{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8f4e10ba",
   "metadata": {},
   "source": [
    "## Numerische Lösung eines Zweikörperproblems ##"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c744b28f",
   "metadata": {},
   "source": [
    "*Notebook erstellt am 20.11.2022 von C. Rockstuhl, überarbeitet von Y. Augenstein*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0cff3b2",
   "metadata": {},
   "source": [
    "Wir wollen in diesem Notebook das Zweikörperproblem lösen, wie es im Rahmen der Planetenbewegung diskutiert wurde. Es gibt verschiedene Möglichkeiten, sich diesem Thema zu nähern. Wir würden hier ganz allgemein zwei Körper betrachten, die sich gegenseitig über die Gravitationskraft anziehen und die sich in einem Inertialsystem befinden. Die beiden Körper sind charakterisiert durch ihre Massen $m_1$ und $m_2$. Es gibt darüberhinaus keine weiteren Kräfte, welche auf diese beiden Körper wirken.\n",
    "\n",
    "### Setting\n",
    "\n",
    "Geometrische Größen, die das System beschreiben, sind die absoluten Raumkoordinaten der beiden Körper\n",
    "\n",
    "$$\n",
    "\\mathbf{r}_1=x_1\\mathbf{e}_x+y_1\\mathbf{e}_y+z_1\\mathbf{e}_z\n",
    "$$\n",
    "\n",
    "und \n",
    "\n",
    "$$\n",
    "\\mathbf{r}_2=x_2\\mathbf{e}_x+y_2\\mathbf{e}_y+z_2\\mathbf{e}_z \\quad .\n",
    "$$\n",
    "\n",
    "Darüberhinaus können wir auch noch die Schwerpunktskoordinate definieren\n",
    "\n",
    "$$\n",
    "\\mathbf{R}=\\frac{m_1\\mathbf{r}_1+m_2\\mathbf{r}_2}{m_1+m_2}\n",
    "$$\n",
    "\n",
    "und die Relativkoordinate\n",
    "\n",
    "$$\n",
    "\\mathbf{r}=\\mathbf{r}_2-\\mathbf{r}_1 \\quad .\n",
    "$$\n",
    "\n",
    "Die von Körper 2 auf Körper 1 wirkende Gravitationskraft ist gegeben als\n",
    "\n",
    "$$\n",
    "\\mathbf{F}_{12}=G\\frac{m_1m_2}{|\\mathbf{r}|^2}\\frac{\\mathbf{r}}{|\\mathbf{r}|}\n",
    "$$\n",
    "\n",
    "und die von Körper 1 auf Körper 2 wirkende Gravitatiationskraft ist gerade genau entgegegengesetzt und gleich groß (*actio=reactio*), $\\mathbf{F}_{12}=-\\mathbf{F}_{21}$\n",
    "\n",
    "$$\n",
    "\\mathbf{F}_{21}=-G\\frac{m_1m_2}{|\\mathbf{r}|^2}\\frac{\\mathbf{r}}{|\\mathbf{r}|} \\quad .\n",
    "$$\n",
    "\n",
    "Die von uns zu lösenden Bewegungsgleichungen lauten also:\n",
    "\n",
    "\\begin{align*}\n",
    "m_1\\ddot{\\mathbf{r}}_1&=\\mathbf{F}_{12} \\\\\n",
    "m_2\\ddot{\\mathbf{r}}_2&=\\mathbf{F}_{21} \\quad .\n",
    "\\end{align*}\n",
    "\n",
    "Nach Division durch die Masse können wir die entsprechenden Bewegungsgleichungen für die Ortskoordinate konkretisieren zu\n",
    "\n",
    "\\begin{align*}\n",
    "\\ddot{\\mathbf{r}}_1&=Gm_2\\frac{\\mathbf{r}}{|\\mathbf{r}|^3} \\\\\n",
    "\\ddot{\\mathbf{r}}_2&=-Gm_1\\frac{\\mathbf{r}}{|\\mathbf{r}|^3} \\quad .\n",
    "\\end{align*}\n",
    "\n",
    "Beachten Sie, dass es sich hierbei um insgesamt 6 gekoppelte Differentialgleichungen handelt, die wir im Folgenden numerisch lösen müssen. In Komponenten aufgeschrieben lauten diese\n",
    "\n",
    "\\begin{align*}\n",
    "\\ddot{x}_1&=Gm_2\\frac{x_2-x_1}{|\\mathbf{r}|^3}\\\\\n",
    "\\ddot{y}_1&=Gm_2\\frac{y_2-y_1}{|\\mathbf{r}|^3}\\\\\n",
