]", 
    RowBox[{"plotenergy", "[", "duration", "]"}]}], ",", 
   "\[IndentingNewLine]", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"location", ",", 
       RowBox[{"14", "*", 
        RowBox[{"10", "^", "7"}]}]}], "}"}], ",", 
     RowBox[{"10", "^", "8"}], ",", 
     RowBox[{"10", "^", "9"}], ",", "100", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"mass", ",", 
       RowBox[{"6", "*", 
        RowBox[{"10", "^", "24"}]}]}], "}"}], ",", 
     RowBox[{"10", "^", "23"}], ",", 
     RowBox[{"2", "*", 
      RowBox[{"10", "^", "28"}]}], ",", 
     RowBox[{"10", "^", "19"}], ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"v", ",", "60000"}], "}"}], ",", "1000", ",", "200000", ",", 
     "1000", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"duration", ",", "1000"}], "}"}], ",", "1", ",", "5000", ",", 
     "10", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}]}], 
  "]"}]], "Input",
 CellChangeTimes->{
  3.576355883412498*^9, {3.576356539222117*^9, 3.576356566023761*^9}, {
   3.5764506188820457`*^9, 3.576450620623019*^9}, {3.576450808526293*^9, 
   3.576450827423411*^9}, {3.756669304959149*^9, 3.756669306722452*^9}, {
   3.756669841224223*^9, 3.756669899840148*^9}, {3.756670075733303*^9, 
   3.756670077196085*^9}, {3.756670303303937*^9, 3.7566703074639063`*^9}, {
   3.756691480077755*^9, 3.756691486677285*^9}},
 CellLabel->"In[42]:=",ExpressionUUID->"c7a55362-2387-44c1-b65f-d7aef42ff24f"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`duration$$ = 1000, $CellContext`location$$ =
     140000000, $CellContext`mass$$ = 
    6000000000000000000000000, $CellContext`v$$ = 60000, Typeset`show$$ = 
    True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`location$$], 140000000}, 100000000, 1000000000, 
      100}, {{
       Hold[$CellContext`mass$$], 6000000000000000000000000}, 
      100000000000000000000000, 20000000000000000000000000000, 
      10000000000000000000}, {{
       Hold[$CellContext`v$$], 60000}, 1000, 200000, 1000}, {{
       Hold[$CellContext`duration$$], 1000}, 1, 5000, 10}}, Typeset`size$$ = {
    540., {126., 134.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = True, $CellContext`location$79352$$ = 
    0, $CellContext`mass$79353$$ = 0, $CellContext`v$79354$$ = 
    0, $CellContext`duration$79355$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`duration$$ = 1000, $CellContext`location$$ = 
        140000000, $CellContext`mass$$ = 
        6000000000000000000000000, $CellContext`v$$ = 60000}, 
      "ControllerVariables" :> {
        Hold[$CellContext`location$$, $CellContext`location$79352$$, 0], 
        Hold[$CellContext`mass$$, $CellContext`mass$79353$$, 0], 
        Hold[$CellContext`v$$, $CellContext`v$79354$$, 0], 
        Hold[$CellContext`duration$$, $CellContext`duration$79355$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> ($CellContext`init = {{$CellContext`location$$, \
$CellContext`location$$, $CellContext`mass$$, -$CellContext`v$$, \
$CellContext`v$$}, {
          0, 0, 2 10^30, 0, 
           0}}; $CellContext`plotenergy[$CellContext`duration$$]), 
      "Specifications" :> {{{$CellContext`location$$, 140000000}, 100000000, 
         1000000000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`mass$$, 6000000000000000000000000}, 
         100000000000000000000000, 20000000000000000000000000000, 
         10000000000000000000, Appearance -> 
         "Labeled"}, {{$CellContext`v$$, 60000}, 1000, 200000, 1000, 
         Appearance -> "Labeled"}, {{$CellContext`duration$$, 1000}, 1, 5000, 
         10, Appearance -> "Labeled"}}, "Options" :> {}, 
      "DefaultOptions" :> {}],
     ImageSizeCache->{606., {242., 250.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{
  3.5764519278918743`*^9, 3.7566341670318117`*^9, {3.756669247572939*^9, 
   3.756669261931609*^9}, {3.75666929886977*^9, 3.756669338339328*^9}, 
   3.756669501314036*^9, 3.756669642728661*^9, {3.756669859850212*^9, 
   3.756669920494565*^9}, 3.7566700704505787`*^9, 3.75667023110525*^9, 
   3.7566702701145353`*^9, 3.7566703784641657`*^9, 3.756670680163259*^9, 
   3.7566905790687923`*^9, {3.756690650612351*^9, 3.756690653022594*^9}, 
   3.7566916512344723`*^9},
 CellLabel->"Out[42]=",ExpressionUUID->"53ff7469-fb4e-4ca5-87bc-b2d9fda1872a"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Conclusion", "Section",
 CellChangeTimes->{{3.574965138598028*^9, 
  3.574965144131591*^9}},ExpressionUUID->"77e5a727-5d6e-4f37-b945-\
96116f9426cd"],

