Kepler_Laws_Planetary_Motion.ipynb

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      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Kepler's Law\n",
        "\n",
        "* Kepler used the most accurate measurements of planetary positions available at that time. Although the differences were rather minute, Kepler concluded from his analysis that the planets move on elliptical orbits, where the Sun is located in one focal point (first law) and, in modern language, the area swept by the radial vector from the Sun to a planet is proportional to the elapsed time (second law).\n",
        "* Later Kepler found a relation between the semi-major axes (the line segment from the center through the focus to the perimeter of an ellipse) and the orbital periods, which today is known as Kepler’s third law. Isaac Newton found a theoretical explanation for Kepler’s laws of planetary motion by applying his universal law of gravity and angular momentum conservation.\n",
        "* The Keplerian period, or simply the \"orbital period,\" refers to the time it takes for a celestial body to complete one orbit around another body. This is typically applied to planets orbiting a star or moons orbiting a planet:\n",
        "  > $T = 2\\pi \\sqrt{\\frac{a^3}{GM}}$\n",
        "  \n",
        "  where:\n",
        "\n",
        "  $T$: the orbital period\n",
        "  \n",
        "  $a$: the semi-major axis of the orbit\n",
        "\n",
        "  $G$: is the gravitational constant\n",
        "\n",
        "  $M$: is the mass of the more massive body, typically a star or planet that the smaller object is orbiting\n",
        "\n",
        "* In a system where the two bodies have significant mass, such as a binary star system, you would use the combined mass of the two bodies:\n",
        "  > $T = 2\\pi \\sqrt{\\frac{a^3}{G(M_1 + M_2)}}$\n",
        "  \n",
        "  where:\n",
        "\n",
        "  $T$: the orbital period\n",
        "  \n",
        "  $a$: the semi-major axis of the orbit\n",
        "\n",
        "  $G$: is the gravitational constant\n",
        "\n",
        "  $M$: is the mass of the more massive body, typically a star or planet that the smaller object is orbiting\n",
        "\n",
        "* The general formulation for the period $P$ f a planet moving on an elliptical orbit around a star reads:\n",
        "  > $P^2 = \\frac{4 \\pi^2}{G(M + m)} \\times a^3$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $P$: period\n",
        "\n",
        "  $a$: the semi-major axis of the orbit\n",
        "  \n",
        "  $G$: the gravitational constant\n",
        "\n",
        "  $M$: the mass of the star\n",
        "\n",
        "  $m$: the mass of the planet"
      ],
      "metadata": {
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      }
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "id": "rNLB4gcCPYc6"
      },
      "outputs": [],
      "source": [
        "import math,numpy as np\n",
        "from scipy.constants import year,hour,au,G\n",
        "from astropy.constants import M_sun\n",
        "import matplotlib.pyplot as plt\n",
        "plt.style.use(\"dark_background\")\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"Gravitational Constant: {G}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ffN6Y-VeTMkH",
        "outputId": "cd51436e-cd5e-48ef-848c-bd349087b763"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gravitational Constant: 6.6743e-11\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "massSun = M_sun.value # mass of the Sun in kg\n",
        "print(f\"Mass of Sun: {massSun} kg\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3ZB3YrjESbDf",
        "outputId": "6c681afa-4ae3-415a-ca1e-e307e4954fac"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mass of Sun: 1.988409870698051e+30 kg\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# https://nssdc.gsfc.nasa.gov/planetary/factsheet/\n",
        "massPlanets = 1e24 * np.array([0.33011,4.8675,5.9723,0.64171,1898.19,568.34,86.813,102.413]) # in kg"
      ],
      "metadata": {
        "id": "vtntwnVCShhU"
      },
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "semiMajorPlanets = 1e9 * np.array([57.9,108.21,149.60,227.92,778.57,1433.53,2872.46,4495.06]) # in m"