    "\\ddot{z}_1&=Gm_2\\frac{z_2-z_1}{|\\mathbf{r}|^3}\\\\\n",
    "\\ddot{x}_2&=-Gm_1\\frac{x_2-x_1}{|\\mathbf{r}|^3}\\\\\n",
    "\\ddot{y}_2&=-Gm_1\\frac{y_2-y_1}{|\\mathbf{r}|^3}\\\\\n",
    "\\ddot{z}_2&=-Gm_1\\frac{z_2-z_1}{|\\mathbf{r}|^3} \\quad .\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ae06ba0",
   "metadata": {},
   "source": [
    "### Numerische Differenzierung\n",
    "\n",
    "Genauso wie in früheren Beispielen müssen wir als Erstes diese Differentialgleichungen zweiter Ordnung in Differentialgleichungen erster Ordnung überführen. Wir wählen hier wieder den Ort und die Geschwindigkeit der beiden Körper als die Größen aus, die wir durch Differentialgleichungnen erster Ordnung beschreiben werden. Wir werden eine Vektornotation wählen, in der die zu beschreibenden Größen in einen einzelnen Vektor $\\mathbf{r}$ geschrieben werden. Dieser Vektor ist dann definiert als\n",
    "\n",
    "$$\n",
    "\\mathbf{r}=\\begin{pmatrix}\\mathbf{r}_1\\\\ \\mathbf{r}_2\\\\ \\dot{\\mathbf{r}}_1 \\\\ \\dot{\\mathbf{r}}_2\\end{pmatrix} \\quad .\n",
    "$$\n",
    "\n",
    "Die zeitliche Entwicklung wird dann durch folgende Differentialgleichung beschrieben:\n",
    "\n",
    "$$\n",
    "\\frac{\\mathrm{d}\\mathbf{r}}{\\mathrm{d}t}=\\dot{\\mathbf{r}}=\\begin{pmatrix}\\dot{\\mathbf{r}}_1 \\\\ \\dot{\\mathbf{r}}_2 \\\\ Gm_2\\frac{\\mathbf{r}}{|\\mathbf{r}|^3} \\\\ -Gm_1\\frac{\\mathbf{r}}{|\\mathbf{r}|^3} \\end{pmatrix} \\quad .\n",
    "$$\n",
    "\n",
    "Es ist diese Differentialgleichung, die wir jetzt im Folgenden implementieren möchten. Auch hier ist wieder offensichtlich, dass wir genauso viele Anfangsbedingungen benötigen wie wir Differentialgleichungen erster Ordnung haben. Wir benötigen also den Anfangsort und die Anfangsgeschwindigkeit der beiden Massen. \n",
    "\n",
    "Der folgende Code ist, wie die Ausführungen weiter oben, komplett drei-dimensional aufgeschrieben. Wir würden aber die dritte Raumkoordinate zu null setzen und auch keine Anfangsgeschwindigkeit oder Anfangsposition in dieser Ebene forcieren. Wir können daher effektiv die Bewegung in einer Ebene diskutieren, was die Darstellung erleichtert.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b3b618c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "98910e1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def two_body_problem(t, y, G, m1, m2):\n",
    "    \"\"\"\n",
    "    Die hier beschriebene Differentialgleichung beschreibt die Bewegungsgleichung der\n",
    "    beiden Körper mit den beiden Massen m1 und m2.\n",
    "    t: diskreter Zeitschritt (wird formal immer benötigt, auch wenn die DGL nicht erplizit von der Zeit abhängt)\n",
    "    y: Zustandsvektor, den wir übergeben und dessen Bewegung, also seine zeitliche Veränderung, durch die DGL beschrieben wuird.\n",
    "    \"\"\"\n",
    "    # Berechne hier den Abstandsvektor zwischen den beiden Massen\n",
    "    r1 = y[:3]\n",
    "    r2 = y[3:6]\n",
    "    v1v2 = y[6:]\n",
    "    r_mag = np.linalg.norm(r2 - r1)\n",
    "    c1 = G * m2 * (r2 - r1) / r_mag**3\n",
    "    c2 = -G * m1 * (r2 - r1) / r_mag**3\n",
