{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "km = UNITS.kilometer\n",
    "m = UNITS.meter\n",
    "s = UNITS.second\n",
    "kg = UNITS.kilogram\n",
    "days = UNITS.day\n",
    "degree = UNITS.degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "params = Params(distance = 149.6*10**9 *m,\n",
    "                v_init = 0 * m/ s,\n",
    "                G = 6.67 * 10**-11 * (m**3/(s**2 * kg)),\n",
    "                mass_earth = 5.972 * 10**24* kg,\n",
    "                mass_sun = 1.989 * 10**30 * kg)\n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>x_distance</td>\n",
       "      <td>149600000000.0 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>y_distance</td>\n",
       "      <td>0 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>v_init</td>\n",
       "      <td>0.0 meter / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>angle</td>\n",
       "      <td>90 degree</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>G</td>\n",
       "      <td>6.67e-11 meter ** 3 / kilogram / second ** 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mass_earth</td>\n",
       "      <td>5.972e+24 kilogram</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mass_sun</td>\n",
       "      <td>1.9890000000000002e+30 kilogram</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "x_distance                            149600000000.0 meter\n",
       "y_distance                                         0 meter\n",
       "v_init                                  0.0 meter / second\n",
       "angle                                            90 degree\n",
       "G             6.67e-11 meter ** 3 / kilogram / second ** 2\n",
       "mass_earth                              5.972e+24 kilogram\n",
       "mass_sun                   1.9890000000000002e+30 kilogram\n",
       "dtype: object"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params2 = Params(x_distance = 149.6*10**9 *m,\n",
    "                 y_distance = 0 *m,\n",
    "                v_init = 0 * m/ s,\n",
    "                angle = 90 * degree,\n",
    "                G = 6.67 * 10**-11 * (m**3/(s**2 * kg)),\n",
    "                mass_earth = 5.972 * 10**24* kg,\n",
    "                mass_sun = 1.989 * 10**30 * kg)\n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def make_system2(params2):\n",
    "    \"\"\"Makes a System object for the given conditions.\n",
    "    \n",
    "    params: Params object\n",
    "    \n",
    "    returns: System object\n",
    "    \"\"\"\n",
    "    angle, v_init = params2.angle, params2.v_init\n",
    "    x_distance = params2.x_distance\n",
    "    y_distance = params2.y_distance\n",
    "    \n",
    "    theta = np.deg2rad(angle)\n",
    "    vx, vy = pol2cart(theta, v_init)\n",
    "    \n",
    "    R = Vector(x_distance, y_distance)\n",
    "    V = Vector(vx, vy)\n",
    "    \n",
    "    init = State(R=R, V=V)\n",
    "    \n",
    "    t_end =  3.154 *10**7 *s\n",
    "    dt = t_end / 10**4\n",
    "    \n",
    "    return System(params2, init=init, t_end=t_end, dt=dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def make_system(params):\n",
    "    \"\"\"Makes a System object for the given conditions.\n",
    "    \n",
    "    params: Params object\n",
    "    \n",
    "    returns: System object\n",
    "    \"\"\"\n",
    "    \n",
    "    distance = params.distance\n",
    "    v_init = params.v_init\n",
    "    \n",
    "    init = State(r=distance, v=v_init)\n",
    "    t_end =  9.072* 10**6 *s\n",
    "    dt = t_end / 10**4\n",
    "    \n",
    "    return System(params, init=init, t_end=t_end, dt=dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "      <td>x_distance</td>\n",
       "      <td>149600000000.0 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>y_distance</td>\n",
       "      <td>0 meter</td>\n",
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       "    <tr>\n",
       "      <td>v_init</td>\n",
       "      <td>0.0 meter / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>angle</td>\n",
       "      <td>90 degree</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>G</td>\n",
       "      <td>6.67e-11 meter ** 3 / kilogram / second ** 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mass_earth</td>\n",
       "      <td>5.972e+24 kilogram</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mass_sun</td>\n",
       "      <td>1.9890000000000002e+30 kilogram</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>init</td>\n",
       "      <td>R           [149600000000.0 meter, 0.0 meter]\n",
       "...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>t_end</td>\n",
       "      <td>31540000.0 second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>dt</td>\n",
       "      <td>3154.0 second</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "x_distance                                 149600000000.0 meter\n",
       "y_distance                                              0 meter\n",
       "v_init                                       0.0 meter / second\n",
       "angle                                                 90 degree\n",
       "G                  6.67e-11 meter ** 3 / kilogram / second ** 2\n",
       "mass_earth                                   5.972e+24 kilogram\n",
       "mass_sun                        1.9890000000000002e+30 kilogram\n",
       "init          R           [149600000000.0 meter, 0.0 meter]\n",
       "...\n",
       "t_end                                         31540000.0 second\n",
       "dt                                                3154.0 second\n",
       "dtype: object"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system = make_system2(params2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def slope_func2(state, t, system):\n",
    "    \n",
    "    \n",
    "\n",
    "    R,V = state\n",
    "    mass_sun = system.mass_sun\n",
    "    G = system.G\n",
    "    r_mag = R.mag\n",
    "    r_unit_vector = R.hat()\n",
    "    \n",
    "    drdt = V\n",
    "    dvdt = ((-G* mass_sun)/(r_mag**2))*r_unit_vector\n",
    "    \n",
    "    return drdt, dvdt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def slope_func(state, t, system):\n",