      ],
      "metadata": {
        "id": "6cbco813S3rD"
      },
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# use Kepler’s third law to calculate period in s\n",
        "TTestMass = 2*math.pi*(G*massSun)**(-1/2)*semiMajorPlanets**(3/2)\n",
        "TTwoBody = 2*math.pi*(G*(massSun+massPlanets))**(-1/2)*semiMajorPlanets**(3/2)"
      ],
      "metadata": {
        "id": "P_RIIcvPTJ6v"
      },
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"PERIOD T[yr]  DEVIATION TEST MASS[hr]  DEVIATION RELATIVE[rel]\")\n",
        "for testValue,bodyValue in zip(TTestMass,TTwoBody):\n",
        "  dev = testValue-bodyValue\n",
        "  if dev>hour:\n",
        "    line = \"{0:6.2f}          {1:<7.1f}                   {2:.1e}\"\n",
        "  else:\n",
        "    line = \"{0:6.2f}          {1:7.4f}                    {2:.1e}\"\n",
        "  print(line.format(bodyValue/year,dev/hour,dev/testValue))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Pz7ObvSWTwyx",
        "outputId": "bb2a404b-daac-48c2-eb80-023bd1017630"
      },
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "PERIOD T[yr]  DEVIATION TEST MASS[hr]  DEVIATION RELATIVE[rel]\n",
            "  0.24           0.0002                    8.3e-08\n",
            "  0.62           0.0066                    1.2e-06\n",
            "  1.00           0.0132                    1.5e-06\n",
            "  1.88           0.0027                    1.6e-07\n",
            " 11.88          49.6                      4.8e-04\n",
            " 29.68          37.2                      1.4e-04\n",
            " 84.20          16.1                      2.2e-05\n",
            "164.82          37.2                      2.6e-05\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**The deviation from the test-mass approximation is larger for the outer planets (Jupiter,Saturn, Uranus, and Neptune), as they are much more massive than the inner planets (Mercury, Venus, Earth, and Mars)**\n",
        "\n",
        "**Nevertheless, the relative error of the orbital period is small.**"
      ],
      "metadata": {
        "id": "bvegy353VIcy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plotting the period in hr versus the semi-major axis in AU\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.title(\"Power Law - Kepler Law for Planets\")\n",
        "plt.loglog(semiMajorPlanets/au,TTestMass/year,\"white\",linestyle=\"--\",label=\"Primary Mass Test\")\n",
        "plt.loglog(semiMajorPlanets/au,TTwoBody/year,\"ro\",linestyle=\":\",label=\"Planets\")\n",
        "plt.legend(loc=\"lower right\")\n",
        "plt.xlabel(\"Semi-Major Axis [AU]\")\n",
        "plt.ylabel(\"Orbital Period [YEAR]\")\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        },
        "id": "AaE303n9X4Hj",
        "outputId": "0c3c2513-a0d2-454a-ec66-1f5edb978b6b"
      },
      "execution_count": 45,
      "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": [
        "\n"
      ],
      "metadata": {
        "id": "jHcuW4rvYZ2Z"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def KeplerPeriod(semiMajor:int,MassOne:int or float,MassTwo:int or float or None=None)->int or float:\n",
        "  \"\"\"\n",
        "    Calculate the orbital period using Kepler's third law.\n",
        "\n",
        "    Parameters:\n",
        "    semiMajor (float): Semi-major axis of the orbit (in astronomical units, AU).\n",
        "    MassOne (float): Mass of the primary body (in solar masses).\n",
        "    MassTwo (float, optional): Mass of the secondary body (in solar masses), if applicable.\n",
        "\n",
        "    Returns:\n",
        "    float: Orbital period (in years).\n",
        "  \"\"\"\n",
        "  # Gravitational constant in AU^3 / solar mass / year^2\n",
        "  gravitationalConstant = 39.47841760435743\n",
        "  # If M2 is given, use the combined mass of the two bodies\n",
        "  mass = MassOne if MassTwo is None else MassOne+MassTwo\n",
        "  # Calculate the orbital period using Kepler's third law\n",
        "  orbitalPeriod = 2*math.pi*math.sqrt(semiMajor**3/(gravitationalConstant*mass))\n",
        "  return orbitalPeriod"
