{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "507e7ff6",
   "metadata": {},
   "source": [
    "# 09 · Physics and Space Research\n",
    "\n",
    "From deriving equations to simulating orbits, Python covers the whole loop of physical science: **SymPy**\n",
    "does the algebra, **SciPy** solves what has no closed form, **NumPy** analyses signals, and **Astropy**,\n",
    "the community library of astronomy, keeps units and constants right.\n",
    "\n",
    "**You will learn**\n",
    "1. Symbolic mathematics: derive a pendulum's equation of motion with SymPy\n",
    "2. Numerical simulation: solve it with SciPy and see where the textbook approximation fails\n",
    "3. Signal analysis: recover a pendulum's frequency with the Fourier transform\n",
    "4. Units and constants with Astropy, and Kepler's third law checked on the real planets\n",
    "5. Integrating an orbit and validating it with conservation of energy and angular momentum\n",
    "6. Sky coordinates: converting between reference frames"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1da846df",
   "metadata": {},
   "source": [
    "## 1. Deriving the equation of motion symbolically\n",
    "For a pendulum of length $L$ the Lagrangian is kinetic minus potential energy,\n",
    "$\\mathcal{L} = \\tfrac12 m L^2 \\dot\\theta^2 + m g L \\cos\\theta$. The Euler-Lagrange equation gives the\n",
    "motion; SymPy does the calculus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e6eac297",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-17T23:29:20.245149Z",
     "iopub.status.busy": "2026-10-17T23:29:20.244745Z",
     "iopub.status.idle": "2026-10-17T23:29:21.200612Z",
     "shell.execute_reply": "2026-10-17T23:29:21.198920Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{g \\sin{\\left(\\theta{\\left(t \\right)} \\right)}}{L} = \\frac{d^{2}}{d t^{2}} \\theta{\\left(t \\right)}$"
      ],
      "text/plain": [
       "Eq(-g*sin(theta(t))/L, Derivative(theta(t), (t, 2)))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sp\n",
    "\n",
    "t = sp.symbols(\"t\")\n",
    "m, g, L = sp.symbols(\"m g L\", positive=True)\n",
    "theta = sp.Function(\"theta\")(t)\n",
    "lagrangian = sp.Rational(1, 2) * m * L**2 * theta.diff(t)**2 + m * g * L * sp.cos(theta)\n",
    "euler_lagrange = sp.diff(lagrangian.diff(theta.diff(t)), t) - lagrangian.diff(theta)\n",
    "eq = sp.Eq(sp.solve(euler_lagrange, theta.diff(t, 2))[0], theta.diff(t, 2))\n",
    "eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8739fcc0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-17T23:29:21.205724Z",
     "iopub.status.busy": "2026-10-17T23:29:21.205118Z",
     "iopub.status.idle": "2026-10-17T23:29:21.433901Z",
     "shell.execute_reply": "2026-10-17T23:29:21.431813Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(theta(t), theta0*cos(sqrt(g)*t/sqrt(L)))\n",
      "small-angle period: 2*pi*sqrt(L)/sqrt(g)\n"
     ]
    }
   ],
   "source": [
    "# for small angles sin(θ) ≈ θ and the equation has a closed-form solution with period 2π√(L/g)\n",
    "theta0 = sp.symbols(\"theta0\")\n",
    "small = sp.dsolve(theta.diff(t, 2) + g / L * theta, theta, ics={theta.subs(t, 0): theta0, theta.diff(t).subs(t, 0): 0})\n",
    "print(small)\n",
    "print(\"small-angle period:\", sp.simplify(2 * sp.pi / sp.sqrt(g / L)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec038b0a",
   "metadata": {},
   "source": [
    "## 2. Simulating the full pendulum\n",
