Radial_Fall_Related_Equations.ipynb

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      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Radial Fall\n",
        "\n",
        "* Radial fall refers to the motion of an object toward a massive celestial body along a radial trajectory, typically influenced by gravitational forces. This concept is fundamental in understanding the behavior of objects, such as stars, planets, or particles, as they move under the influence of gravity.\n",
        "* As an object undergoes radial fall, it experiences an increasing gravitational force, leading to an acceleration toward the massive body. The gravitational potential energy decreases as the object falls closer to the massive body. Radial fall is governed by the inverse square law, where the force and acceleration depend inversely on the square of the radial distance.\n",
        "\n",
        "  ## Gravitational Force\n",
        "  > $F = \\frac{G \\cdot M \\cdot m}{r^2}$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $F$: the gravitational force\n",
        "\n",
        "  $G$: the gravitational constant\n",
        "\n",
        "  $M$: the mass of the celestial body\n",
        "\n",
        "  $m$: the mass of the falling object or secondary body\n",
        "\n",
        "  $r$: the radial distance between the centers of mass\n",
        "\n",
        "  ## Gravitational Potential Energy\n",
        "  > $U = -\\frac{G \\cdot M \\cdot m}{r}$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $U$: potential energy\n",
        "\n",
        "  ## Acceleration Due to Gravity\n",
        "  > $a = \\frac{G \\cdot M}{r^2}$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $a$: acceleration\n",
        "\n",
        "* In terms of the vertical height ($h$) above surface:\n",
        "> $h = r - R_{\\text{E}}$\n",
        "\n",
        "  $h^{..} = - \\frac{GM_{E}}{(R_{E}+h)^2}$\n",
        "\n",
        "* Assuming a total energy $E=0$(zero velocity at infinity), energy conservation implies:\n",
        "\n",
        "  > $\\text{infall velocity(v)} = -h^{'} = \\sqrt{\\frac{2GM_{E}}{R_{E}+h}}$\n",
        "\n",
        "  **In particular, the impact velocity at the surface of Earth (h=0) is** $v_{0} = \\sqrt{\\frac{2GM_{E}}{R_{E}+0}} = 11.2$ km/s.\n",
        "\n",
        "* Even for an object following a non-radial trajectory, we can use the kinetic energy:\n",
        "  > $E_{\\text{kinetic}} = \\frac{1}{2} \\times mv_{0}^{2}$ to estimate the typical energy gained by an object of mass $m$ falling into the gravity well of Earth.\n",
        "\n",
        "* To compute the motion of an asteroid in Earth’s atmosphere, the following equation of motion has to be solved (we still assume one-dimensional motion in radial direction):\n",
        "  > $h^{''} = - \\frac{GM_{E}}{(R_{E}+h)^2} + (\\frac{1}{2m} \\times p_{\\text{air}}(h)C_{D}Ah^2)$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $A$: $\\pi \\times R^2$ (cross section area)\n",
        "\n",
        "  **The asteroid experiences air resistance proportional to the square of its velocity (this law applies to fast-moving objects for which the air flowing around the object becomes turbulent). The asteroid is assumed to be spherical with radius $R$**.\n",
        "\n",
        "  **The drag coefficient for a spherical body is $C_{D} = 0.5$**.\n",
        "\n",
        "  The dependence of the density of Earth’s atmosphere on altitude can be approximated by the barometric height formula:\n",
        "  > $p_{\\text{air}}(h) = 1.3 \\times \\exp(\\frac{-h}{8.4})$\n",
        "\n",
        "  More generally, the barometric height formula is given by:\n",
        "\n",
        "  > $P(h) = P_0 \\left(1 - \\frac{L \\cdot h}{T_0}\\right)^{\\frac{g \\cdot M}{R \\cdot L}}$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $P(h)$: the pressure at altitude h\n",
        "\n",
        "  $P_{0}$: the pressure at sea level (standard atmospheric pressure)\n",
        "\n",
        "  $L$: the temperature lapse rate (rate of temperature decrease with altitude)\n",
        "\n",
        "  $T_{0}$: the standard temperature at sea level\n",
        "\n",
        "  $g$: the acceleration due to gravity\n",
        "\n",
        "  $M$: the molar mass of Earth's air\n",
        "\n",
        "  $R$: the universal gas constant\n",
        "\n",
        "  **The most widely used value is based on the International System of Units (SI), where the universal gas constant is approximately:** $R \\approx 8.314 \\, \\text{J/(mol·K)}$"
      ],
      "metadata": {
        "id": "V8KKUsX6F3tF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        "!pip install numkit"