      ],
      "metadata": {
        "id": "XixPQ3WsUVGM"
      },
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# with a semi-major axis of 1 AU (Earth's distance from the Sun)\n",
        "a = 1 # in AU\n",
        "massPrimary = 1 # mass of the Sun in solar masses\n",
        "# The function returns an orbital period of 1 year, which is expected for an Earth-like orbit around a Sun-like star.\n",
        "orbitalPeriod = KeplerPeriod(semiMajor=a,MassOne=massPrimary)\n",
        "print(f\"Orbital Period: {orbitalPeriod} year\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CnuO9f7EWP0C",
        "outputId": "709ad419-c3af-49fe-8f3d-aac4a82f5a6d"
      },
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Orbital Period: 1.0 year\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "semiMajorforNeptune = 30.1 # in AU\n",
        "mass = 1 # mass of the Sun in solar masses\n",
        "orbitalPeriodNeptune = KeplerPeriod(semiMajor=semiMajorforNeptune,MassOne=mass)\n",
        "print(f\"Orbital Period of Neptune: {orbitalPeriodNeptune} year\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jZbPztSdWqt8",
        "outputId": "983e08d3-37ca-4ccd-95c1-487e7c71a354"
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Orbital Period of Neptune: 165.13903536111624 year\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# the semi-major axis for each planet in astronomical units (au)\n",
        "semiMajors = {\n",
        "    \"Mercury\": 0.387,\n",
        "    \"Venus\": 0.723,\n",
        "    \"Earth\": 1.000,\n",
        "    \"Mars\": 1.524,\n",
        "    \"Jupiter\": 5.203,\n",
        "    \"Saturn\": 9.537,\n",
        "    \"Uranus\": 19.191,\n",
        "    \"Neptune\": 30.069\n",
        "}"
      ],
      "metadata": {
        "id": "TFe2XtRTXOr8"
      },
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "massSun = 1 # Mass of the Sun in solar masses\n",
        "gravitationalConstant = 39.47841760435743 # Gravitational constant in AU^3 / solar mass / year^2"
      ],
      "metadata": {
        "id": "sBQ2I8zRXog9"
      },
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the orbital periods using Kepler's third law\n",
        "orbitalPeriods = {planet:2*np.pi*np.sqrt(a**3/(gravitationalConstant*massSun)) for planet,a in semiMajors.items()}"
      ],
      "metadata": {
        "id": "Ay0BZZjFZhtT"
      },
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "arraySemiMajors = np.array(list(semiMajors.values()))\n",
        "arrayOrbitalPeriods = np.array(list(orbitalPeriods.values()))"
      ],
      "metadata": {
        "id": "Ai2IGIsIZxtM"
      },
      "execution_count": 52,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# The plot displays the relationship between the semi-major axis and orbital period for the planets in our solar system on a double-logarithmic scale.\n",
        "# The slope of the line in the double-logarithmic plot corresponds to the exponent 3/2 in Kepler's third law.\n",
        "plt.figure(figsize=(11,6))\n",
        "plt.title(\"Orbital Period vs. Semi-Major Axis of the Planets - Power/Log Law\")\n",
        "plt.loglog(arraySemiMajors,arrayOrbitalPeriods,\"o-\")\n",
        "# Create a linear fit to the log of the data to represent the power law\n",
        "coefficients = np.polyfit(\n",
        "    np.log(arraySemiMajors),\n",
        "    np.log(arrayOrbitalPeriods),\n",
        "    1\n",
        ")\n",
        "polynomial = np.poly1d(coefficients)\n",
        "periodsFit = np.exp(polynomial(np.log(arraySemiMajors)))\n",
        "plt.loglog(arraySemiMajors,periodsFit,label=f\"Slope (Exponent): {coefficients[0]:.2f}\")\n",
        "for planet,semiMajor in semiMajors.items():\n",
        "  plt.annotate(\n",
        "      planet,\n",
        "      (semiMajor,orbitalPeriods[planet]),\n",
        "      textcoords=\"offset points\",\n",
        "      xytext=(-10,10),\n",
        "      ha=\"center\"\n",
        "  )\n",
        "plt.xlabel(\"Semi-Major Axis (AU)\")\n",
        "plt.ylabel(\"Orbital Period (YEAR)\")\n",
        "plt.legend()\n",
        "plt.grid(True,which=\"both\",ls=\"--\")\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 527
        },