Cell[TextData[{
 "For a given mass and location, there is a certain range of initial velocity \
for the planet to orbit around the sun. Below that range, the planet will \
collide with the sun and above that range, the planet will move away from the \
sun. For a given initial velocity and location, the mass of the planet will \
have an impact on the trajectory of the sun (once the mass of the planet is \
large enough). For a given mass and initial velocity, the location of the \
planet with respect to the sun will also have an impact on its own \
trajectory. \n\nBy calculating and plotting gravitational potential energy \
(in blue), the kinetic energy (in orange), and the total energy of the \
system, we showed that the potential energy (in blue) and the kinetic energy \
(in orange) change with time while the total energy seems to be conserved at \
a constant level.\n\nBelow is the graph of potential energy, kinetic energy, \
and total energy in the system with the Earth orbiting around the Sun:\n",
 Cell[BoxData[
  GraphicsBox[{{{}, {{}, {}, 
      {RGBColor[0, 0, 1], LineBox[CompressedData["
1:eJw9m3c81e/7x6WlLS1tpSFUUqKUXikjFEkyGvbeezuLc3AOokGympq0tItK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        "]]}}, {}}, {{}, {{}, {}, 
      {RGBColor[1, 0.5, 0], LineBox[CompressedData["
1:eJw923k8lVvUB3CpWyqiUknSqVTSpEFp9GuSNFGKUjkJITJzzIdjOAcHDUqJ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        "]]}}, {}}, {{}, {{}, {}, 
      {RGBColor[1, 0, 0], LineBox[CompressedData["
1:eJw913lYzP/+//GSJXtZyxqHhBBCQj2QZEkhREmrdu37NjPNTDNNG4qypA+l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        "]]}}, {}}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->True,
   AxesLabel->{
     FormBox["\"duration (days)\"", TraditionalForm], 
     FormBox[
     "\"energy (\\!\\(\\*FractionBox[\\(kg*\\*SuperscriptBox[\\(km\\), \
\\(2\\)]\\), SuperscriptBox[\\(h\\), \\(2\\)]]\\) ~ 0.0772 Joule)\"", 
      TraditionalForm]},
   AxesOrigin->{1., -7.192943943948959*^34},
   Method->{},
   PlotRange->{All, All},
   PlotRangeClipping->True,
   PlotRangePadding->{Automatic, Automatic}]],
  CellChangeTimes->{3.576449930482471*^9},ExpressionUUID->
  "024a0d1f-38f8-4331-81b7-a50c8803e761"],
 "\n\nAnd below is the graph of potential energy, kinetic energy, and total \
energy in the system with the Earth moving away from the Sun:\n",
 Cell[BoxData[
  GraphicsBox[{{{}, {{}, {}, 
      {RGBColor[0, 0, 1], LineBox[CompressedData["
1:eJw113lYjP3bBvCxlyWhKFkGUUKSpUV02rOPikrUqKS9ad9rpmmZmplKRPZB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        "]]}}, {}}, {{}, {{}, {}, 
      {RGBColor[1, 0.5, 0], LineBox[CompressedData["
1:eJw91Xc81X3cx3FF0RZticoqFZrSereQUUakKCMKGcfeHM4xDo5UKC1cpbRJ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        
        "]]}}, {}}, {{}, {{}, {}, 
      {RGBColor[1, 0, 0], LineBox[CompressedData["
1:eJw92ndczf////EjKyshhHDsJJVkk7uMQlRGwzxNbae965xTnU6nzik76a2D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        "]]}}, {}}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->True,
   AxesLabel->{
     FormBox["\"duration (days)\"", TraditionalForm], 
     FormBox[
     "\"energy (\\!\\(\\*FractionBox[\\(kg*\\*SuperscriptBox[\\(km\\), \
