{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 1 — Orbit as Continuous Free Fall\n",
    "\n",
    "## Goal\n",
    "\n",
    "Turn Newton's vector equation into a numerical orbit, compare two integration methods, and use energy conservation as an accuracy check.\n",
    "\n",
    "By the end you should be able to explain why an attractive force does not imply that every object falls directly into the star."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "We use astronomical units (AU), years, and solar masses. In these units the Sun's gravitational parameter is approximately $\\mu=GM_\\odot=4\\pi^2\\ \\mathrm{AU^3\\,yr^{-2}}$. This keeps the numbers readable and makes a circular orbit at 1 AU have a period of 1 year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:47.168208Z",
     "iopub.status.busy": "2026-07-29T07:42:47.167991Z",
     "iopub.status.idle": "2026-07-29T07:42:47.367923Z",
     "shell.execute_reply": "2026-07-29T07:42:47.367428Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "MU = 4 * np.pi**2  # AU^3 / yr^2\n",
    "\n",
    "def acceleration(position):\n",
    "    radius = np.linalg.norm(position)\n",
    "    return -MU * position / radius**3\n",
    "\n",
    "def specific_energy(position, velocity):\n",
    "    return 0.5 * np.sum(velocity**2, axis=-1) - MU / np.linalg.norm(position, axis=-1)\n",
    "\n",
    "def angular_momentum_z(position, velocity):\n",
    "    return position[..., 0] * velocity[..., 1] - position[..., 1] * velocity[..., 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steps\n",
    "\n",
    "### 1. Implement two approximations\n",
    "\n",
    "Explicit Euler uses the slope at the beginning of each step. Velocity Verlet uses acceleration at both ends of the step and is much better suited to conservative orbital motion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:47.369302Z",
     "iopub.status.busy": "2026-07-29T07:42:47.369203Z",
     "iopub.status.idle": "2026-07-29T07:42:47.371677Z",
     "shell.execute_reply": "2026-07-29T07:42:47.371308Z"
    }
   },
   "outputs": [],
   "source": [
    "def integrate_orbit(method, position0, velocity0, total_time=2.0, dt=0.002):\n",
    "    times = np.arange(0.0, total_time + dt, dt)\n",
    "    positions = np.empty((len(times), 2))\n",
    "    velocities = np.empty((len(times), 2))\n",
    "    positions[0], velocities[0] = position0, velocity0\n",
    "\n",
    "    for step in range(len(times) - 1):\n",
    "        position = positions[step]\n",
    "        velocity = velocities[step]\n",
    "        old_acceleration = acceleration(position)\n",
    "\n",
    "        if method == \"euler\":\n",
    "            positions[step + 1] = position + velocity * dt\n",
    "            velocities[step + 1] = velocity + old_acceleration * dt\n",
    "        elif method == \"verlet\":\n",
    "            new_position = position + velocity * dt + 0.5 * old_acceleration * dt**2\n",
    "            new_acceleration = acceleration(new_position)\n",
    "            new_velocity = velocity + 0.5 * (old_acceleration + new_acceleration) * dt\n",
    "            positions[step + 1] = new_position\n",
    "            velocities[step + 1] = new_velocity\n",
    "        else:\n",
    "            raise ValueError(\"method must be 'euler' or 'verlet'\")\n",
    "\n",
    "    return times, positions, velocities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Launch a planet\n",
    "\n",
    "At 1 AU, circular speed is $2\\pi$ AU/yr. We use 85% of that speed, so predict the orbit before running the cell: circle, bound ellipse, or escape?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:47.372761Z",
     "iopub.status.busy": "2026-07-29T07:42:47.372698Z",
     "iopub.status.idle": "2026-07-29T07:42:47.435403Z",
     "shell.execute_reply": "2026-07-29T07:42:47.434943Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_position = np.array([1.0, 0.0])\n",
    "initial_velocity = np.array([0.0, 0.85 * 2 * np.pi])\n",
    "\n",
    "euler = integrate_orbit(\"euler\", initial_position, initial_velocity)\n",
    "verlet = integrate_orbit(\"verlet\", initial_position, initial_velocity)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(7, 7))\n",
    "axis.plot(euler[1][:, 0], euler[1][:, 1], label=\"Euler\", alpha=0.8)\n",
    "axis.plot(verlet[1][:, 0], verlet[1][:, 1], label=\"Velocity Verlet\", linewidth=2)\n",
    "axis.scatter(0, 0, s=180, color=\"gold\", edgecolor=\"black\", label=\"Sun\", zorder=3)\n",
    "axis.set(xlabel=\"x [AU]\", ylabel=\"y [AU]\", title=\"Same physics, different numerical methods\")\n",
    "axis.set_aspect(\"equal\")\n",
    "axis.grid(alpha=0.25)\n",
    "axis.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Test the simulation with conservation laws\n",
    "\n",
    "A plausible-looking curve is not enough. In the isolated two-body problem, specific energy and angular momentum should remain constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:47.450845Z",