    "    \"\"\"Compute derivatives of the state.\n",
    "    \n",
    "    state: position, velocity\n",
    "    t: time\n",
    "    system: System object\n",
    "    \n",
    "    returns: derivatives of y and v\n",
    "    \"\"\"\n",
    "    r, v = state\n",
    "    mass_sun = system.mass_sun\n",
    "    G = system.G\n",
    "    \n",
    "    drdt = v\n",
    "    dvdt = (-G* mass_sun)/(r**2)\n",
    "    \n",
    "    return drdt, dvdt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0., 0.]) <Unit('meter / second')>,\n",
       " array([-0.00592785, -0.        ]) <Unit('meter / second ** 2')>)"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope_func2(system.init, 0, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def event_func(state, t, system):\n",
    "\n",
    "    R, V = state\n",
    "    surfaces_touching = R.mag - ((6.371 *10**6 * m) + 695.51 *10**6 * m)\n",
    "    \n",
    "    return surfaces_touching"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
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       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>success</td>\n",
       "      <td>True</td>\n",
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       "    <tr>\n",
       "      <td>message</td>\n",
       "      <td>The solver successfully reached the end of the...</td>\n",
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       "success                                                 True\n",
       "message    The solver successfully reached the end of the...\n",
       "dtype: object"
      ]
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     },
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   "source": [
    "results, details = run_ode_solver(system, slope_func2, events=event_func)\n",
    "details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
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       "      <th></th>\n",
       "      <th>R</th>\n",
       "      <th>V</th>\n",
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       "      <td>0</td>\n",
       "      <td>[149600000000.0 meter, 0.0 meter]</td>\n",
       "      <td>[0.0 meter / second, 0.0 meter / second]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3154</td>\n",
       "      <td>[149599970515.70062 meter, 0.0 meter]</td>\n",
       "      <td>[-18.696448559795822 meter / second, 0.0 meter...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6308</td>\n",
       "      <td>[149599882062.79086 meter, 0.0 meter]</td>\n",
       "      <td>[-37.392911858950995 meter / second, 0.0 meter...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9462</td>\n",
       "      <td>[149599734641.201 meter, 0.0 meter]</td>\n",
       "      <td>[-56.0894046368866 meter / second, 0.0 meter /...</td>\n",
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       "    <tr>\n",
       "      <td>12616</td>\n",
       "      <td>[149599528250.8148 meter, 0.0 meter]</td>\n",
       "      <td>[-74.78594163315154 meter / second, 0.0 meter ...</td>\n",
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       "                                           R  \\\n",
       "0          [149600000000.0 meter, 0.0 meter]   \n",
       "3154   [149599970515.70062 meter, 0.0 meter]   \n",
       "6308   [149599882062.79086 meter, 0.0 meter]   \n",
       "9462     [149599734641.201 meter, 0.0 meter]   \n",
       "12616   [149599528250.8148 meter, 0.0 meter]   \n",
       "\n",
       "                                                       V  \n",
       "0               [0.0 meter / second, 0.0 meter / second]  \n",
       "3154   [-18.696448559795822 meter / second, 0.0 meter...  \n",
       "6308   [-37.392911858950995 meter / second, 0.0 meter...  \n",
       "9462   [-56.0894046368866 meter / second, 0.0 meter /...  \n",
       "12616  [-74.78594163315154 meter / second, 0.0 meter ...  "
      ]
     },
     "execution_count": 13,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "      <td>[9.466097861076322e+16 meter, 0.0 meter]</td>\n",
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       "      <td>[9.467249174376258e+16 meter, 0.0 meter]</td>\n",
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       "      <td>31533692</td>\n",
       "      <td>[9.468400487676194e+16 meter, 0.0 meter]</td>\n",
       "      <td>[3650327520.4039083 meter / second, 0.0 meter ...</td>\n",
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       "      <td>31536846</td>\n",
       "      <td>[9.46955180097613e+16 meter, 0.0 meter]</td>\n",
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       "      <td>[9.470703114276066e+16 meter, 0.0 meter]</td>\n",
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       "                                                 R  \\\n",
       "31527384  [9.466097861076322e+16 meter, 0.0 meter]   \n",
       "31530538  [9.467249174376258e+16 meter, 0.0 meter]   \n",
       "31533692  [9.468400487676194e+16 meter, 0.0 meter]   \n",
       "31536846   [9.46955180097613e+16 meter, 0.0 meter]   \n",
       "31540000  [9.470703114276066e+16 meter, 0.0 meter]   \n",
       "\n",
       "                                                          V  \n",
       "31527384  [3650327520.4039083 meter / second, 0.0 meter ...  \n",
       "31530538  [3650327520.4039083 meter / second, 0.0 meter ...  \n",
       "31533692  [3650327520.4039083 meter / second, 0.0 meter ...  \n",
       "31536846  [3650327520.4039083 meter / second, 0.0 meter ...  \n",
       "31540000  [3650327520.4039083 meter / second, 0.0 meter ...  "
      ]
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     "execution_count": 14,
     "metadata": {
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    "results.tail()"
   ]
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   "outputs": [
    {
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       "[<matplotlib.lines.Line2D at 0x7f265450d278>]"
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     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = results.R.extract('x')\n",
    "y = results.R.extract('y')\n",
    "\n",
    "plot(x,y, label='trajectory')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}