      ],
      "metadata": {
        "id": "tKyqkQ9Knhd3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "VzVfmvWXFnqU"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import astropy.units as unit\n",
        "from astropy.constants import G,M_earth,R_earth\n",
        "%matplotlib inline\n",
        "plt.style.use(\"dark_background\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"Earth Radius: {R_earth}\")\n",
        "print(f\"Earth Mass: {M_earth}\")\n",
        "print(f\"Gravitational Constant: {G}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "afgQDBaqL81y",
        "outputId": "484dfac4-da78-4fbd-c575-d31590a5c2c8"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Earth Radius: 6378100.0 m\n",
            "Earth Mass: 5.972167867791379e+24 kg\n",
            "Gravitational Constant: 6.6743e-11 m3 / (kg s2)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# asteroid parameters\n",
        "asteroidRadius = 34*unit.m # radius\n",
        "asteroidVolume = (4*np.pi/3)*asteroidRadius**3 # volume\n",
        "asteroidDensity = 2.2e3*unit.kg/unit.m**3 # density\n",
        "asteroidMass = asteroidDensity*asteroidVolume # mass"
      ],
      "metadata": {
        "id": "rcopIcoUMEN3"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "h0 = 300*unit.km # we choose 300 km, the internal space station (ISS) orbits Earth 400 km above ground\n",
        "v0 = np.sqrt(2*G*M_earth/(R_earth+h0))\n",
        "print(f\"Infall Velocity: {v0}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3vIadg1wMn5m",
        "outputId": "010e9b1c-950c-45e2-8bb1-9c3c81f953d1"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Infall Velocity: 10925.90459431552 m / s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def RadialFall(timeEnd:int,initialHeight:int or float)->tuple:\n",
        "  g = 9.81  # Acceleration due to gravity in m/s^2\n",
        "  timeInterval = np.linspace(0,timeEnd,1000) # time points\n",
        "  height = initialHeight-0.5*g*timeInterval**2\n",
        "  return timeInterval,height"
      ],
      "metadata": {
        "id": "5EkZaH6oNBzI"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "timeEnd = 10 # seconds\n",
        "initialHeight = 100 # meters"
      ],
      "metadata": {
        "id": "Zc9vam23mDZQ"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "timePoints,height = RadialFall(timeEnd,initialHeight)"
      ],
      "metadata": {
        "id": "YUIZLnZamG8r"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10,5))\n",
        "plt.title(\"Radial Fall Simulation\")\n",
        "plt.plot(timePoints,height,label=\"Radial Fall\")\n",
        "plt.xlabel(\"Time (sec)\")\n",
        "plt.ylabel(\"Height (m)\")\n",
        "plt.axhline(0,color=\"red\",linestyle=\"--\",label=\"Ground Level\")\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        },
        "id": "tPcrW6rDmOmP",
        "outputId": "d57a9609-f017-4fff-b9f0-143b531c9e8b"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def AtmosphericPressureAtAltitude(altitude:int or float)->int or float:\n",
        "  p0 = 101325.0  # Standard atmospheric pressure at sea level in Pascals\n",
        "  L = 0.0065  # Temperature lapse rate in K/m\n",
        "  t0 = 288.15  # Standard temperature at sea level in Kelvin\n",
        "  g = 9.80665  # Acceleration due to gravity in m/s^2\n",
        "  M = 0.0289644  # Molar mass of Earth's air in kg/mol\n",
        "  R = 8.31447  # Universal gas constant in J/(mol·K)\n",
        "  pressure = p0*(1-(L*altitude)/t0)**(g*M/(R*L)) # Barometric height formula\n",
        "  return pressure"
      ],
      "metadata": {
        "id": "GYZiHGOlmgwV"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "altitude = 5000 # meters"
      ],
      "metadata": {
        "id": "CEsBnndem9iC"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "pressure = AtmosphericPressureAtAltitude(altitude)\n",
        "print(f\"At altitude 5000 meters, atmospheric pressure is approximately {pressure:.2f} Pascals.\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BVSUcS3jnJLm",
        "outputId": "1422fa40-189e-4584-8028-1b9e75a3093c"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "At altitude 5000 meters, atmospheric pressure is approximately 54020.53 Pascals.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* The Runge-Kutta method is a numerical integration technique used for solving ordinary differential equations (ODEs), and it's commonly implemented in various programming libraries. We need to express the second derivative, $h^{''}$, as function of $t$, $h$ and $h^{'}$."