     "iopub.status.busy": "2026-07-29T07:42:47.450727Z",
     "iopub.status.idle": "2026-07-29T07:42:47.500975Z",
     "shell.execute_reply": "2026-07-29T07:42:47.500632Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Euler maximum |energy drift|: 3.595e-01\n",
      "Verlet maximum |energy drift|: 1.518e-04\n",
      "Verlet maximum |angular-momentum drift|: 5.821e-15\n"
     ]
    }
   ],
   "source": [
    "def relative_drift(values):\n",
    "    return (values - values[0]) / abs(values[0])\n",
    "\n",
    "euler_energy = specific_energy(euler[1], euler[2])\n",
    "verlet_energy = specific_energy(verlet[1], verlet[2])\n",
    "euler_drift = relative_drift(euler_energy)\n",
    "verlet_drift = relative_drift(verlet_energy)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8, 4))\n",
    "axis.plot(euler[0], euler_drift, label=\"Euler\")\n",
    "axis.plot(verlet[0], verlet_drift, label=\"Velocity Verlet\")\n",
    "axis.axhline(0, color=\"black\", linewidth=0.8)\n",
    "axis.set(xlabel=\"time [yr]\", ylabel=\"relative energy drift\", title=\"Conservation exposes numerical error\")\n",
    "axis.grid(alpha=0.25)\n",
    "axis.legend()\n",
    "plt.show()\n",
    "\n",
    "print(f\"Euler maximum |energy drift|: {np.max(np.abs(euler_drift)):.3e}\")\n",
    "print(f\"Verlet maximum |energy drift|: {np.max(np.abs(verlet_drift)):.3e}\")\n",
    "print(f\"Verlet maximum |angular-momentum drift|: \"\n",
    "      f\"{np.max(np.abs(relative_drift(angular_momentum_z(verlet[1], verlet[2])))):.3e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Explore initial speed\n",
    "\n",
    "If widgets are available, move the slider. The critical escape speed at 1 AU is $\\sqrt{2}$ times circular speed. Predict the transition before trying it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:47.502528Z",
     "iopub.status.busy": "2026-07-29T07:42:47.502447Z",
     "iopub.status.idle": "2026-07-29T07:42:47.505283Z",
     "shell.execute_reply": "2026-07-29T07:42:47.504908Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ipywidgets is optional; call plot_speed_family(1.2) manually.\n"
     ]
    }
   ],
   "source": [
    "def plot_speed_family(speed_fraction=1.0):\n",
    "    velocity0 = np.array([0.0, speed_fraction * 2 * np.pi])\n",
    "    _, positions, velocities = integrate_orbit(\n",
    "        \"verlet\", initial_position, velocity0, total_time=2.0, dt=0.002\n",
    "    )\n",
    "    energy0 = specific_energy(positions[0], velocities[0])\n",
    "    state = \"bound\" if energy0 < 0 else \"unbound / escape boundary\"\n",
    "    fig, axis = plt.subplots(figsize=(5, 5))\n",
    "    axis.plot(positions[:, 0], positions[:, 1])\n",
    "    axis.scatter(0, 0, s=130, color=\"gold\", edgecolor=\"black\")\n",
    "    axis.set(xlabel=\"x [AU]\", ylabel=\"y [AU]\",\n",
    "             title=f\"v = {speed_fraction:.2f} circular speed; {state}\")\n",
    "    axis.set_aspect(\"equal\")\n",
    "    axis.grid(alpha=0.25)\n",
    "    plt.show()\n",
    "\n",
    "try:\n",
    "    from ipywidgets import FloatSlider, interact\n",
    "    interact(\n",
    "        plot_speed_family,\n",
    "        speed_fraction=FloatSlider(value=1.0, min=0.65, max=1.55, step=0.05),\n",
    "    )\n",
    "except ImportError:\n",
    "    print(\"ipywidgets is optional; call plot_speed_family(1.2) manually.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Checks\n",
    "\n",
    "The following check does not prove that Verlet is exact. It verifies the expected relationship for this experiment: its energy error should be smaller than Euler's."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-29T07:42:47.506713Z",
     "iopub.status.busy": "2026-07-29T07:42:47.506603Z",
     "iopub.status.idle": "2026-07-29T07:42:47.509666Z",
     "shell.execute_reply": "2026-07-29T07:42:47.508821Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checks passed: finite trajectory and lower energy drift with Verlet.\n"
     ]
    }
   ],
   "source": [
    "assert np.max(np.abs(verlet_drift)) < np.max(np.abs(euler_drift))\n",
    "assert np.isfinite(verlet[1]).all()\n",
    "print(\"Checks passed: finite trajectory and lower energy drift with Verlet.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Next Steps\n",
    "\n",
    "1. Halve `dt` twice and make a log–log plot of maximum energy error versus timestep.\n",
    "2. Add a second massive body. Which conserved quantities survive?\n",
    "3. Replace Newtonian acceleration with a model including a tiny perturbation and measure orbital precession.\n",
    "\n",
    "**Frontier connection:** orbital dynamics infer unseen mass, enable precision tests of gravity, and provide the starting point for compact binaries whose relativistic motion generates gravitational waves."
   ]
  }
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