    "The real equation $\\ddot\\theta = -\\tfrac{g}{L}\\sin\\theta$ has no elementary solution. `scipy.integrate.solve_ivp`\n",
    "integrates it numerically. Comparing with the small-angle formula shows when the textbook approximation\n",
    "is good enough."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "456011be",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-17T23:29:21.438947Z",
     "iopub.status.busy": "2026-10-17T23:29:21.438535Z",
     "iopub.status.idle": "2026-10-17T23:29:33.939846Z",
     "shell.execute_reply": "2026-10-17T23:29:33.938168Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1100x340 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error of the small-angle period: 0.19% at 10°, 7.3% at 60°\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "G, LEN = 9.81, 1.0\n",
    "def pendulum(t, y):\n",
    "    th, om = y\n",
    "    return [om, -G / LEN * np.sin(th)]\n",
    "\n",
    "t_eval = np.linspace(0, 10, 4000)\n",
    "fig, ax = plt.subplots(1, 2, figsize=(11, 3.4))\n",
    "for amp_deg, color in [(10, \"#0ea5e9\"), (60, \"#f59e0b\"), (150, \"#ef4444\")]:\n",
    "    amp = np.radians(amp_deg)\n",
    "    sol = solve_ivp(pendulum, (0, 10), [amp, 0], t_eval=t_eval, rtol=1e-9, atol=1e-9)\n",
    "    ax[0].plot(sol.t, np.degrees(sol.y[0]), color=color, label=f\"{amp_deg}° (numerical)\")\n",
    "    ax[0].plot(t_eval, amp_deg * np.cos(np.sqrt(G / LEN) * t_eval), \"--\", color=color, alpha=.5)\n",
    "ax[0].set_xlabel(\"time (s)\"); ax[0].set_ylabel(\"angle (°)\"); ax[0].legend(fontsize=8); ax[0].set_title(\"solid: exact, dashed: small-angle\")\n",
    "\n",
    "# period as a function of amplitude, measured from the simulation\n",
    "amps = np.radians(np.linspace(5, 170, 34))\n",
    "def period(amp):\n",
    "    s = solve_ivp(pendulum, (0, 20), [amp, 0], events=lambda t, y: y[1], rtol=1e-10, atol=1e-10, dense_output=True)\n",
    "    crossings = [tc for tc in s.t_events[0] if tc > 1e-6]\n",
    "    return 2 * crossings[0]              # velocity is zero at each turning point, half a period apart\n",
    "T0 = 2 * np.pi * np.sqrt(LEN / G)\n",
    "ax[1].plot(np.degrees(amps), [period(a) / T0 for a in amps], \"o-\", ms=3)\n",
    "ax[1].set_xlabel(\"amplitude (°)\"); ax[1].set_ylabel(\"period / small-angle period\"); ax[1].set_title(\"The period grows with amplitude\")\n",
    "plt.tight_layout(); plt.show()\n",
    "print(f\"error of the small-angle period: {100 * (period(np.radians(10)) / T0 - 1):.2f}% at 10°, \"\n",
    "      f\"{100 * (period(np.radians(60)) / T0 - 1):.1f}% at 60°\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83b5f1f8",
   "metadata": {},
   "source": [
    "## 3. Finding the frequency with a Fourier transform\n",
    "Experiments give noisy measurements, not equations. The fast Fourier transform (FFT) finds the dominant\n",
    "frequency in a noisy signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3bd4b802",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-17T23:29:33.944333Z",
     "iopub.status.busy": "2026-10-17T23:29:33.943562Z",
     "iopub.status.idle": "2026-10-17T23:29:34.892897Z",
     "shell.execute_reply": "2026-10-17T23:29:34.891832Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dominant frequency 0.4833 Hz -> period 2.069 s (simulation: 2.041 s)\n",
      "frequency resolution of a 60 s recording: 0.0167 Hz, so the estimate is exact to within one frequency bin; record longer to resolve finer\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.default_rng(0)\n",