    "    return np.concatenate([v1v2, c1, c2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f64e0dda",
   "metadata": {},
   "source": [
    "Nach der Definition der Differentialgleichung, die die zeitliche Entwicklung von Ort und Geschwindigkeit beschreibt, können wir die eigentliche Simulation laufen lassen. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "58c302c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gravitationskonstante\n",
    "G = 6.67259e-20  # (km**3/kg/s**2)\n",
    "\n",
    "# Zeitintervall (Anfang und Ende), innerhalb dessen wir die DGL lösen möchten  \n",
    "time_interval = [0, 1000]\n",
    "\n",
    "# Details zum Körper 1. Wir geben diesem hier zunächst eine sehr hohe Masse und setzen \n",
    "# ihn in die Mitte des Koordinatensystem und geben dem Körper keine Anfangsgeschwindigkeit.\n",
    "# In guter Näherung können wir so ein System bestehend aus Sonne und Erde beschreiben.\n",
    "m1 = 1e26          # Masse (kg)\n",
    "r10 = np.array([0, 0, 0])  # Anfangsort (km)\n",
    "v10 = np.array([0, 0, 0])    # Anfangsgeschwindigkeit (km/s)\n",
    "\n",
    "# Details zum Körper 2\n",
    "m2 = 1e23                     # Masse (kg)\n",
    "r20 = np.array([3000, 0, 0])  # Anfangsort (km)\n",
    "v20 = np.array([0, 40, 0])    # Anfangsgeschwindigkeit (km/s)\n",
    "\n",
    "# [x1 (0), y1 (1), z1 (2), x2 (3), y2 (4), z2 (5), vx1 (6), vy1 (7), vz1 (8), vx2 (9), vy2 (10), vz2 (11)]\n",
    "y0 = np.concatenate((r10, r20, v10, v20))\n",
    "\n",
    "y = solve_ivp(two_body_problem, time_interval, y0, method='DOP853', args=(G, m1, m2), dense_output=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07463d2c",
   "metadata": {},
   "source": [
    "Nun berechnen wir ein paar relevante Größen (insbesondere die Positionen der beiden Körper) an einer Reihe von uns gewählten Zeitpunkten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2d4eac89",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.linspace(*time_interval, 1000)\n",
    "\n",
    "sol = y.sol(t)\n",
    "r1 = sol[:3]\n",
    "r2 = sol[3:6]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5525d543",
   "metadata": {},
   "source": [
    "Alles was jetzt kommt dient nur der Visualisierung."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2e8ea119",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"axes.grid\"] = True\n",
    "plt.style.use(\"dark_background\")\n",
    "\n",
    "fig = plt.figure(figsize=plt.figaspect(0.5))\n",
    "\n",
    "ax1 = fig.add_subplot(1, 2, 1)\n",
    "\n",
    "ax1.plot(*r1[:2], \"cyan\")\n",
    "ax1.plot(*r2[:2], \"red\")\n",
    "ax1.set_xlabel(\"X (km)\")\n",
    "ax1.set_ylabel(\"Y (km)\")\n",
    "\n",
    "ax2 = fig.add_subplot(1, 2, 2, projection=\"3d\")\n",
    "\n",
    "ax2.plot3D(*r1, \"cyan\")\n",
    "ax2.plot3D(*r2, \"red\")\n",
    "\n",
    "ax2.set_xlabel(\"X (km)\")\n",
    "ax2.set_ylabel(\"Y (km)\")\n",
    "ax2.set_zlabel(\"Z (km)\")\n",
    "\n",
    "fig.suptitle(\"Zwei-Körper Problem\")\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "724895e5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c89b172e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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