      ],
      "metadata": {
        "id": "nQcucnoBn5Za"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.integrate import odeint"
      ],
      "metadata": {
        "id": "hR-hgmDLnfrN"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "dragCoeff = 0.5 # drag coefficient"
      ],
      "metadata": {
        "id": "RaXt6sHIoUDU"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# asteroid parameters\n",
        "asteroidRadius = 34*unit.m # radius\n",
        "asteroidVolume = (4*np.pi/3)*asteroidRadius**3 # volume\n",
        "asteroidDensity = 2.2e3*unit.kg/unit.m**3 # density\n",
        "asteroidMass = asteroidDensity*asteroidVolume # mass\n",
        "h0 = 300*unit.km # we choose 300 km, the internal space station (ISS) orbits Earth 400 km above ground\n",
        "v0 = np.sqrt(2*G*M_earth/(R_earth+h0))\n",
        "print(f\"Infall Velocity: {v0}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2VShFgd0piDM",
        "outputId": "dda86fe1-a542-4231-895e-0c2278ebefe4"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Infall Velocity: 10925.90459431552 m / s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# barometric height formula\n",
        "def BarometricHeightFormula(height:int or float)->int or float:\n",
        "  return 1.3*np.exp(-height/4.8e3)"
      ],
      "metadata": {
        "id": "G_kKzrbKocLY"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        " # acceleration of the asteroid\n",
        " def AccelerationAsteroid(time:int,height:int or float,hFirstIntegrate:int or float,mass:int or float,radius:int or float)->int or float:\n",
        "  airResistance = 0.5*BarometricHeightFormula(height)*dragCoeff*np.pi*radius**2*hFirstIntegrate**2\n",
        "  gravityAtHeight = G.value*M_earth.value/(R_earth.value+height)**2\n",
        "  return -gravityAtHeight+airResistance/mass"
      ],
      "metadata": {
        "id": "QHDygq4dolZ3"
      },
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# initial data\n",
        "data = [[0,h0.to(unit.m).value,-v0.value]]\n",
        "print(f\"Initial Data:\\n{data}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wqU7CohapTcS",
        "outputId": "7dc8f18d-3c8b-4b8b-982e-bfff4d1bd01d"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial Data:\n",
            "[[0, 300000.0, -10925.90459431552]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# initialization of loop variables\n",
        "time,height,hFirst = tuple(data[0])"
      ],
      "metadata": {
        "id": "_7rJ9N9spsLd"
      },
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "initialAccelerationAsteroid = AccelerationAsteroid(\n",
        "    time=time,\n",
        "    height=height,\n",
        "    hFirstIntegrate=hFirst,\n",
        "    mass=asteroidMass.value,\n",
        "    radius=asteroidRadius.value\n",
        "    )"
      ],
      "metadata": {
        "id": "7t6bWkScrzuV"
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Initial acceleration = {:.2f} m/s^2\".format(initialAccelerationAsteroid))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QxiQXS8dp8kZ",
        "outputId": "3182d556-26f3-4ed8-a2b9-7d1182baaacf"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial acceleration = -8.94 m/s^2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        " # acceleration of the asteroid\n",
        " def AccelerationAsteroidReturnIntegrate(time:int,state:list,mass:int or float,radius:int or float)->int or float:\n",
        "  height = 300000.0\n",
        "  hFirstIntegrate = -10925.90459431552\n",
        "  airResistance = 0.5*BarometricHeightFormula(height)*dragCoeff*np.pi*radius**2*hFirstIntegrate**2\n",
        "  gravityAtHeight = G.value*M_earth.value/(R_earth.value+height)**2\n",
        "  hSecondIntegrate = -gravityAtHeight+airResistance/mass # acceleration\n",
        "  return [hFirstIntegrate,hSecondIntegrate]"
      ],
      "metadata": {
        "id": "AVeblM2Uuqu6"
      },
      "execution_count": 78,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "timePoints = np.linspace(0,1000,100)"
      ],
      "metadata": {
        "id": "Y7V55kdIu5js"
      },
      "execution_count": 79,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "initialConditions = [height,hFirst]\n",
        "print(f\"Initial Conditions: {initialConditions}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "exs65083ss8F",
        "outputId": "a1f89088-56eb-4466-9f15-c989921f5cd7"
      },
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial Conditions: [300000.0, -10925.90459431552]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "solution = odeint(\n",
        "    AccelerationAsteroidReturnIntegrate,\n",
        "    y0=initialConditions,\n",
        "    t=timePoints,\n",
        "    args=(asteroidMass.value,asteroidRadius.value)\n",
        ")"
      ],
      "metadata": {
        "id": "nmAkcnW9vFeW"
      },
      "execution_count": 81,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Access results\n",
        "heightValues,hFirstIntegrateValues = solution[:,0],solution[:,1]"
      ],
      "metadata": {
        "id": "3HM9YgKKvjfa"
      },
      "execution_count": 83,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(timePoints,heightValues,label='Height')\n",
        "plt.title('Radial Fall Simulation')\n",
        "plt.xlabel('Time (seconds)')\n",
        "plt.ylabel('Height (meters)')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "aFM9zYIhwTtz",
        "outputId": "6486b19c-3adf-4b6c-d25f-df5bce713e94"
      },
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(timePoints,hFirstIntegrateValues,label='Velocity')\n",
        "plt.title('Radial Fall Simulation')\n",
        "plt.xlabel('Time (seconds)')\n",
        "plt.ylabel('Velocity (m/s)')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "nirCLqxYwlSL",
        "outputId": "45098a2d-c4ab-425d-8736-d228d7a52241"
      },
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "wQES4SJIyPkk"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}