    "amp = np.radians(30)\n",
    "fs, duration = 100, 60                            # 100 samples per second, one minute\n",
    "tt = np.arange(0, duration, 1 / fs)\n",
    "signal = solve_ivp(pendulum, (0, duration), [amp, 0], t_eval=tt, rtol=1e-9).y[0]\n",
    "measured = signal + rng.normal(0, 0.08, tt.size)   # sensor noise\n",
    "\n",
    "spectrum = np.abs(np.fft.rfft(measured * np.hanning(tt.size)))\n",
    "freqs = np.fft.rfftfreq(tt.size, 1 / fs)\n",
    "f_peak = freqs[np.argmax(spectrum[1:]) + 1]\n",
    "print(f\"dominant frequency {f_peak:.4f} Hz -> period {1 / f_peak:.3f} s (simulation: {period(amp):.3f} s)\")\n",
    "print(f\"frequency resolution of a {duration} s recording: {1 / duration:.4f} Hz, so the estimate is exact \"\n",
    "      \"to within one frequency bin; record longer to resolve finer\")\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(11, 3))\n",
    "ax[0].plot(tt[:500], measured[:500], lw=.8); ax[0].set_xlabel(\"time (s)\"); ax[0].set_title(\"noisy measurement\")\n",
    "ax[1].plot(freqs, spectrum); ax[1].set_xlim(0, 2); ax[1].set_xlabel(\"frequency (Hz)\"); ax[1].set_title(\"amplitude spectrum\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c374722",
   "metadata": {},
   "source": [
    "## 4. Units, constants and Kepler's third law with Astropy\n",
    "Unit mistakes have destroyed spacecraft. Astropy attaches units to numbers, converts them, and refuses\n",
    "to add incompatible quantities. Kepler's third law says $T^2 = \\frac{4\\pi^2}{G M_\\odot} a^3$: the square of\n",
    "a planet's orbital period grows with the cube of its distance from the Sun."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c7aae318",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-17T23:29:34.897077Z",
     "iopub.status.busy": "2026-10-17T23:29:34.896680Z",
     "iopub.status.idle": "2026-10-17T23:29:35.475632Z",
     "shell.execute_reply": "2026-10-17T23:29:35.473681Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Name   = Gravitational constant\n",
      "  Value  = 6.6743e-11\n",
      "  Uncertainty  = 1.5e-15\n",
      "  Unit  = m3 / (kg s2)\n",
      "  Reference = CODATA 2022 \n",
      "   Name   = Solar mass\n",
      "  Value  = 1.988409870698051e+30\n",
      "  Uncertainty  = 4.468805426856864e+25\n",
      "  Unit  = kg\n",
      "  Reference = IAU 2015 Resolution B 3 + CODATA 2022 \n",
      " 149597870.7 km | 63241.07708426628 AU\n",
      "refused: Can only apply 'add' function to quantities with compatible dimensions\n",
      "\n",
      "planet    observed (yr)  Kepler (yr)    error\n",
      "Mercury           0.241        0.241    0.00%\n",
      "Venus             0.615        0.615   -0.01%\n",
      "Earth             1.000        1.000    0.00%\n",
      "Mars              1.881        1.881    0.00%\n",
      "Jupiter          11.862       11.870    0.06%\n",
      "Saturn           29.457       29.453   -0.01%\n",
      "Uranus           84.021       84.073    0.06%\n",
      "Neptune         164.769      164.887    0.07%\n"
     ]
    }
   ],
   "source": [
    "import astropy.units as u\n",
    "from astropy import constants as const\n",
    "\n",
    "print(const.G, \"\\n\", const.M_sun, \"\\n\", (1 * u.au).to(u.km), \"|\", (1 * u.lyr).to(u.au))\n",
    "try:\n",
    "    1 * u.m + 1 * u.s\n",
    "except u.UnitConversionError as e:\n",
    "    print(\"refused:\", e)\n",
    "\n",
    "# semi-major axes (AU) and observed sidereal orbital periods (days)\n",