        "id": "dSzEB1gMZ_IF",
        "outputId": "30b93b7c-64cf-498b-b502-d171476cbe2a"
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1100x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Each point on the graph represents one of the planets, with their names annotated for clarity.**\n",
        "\n",
        "**The line through the points represents the best fit to the power law relationship, demonstrating how well Kepler's third law describes the motion of the planets.**"
      ],
      "metadata": {
        "id": "a1zDATxIcM6m"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Interval Example"
      ],
      "metadata": {
        "id": "Dsd-0KYqnj6d"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Calculate orbital periods for each semi-major axis\n",
        "orbital_periods = [kepler_period(a, M_star) for a in semi_major_axes]\n",
        "\n",
        "# Plot the results\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(semi_major_axes, orbital_periods)\n",
        "plt.xlabel('Semi-Major Axis (AU)')\n",
        "plt.ylabel('Orbital Period (years)')\n",
        "plt.title('Change in Orbital Period as a Secondary Body Moves Away from Its Star')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "LPVjd4k_nfdV"
      },
      "execution_count": 53,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "gravitationalConstant = 39.47841760435743  # gravitational constant in AU^3 / solar mass / year^2\n",
        "massStar = 1  # mass of the star in solar masses (assuming a star similar to our Sun)"
      ],
      "metadata": {
        "id": "xl4EXstaba0V"
      },
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def KeplerPeriod(semiMajor:int or float,massPrimarly:int or float)->int or float:\n",
        "  \"\"\"\n",
        "    Calculate the orbital period using Kepler's Third Law.\n",
        "\n",
        "    Parameters:\n",
        "    semiMajor (float): Semi-major axis of the orbit (in astronomical units, AU).\n",
        "    massPrimarly (float): Mass of the primary star (in solar masses).\n",
        "\n",
        "    Returns:\n",
        "    float: Orbital period (in years).\n",
        "  \"\"\"\n",
        "  return 2*np.pi*np.sqrt(semiMajor**3/(gravitationalConstant*massPrimarly))"
      ],
      "metadata": {
        "id": "_ALwMZj6nsp-"
      },
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "semiMajorAxes = np.linspace(0.1,50,500) # From 0.1 AU to 50 AU"
      ],
      "metadata": {
        "id": "5A9mGOdZoAev"
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "periodsList = [KeplerPeriod(ax,massStar) for ax in semiMajorAxes]"
      ],
      "metadata": {
        "id": "FC_Lq-d5od1k"
      },
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(12,7))\n",
        "plt.title(\"Change in Orbital Period as a Secondary Body Moves Away from Its Star\")\n",
        "plt.plot(semiMajorAxes,periodsList)\n",
        "plt.xlabel(\"Semi-Major Axis (AU)\")\n",
        "plt.ylabel(\"Orbital Period (years)\")\n",
        "plt.grid(True)\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 563
        },
        "id": "546nCI4SovTD",
        "outputId": "64bc65a3-facb-4998-ee88-ee743541df48"
      },
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x700 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def ModelOrbitalVariation(primaryMass:int or float,minSemiMajor:int or float,maxSemiMajor:int or float,countPoint:int)->tuple:\n",
        "  \"\"\"\n",
        "    Model how the orbital period of a secondary body changes as it moves away from its primary star.\n",
        "\n",
        "    Parameters:\n",
        "    primaryMass (float): Mass of the primary star (in solar masses).\n",
        "    minSemiMajor (float): Minimum semi-major axis to consider (in AU).\n",
        "    maxSemiMajor (float): Maximum semi-major axis to consider (in AU).\n",
        "    countPoint (int): Number of data points to model between the minimum and maximum semi-major axis.\n",
        "\n",
        "    Returns:\n",
        "    tuple: Tuple containing arrays of semi-major axes and corresponding orbital periods.\n",
        "  \"\"\"\n",
        "  semiMajors = np.linspace(minSemiMajor,maxSemiMajor,countPoint)\n",