\\(2\\)]\\), SuperscriptBox[\\(h\\), \\(2\\)]]\\) ~ 0.0772 Joule)\"", 
      TraditionalForm]},
   AxesOrigin->{1., -5.241957340766686*^34},
   Method->{},
   PlotRange->{All, All},
   PlotRangeClipping->True,
   PlotRangePadding->{Automatic, Automatic}]],
  CellChangeTimes->{3.576449930482471*^9, 3.5764504068508863`*^9},
  ExpressionUUID->"55fe1b05-d248-4126-afa9-733ca60648a4"],
 "\n\nAnd below is the graph of potential energy, kinetic energy, and total \
energy in the system with the Earth colapsing into the Sun:\n",
 Cell[BoxData[
  GraphicsBox[{{{}, {{}, {}, 
      {RGBColor[0, 0, 1], LineBox[CompressedData["
1:eJw113dczf/7BvBjJ8qRaFjZ2dmVcGVVZrKi6LSL0mnvOqd52iGEkB2i7MyO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        "]]}}, {}}, {{}, {{}, {}, 
      {RGBColor[1, 0.5, 0], LineBox[CompressedData["
1:eJw92Hdczf3/x/Ejo2RFJBIHIQlF2eMZIbO0CR0NitRp7zqd01mNU0aUmZ2d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        "]]}}, {}}, {{}, {{}, {}, 
      {RGBColor[1, 0, 0], LineBox[CompressedData["
1:eJxF1HVY1Pn39/ExsVgRXcVYl3VtUVFcQTFeioEJiIRijCAhCA7dMMEwPSAq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        "]]}}, {}}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->True,
   AxesLabel->{
     FormBox["\"duration (days)\"", TraditionalForm], 
     FormBox[
     "\"energy (\\!\\(\\*FractionBox[\\(kg*\\*SuperscriptBox[\\(km\\), \
\\(2\\)]\\), SuperscriptBox[\\(h\\), \\(2\\)]]\\) ~ 0.0772 Joule)\"", 
      TraditionalForm]},
   AxesOrigin->{1., -1.1442731613546851`*^36},
   Method->{},
   PlotRange->{All, All},
   PlotRangeClipping->True,
   PlotRangePadding->{Automatic, Automatic}]],
  CellChangeTimes->{3.576449930482471*^9, 3.5764504068508863`*^9, 
   3.576451242414836*^9},ExpressionUUID->
  "7914f3ca-3cf1-469b-a0f6-bf705811a38a"],
 "\n\nFurther investigation:\nWe could add more planets and make the system \
more similar to the real solar system.\nAnd we could compare our method to \
Euler\[CloseCurlyQuote]s method, runge kutta, or NDSolve to see if the energy \
is better conserved. "
}], "Text",
 CellChangeTimes->{{3.574965188129991*^9, 3.574965190889635*^9}, {
   3.5749653265651712`*^9, 3.574965432026437*^9}, {3.576351525509294*^9, 
   3.5763515261011467`*^9}, 3.576351559550186*^9, {3.576351741441827*^9, 
   3.5763517546160917`*^9}, {3.576351814665182*^9, 3.5763518828069553`*^9}, {
   3.576352541133308*^9, 3.576352556823826*^9}, {3.57635424251956*^9, 
   3.5763542469921227`*^9}, {3.57635532041194*^9, 3.57635532077398*^9}, {
   3.576355364553274*^9, 3.576355389928789*^9}, {3.576356611328923*^9, 
   3.5763566383651648`*^9}, {3.576356702134635*^9, 3.576356722476282*^9}, {
   3.576356801996066*^9, 3.576356968939713*^9}, {3.5763570284758987`*^9, 
   3.576357114648753*^9}, {3.576357184544429*^9, 3.5763572505112257`*^9}, {
   3.576357347513125*^9, 3.576357355560851*^9}, {3.576449665001449*^9, 
   3.576449720906197*^9}, {3.576449755438583*^9, 3.5764498009347258`*^9}, 
   3.576450404720973*^9, {3.576450509221829*^9, 3.576450545787116*^9}, 
   3.5764512924184523`*^9, {3.576451378014289*^9, 3.5764513854752083`*^9}, {
   3.5764514627973223`*^9, 
   3.5764514767150927`*^9}},ExpressionUUID->"e057a60d-8a61-45bc-8209-\
bc11ece804fe"],