    "planets = {\"Mercury\": (0.3871, 87.969), \"Venus\": (0.7233, 224.701), \"Earth\": (1.0000, 365.256),\n",
    "           \"Mars\": (1.5237, 686.980), \"Jupiter\": (5.2034, 4332.59), \"Saturn\": (9.5371, 10759.22),\n",
    "           \"Uranus\": (19.191, 30688.5), \"Neptune\": (30.069, 60182.0)}\n",
    "print(f\"\\n{'planet':<9}{'observed (yr)':>14}{'Kepler (yr)':>13}{'error':>9}\")\n",
    "for name, (a_au, t_days) in planets.items():\n",
    "    predicted = (2 * np.pi * np.sqrt((a_au * u.au) ** 3 / (const.G * const.M_sun))).to(u.yr)\n",
    "    observed = (t_days * u.day).to(u.yr)\n",
    "    print(f\"{name:<9}{observed.value:>14.3f}{predicted.value:>13.3f}{100 * (predicted / observed - 1).value:>8.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bdb9619",
   "metadata": {},
   "source": [
    "## 5. Integrating an orbit, checked by conservation laws\n",
    "We launch a satellite into an elliptical Earth orbit and integrate Newton's law of gravitation. A\n",
    "numerical solution is only trustworthy if it respects the physics: **energy** and **angular momentum**\n",
    "must stay constant. Comparing a sloppy and a precise integration shows why tolerances matter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "75189204",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-17T23:29:35.479723Z",
     "iopub.status.busy": "2026-10-17T23:29:35.479371Z",
     "iopub.status.idle": "2026-10-17T23:29:36.372835Z",
     "shell.execute_reply": "2026-10-17T23:29:36.371109Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rtol=0.001: 56 steps, relative energy drift 2.5e-02, angular momentum drift 1.1e-02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rtol=1e-10: 1093 steps, relative energy drift 7.8e-10, angular momentum drift 3.0e-10\n",
      "after one day the loose integration places the satellite 3,834 km from where it really is\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = (const.G * const.M_earth).to(u.km**3 / u.s**2).value      # Earth's gravitational parameter, km^3/s^2\n",
    "r0 = 6378 + 500                                                  # 500 km altitude, km\n",
    "v_circ = np.sqrt(mu / r0)\n",
    "state0 = [r0, 0, 0, 1.25 * v_circ]                               # 25% faster than circular: an ellipse\n",
    "\n",
    "def two_body(t, s):\n",
    "    x, y, vx, vy = s\n",
    "    r3 = (x * x + y * y) ** 1.5\n",
    "    return [vx, vy, -mu * x / r3, -mu * y / r3]\n",
    "\n",
    "T_orbit = 24 * 3600                                               # one day, about 4.4 orbits\n",
    "tt = np.linspace(0, T_orbit, 4000)\n",
    "def run(rtol):\n",
    "    sol = solve_ivp(two_body, (0, T_orbit), state0, rtol=rtol, atol=min(rtol * 1e-3, 1e-6), dense_output=True)\n",
    "    x, y, vx, vy = sol.sol(tt)                                    # evaluate the solution on a fine grid\n",
    "    energy = 0.5 * (vx**2 + vy**2) - mu / np.hypot(x, y)\n",
    "    h = x * vy - y * vx\n",
    "    return sol, (x, y), energy, h\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(11, 4))\n",
    "final = {}\n",
    "for rtol, color in [(1e-3, \"#ef4444\"), (1e-10, \"#22c55e\")]:\n",
    "    sol, (x, y), energy, h = run(rtol)\n",
    "    final[rtol] = np.array([x[-1], y[-1]])\n",
    "    ax[0].plot(x, y, color=color, lw=.8, label=f\"rtol={rtol:g} ({sol.t.size} steps)\")\n",
    "    ax[1].plot(tt / 3600, (energy - energy[0]) / abs(energy[0]), color=color, label=f\"rtol={rtol:g}\")\n",