        "  orbitalPeriods = KeplerPeriod(semiMajors,primaryMass)\n",
        "  return (semiMajors,orbitalPeriods)"
      ],
      "metadata": {
        "id": "bjmn0RVApAfD"
      },
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def VariationPlot(semiMajorAxs:list,orbitalPeriods:list):\n",
        "  \"\"\"\n",
        "    Plot the variation of the orbital period with the semi-major axis.\n",
        "\n",
        "    Parameters:\n",
        "    semiMajorAxs (array): Array of semi-major axes (in AU).\n",
        "    orbitalPeriods (array): Array of orbital periods (in years).\n",
        "  \"\"\"\n",
        "  plt.figure(figsize=(10,5))\n",
        "  plt.title(\"Orbital Period Variation with Semi-Major Axis\")\n",
        "  plt.plot(semiMajorAxs,orbitalPeriods)\n",
        "  plt.xlabel(\"Semi-Major Axis (AU)\")\n",
        "  plt.ylabel(\"Orbital Period (years)\")\n",
        "  plt.grid(True)\n",
        "  plt.show()"
      ],
      "metadata": {
        "id": "7lYuOgE2qQsY"
      },
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "primaryMass = 1 # Mass of the Sun in solar masses\n",
        "minSemiMajor = 0.1 # Starting at 0.1 AU\n",
        "maxSemiMajor = 100 # Going out to 100 AU\n",
        "modelInputs = 1000 # The resolution of the model"
      ],
      "metadata": {
        "id": "lKV2UOWTq6cn"
      },
      "execution_count": 61,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "semiMajors,periods = ModelOrbitalVariation(primaryMass,minSemiMajor,maxSemiMajor,modelInputs)"
      ],
      "metadata": {
        "id": "Sz4g3EjXrGUa"
      },
      "execution_count": 63,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "VariationPlot(semiMajorAxs=semiMajors,orbitalPeriods=periods)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "SMIFwiMxrQpZ",
        "outputId": "9078a980-d2b7-4512-efb5-f3e72087c148"
      },
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## PDS70"
      ],
      "metadata": {
        "id": "PMUkLVMYtK9J"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "gravitationalConstant = 39.47841760435743  # gravitational constant in AU^3 / solar mass / year^2\n",
        "massPDS70 = 0.76 # Mass of PDS 70 in solar masses"
      ],
      "metadata": {
        "id": "vp--sPawti1Y"
      },
      "execution_count": 65,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def KeplerThirdLawPDS70(semiMajor:int or float,starMass:int or float)->int or float:\n",
        "  \"\"\"\n",
        "    Apply Kepler's Third Law to calculate the orbital period for planets around PDS 70.\n",
        "\n",
        "    Parameters:\n",
        "    semiMajor (float): Semi-major axis of the planet's orbit (in AU).\n",
        "    starMass (float): Mass of the star PDS 70 (in solar masses).\n",
        "\n",
        "    Returns:\n",
        "    float: Orbital period (in years).\n",
        "  \"\"\"\n",
        "  return 2*np.pi*np.sqrt(semiMajor**3/(gravitationalConstant*starMass))"
      ],
      "metadata": {
        "id": "SGN9WjklrVwV"
      },
      "execution_count": 66,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "semiMajor70b = 20 # Semi-major axis of PDS 70 b in AU\n",
        "semiMajor70c = 34.5 # Semi-major axis of PDS 70 c in AU"
      ],
      "metadata": {
        "id": "1ZFQyAM8tprG"
      },
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "orbitalPeriod70b = KeplerThirdLawPDS70(semiMajor70b,massPDS70)\n",
        "orbitalPeriod70c = KeplerThirdLawPDS70(semiMajor70c,massPDS70)"
      ],
      "metadata": {
        "id": "XW0KPtOztyyv"
      },
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"Orbital Period of PDS70-b: {orbitalPeriod70b} Earth years.\")\n",
        "print(f\"Orbital Period of PDS70-c: {orbitalPeriod70c} Earth years.\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jiMKCjhlt_J5",
        "outputId": "8364e940-f499-4659-8a34-49001498b8c0"
      },
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Orbital Period of PDS70-b: 102.5978352085154 Earth years.\n",
            "Orbital Period of PDS70-c: 232.44587655261984 Earth years.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "-SGflJ_LuGza"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}