Cell[CellGroupData[{

Cell["References", "Subsection",
 CellChangeTimes->{{3.5749651695494223`*^9, 
  3.574965171764029*^9}},ExpressionUUID->"907818a8-c441-4ee9-9228-\
1e81ace9f6b0"],

Cell["\<\
Newton' s law of universal gravitation: \
https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation

Newton' s law of motion: 
https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion

Gravitational potential energy: 
https://en.wikipedia.org/wiki/Potential_energy

Kinetic energy: 
https://en.wikipedia.org/wiki/Kinetic_energy
\
\>", "Text",
 CellChangeTimes->{{3.576355333531908*^9, 3.5763553455923433`*^9}, {
  3.756670471813092*^9, 3.756670506919333*^9}, {3.756670545056293*^9, 
  3.756670556486411*^9}, {3.7566706129746428`*^9, 
  3.7566706421351147`*^9}},ExpressionUUID->"d612f914-9ce4-4e95-a84f-\
0b81148985a9"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1136, 935},
WindowMargins->{{70, Automatic}, {Automatic, 0}},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
Magnification:>FEPrivate`If[
  FEPrivate`Equal[FEPrivate`$VersionNumber, 6.], 1.5, 1.5 Inherited],
FrontEndVersion->"11.3 for Mac OS X x86 (32-bit, 64-bit Kernel) (March 5, \
2018)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 145, 3, 46, "Input",ExpressionUUID->"a12fbfd2-1fb6-4d02-86f1-6e5903a024e5"],
Cell[705, 25, 74, 0, 101, "Section",ExpressionUUID->"a8b193a2-d35e-4225-b8b6-61c01341e96b"],
Cell[CellGroupData[{
Cell[804, 29, 312, 5, 197, "Title",ExpressionUUID->"3ef80519-7412-442c-a71a-653fa43f8339"],
Cell[CellGroupData[{
Cell[1141, 38, 159, 3, 101, "Section",ExpressionUUID->"44306c87-f959-405a-86b9-78df6cb38e2c"],
Cell[1303, 43, 6334, 158, 1181, "Text",ExpressionUUID->"5f4276fe-6a81-4129-948f-3d66d4f0b83e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[7674, 206, 154, 3, 101, "Section",ExpressionUUID->"55e11d3b-89c1-42f7-8b23-3f4ae359e0fc"],
Cell[7831, 211, 341, 5, 53, "Text",ExpressionUUID->"f1c47c8d-ce42-4414-9513-6b05987871e6"],
Cell[8175, 218, 24173, 658, 3037, "Input",ExpressionUUID->"d99ccade-ca1a-41d2-aafd-70c81c3cbeb4",
 InitializationCell->True]
}, Open  ]],
Cell[CellGroupData[{
Cell[32385, 881, 214, 4, 101, "Section",ExpressionUUID->"756b34c1-e282-4df5-a0cb-d3b138c65bd2"],
Cell[CellGroupData[{
Cell[32624, 889, 3949, 103, 419, "Input",ExpressionUUID->"ce548c54-d1eb-4d70-bc87-44ef380268c1"],
Cell[36576, 994, 3906, 73, 633, "Output",ExpressionUUID->"2968910d-4c8d-427d-8097-257ea93024bd"]
}, Open  ]],
Cell[40497, 1070, 126, 2, 46, "Input",ExpressionUUID->"dd7cfa72-6dd9-447e-bf9a-2db9105e3ae0"]
}, Open  ]],
Cell[CellGroupData[{
Cell[40660, 1077, 223, 4, 101, "Section",ExpressionUUID->"8555bebd-9f10-4fda-8251-454dff0d6578"],
Cell[CellGroupData[{
Cell[40908, 1085, 2227, 57, 233, "Input",ExpressionUUID->"c7a55362-2387-44c1-b65f-d7aef42ff24f"],
Cell[43138, 1144, 3666, 68, 520, "Output",ExpressionUUID->"53ff7469-fb4e-4ca5-87bc-b2d9fda1872a"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[46853, 1218, 155, 3, 101, "Section",ExpressionUUID->"77e5a727-5d6e-4f37-b945-96116f9426cd"],
Cell[47011, 1223, 117373, 1949, 1616, "Text",ExpressionUUID->"e057a60d-8a61-45bc-8209-bc11ece804fe"],
Cell[CellGroupData[{
Cell[164409, 3176, 160, 3, 81, "Subsection",ExpressionUUID->"907818a8-c441-4ee9-9228-1e81ace9f6b0"],
Cell[164572, 3181, 639, 18, 433, "Text",ExpressionUUID->"d612f914-9ce4-4e95-a84f-0b81148985a9"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)