    "    print(f\"rtol={rtol:g}: {sol.t.size} steps, relative energy drift {abs(energy[-1] / energy[0] - 1):.1e}, \"\n",
    "          f\"angular momentum drift {abs(h[-1] / h[0] - 1):.1e}\")\n",
    "print(f\"after one day the loose integration places the satellite {np.linalg.norm(final[1e-3] - final[1e-10]):,.0f} km \"\n",
    "      \"from where it really is\")\n",
    "ax[0].add_patch(plt.Circle((0, 0), 6378, color=\"#3b82f6\")); ax[0].set_aspect(\"equal\"); ax[0].legend(); ax[0].set_title(\"orbit (km)\")\n",
    "ax[1].set_xlabel(\"hours\"); ax[1].set_ylabel(\"relative energy error\"); ax[1].legend(); ax[1].set_title(\"conservation check\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae89fab0",
   "metadata": {},
   "source": [
    "## 6. Sky coordinates\n",
    "Astronomers describe positions in different frames: equatorial (right ascension, declination), galactic,\n",
    "ecliptic. Astropy converts between them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f10581f9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-17T23:29:36.376533Z",
     "iopub.status.busy": "2026-10-17T23:29:36.376141Z",
     "iopub.status.idle": "2026-10-17T23:29:36.831427Z",
     "shell.execute_reply": "2026-10-17T23:29:36.829853Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sirius                   RA  101.29°  Dec -16.72°  ->  galactic l  227.23°  b  -8.89°\n",
      "Betelgeuse               RA   88.79°  Dec   7.41°  ->  galactic l  199.79°  b  -8.96°\n",
      "Andromeda galaxy (M31)   RA   10.68°  Dec  41.27°  ->  galactic l  121.17°  b -21.57°\n",
      "angular separation Sirius-Betelgeuse: 27d06m15.8s\n"
     ]
    }
   ],
   "source": [
    "from astropy.coordinates import SkyCoord\n",
    "\n",
    "targets = {\"Sirius\": (\"06h45m08.9s\", \"-16d42m58s\"), \"Betelgeuse\": (\"05h55m10.3s\", \"+07d24m25s\"),\n",
    "           \"Andromeda galaxy (M31)\": (\"00h42m44.3s\", \"+41d16m09s\")}\n",
    "for name, (ra, dec) in targets.items():\n",
    "    c = SkyCoord(ra, dec, frame=\"icrs\")\n",
    "    gal = c.galactic\n",
    "    print(f\"{name:<24} RA {c.ra.deg:7.2f}°  Dec {c.dec.deg:6.2f}°  ->  galactic l {gal.l.deg:7.2f}°  b {gal.b.deg:6.2f}°\")\n",
    "sirius, betel = SkyCoord(*targets[\"Sirius\"]), SkyCoord(*targets[\"Betelgeuse\"])\n",
    "print(\"angular separation Sirius-Betelgeuse:\", sirius.separation(betel).to_string(unit=u.deg, precision=1))"
   ]
  },
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    "## Libraries worth knowing\n",
    "| Area | Libraries |\n",
    "|---|---|\n",
    "| symbolic maths | SymPy |\n",
    "| simulation, ODEs, optimisation | SciPy, JAX (differentiable simulation) |\n",
    "| astronomy | Astropy, astroquery (archive queries), Skyfield (precise ephemerides), poliastro/hapsira (astrodynamics), lightkurve (Kepler/TESS light curves) |\n",
    "| particle and nuclear physics | uproot, awkward-array, scikit-hep |\n",
    "| fluids, finite elements | FEniCS, PyClaw |\n",
    "| quantum computing | Qiskit, Cirq, PennyLane |\n",
    "\n",
    "## Exercises\n",
    "1. Add air resistance (a term $-c\\,\\dot\\theta$) to the pendulum and measure how the amplitude decays.\n",
    "2. Increase the launch speed to 1.45 times circular. Is the orbit still bound? Check the sign of the energy.\n",
    "3. Use the planets table to fit $\\log T$ against $\\log a$ with NumPy and recover the exponent 3/2."
   ]
  }
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