Spherical_Astronomy.ipynb

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      "name": "python"
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  "cells": [
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      "cell_type": "markdown",
      "source": [
        "# Spherical Astronomy\n",
        "\n",
        " * In astronomy, the positions of stars are specified by directions on the sky, i.e. two angular coordinates. The radial distance of the star from Earth would be the third coordinate, but distances are not known for all astronomical objects.\n",
        " * As long as distances do not matter, all astronomical objects can be projected in radial directions onto a sphere with Earth at its center (the size of the sphere does not matter, but you can think of it as a distant spherical surface). This is the so-called celestial sphere.\n",
        " * For an observer on Earth, the position of astronomical objects depends on geo-graphical latitude and longitude and varies with the time of day.\n",
        " * To specify positions independent of the observer, angular coordinates with respect to fixed reference directions are used. In the equatorial coordinate system, one reference direction is given by Earth’s rotation axis (or, equivalently, the orientation of the equatorial plane). The orientation of the rotation axis is fixed because of angular momentum conservation.\n",
        " * The angular distance of a star from the equatorial plane is called **declination (dec)** and denoted by $\\delta$. Declination is one of the two coordinates of the equatorial coordinate system. It is analogous to latitude on the Earth's surface, measuring the angular distance of an object north or south of the celestial equator.The other reference direction is defined by the intersection between the equatorial plane and the plane of Earth’s orbital motion around the Sun. The fixed orientation of the orbital plane, which is called ecliptic, is also a consequence of angular momentum conservation (in this case the angular momentum of orbital motion). The second coordinate in the equatorial system, which is called **right ascension (RA)** and its symbol is $\\alpha$. It is analogous to longitude on Earth, measuring the angular distance of an object eastward along the celestial equator, is the angle measured from one of the two points where the celestial sphere is pierced by the line of intersection of the equatorial an orbital planes. The zero point for the right ascension is known as **vernal equinox**, the opposite point as **autumnal equinox**."
      ],
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        "## Declination of the Sun\n",
        "\n",
        "* While the declination of stars is constant, the position of the Sun changes in the equatorial system over the period of a year.\n",
        "* This is a consequence of the inclination of Earth’s rotation axis with respect to the direction perpendicular to the ecliptic, which is equal to $\\epsilon_{0} = 23.44^\\circ$. The obliquity of the ecliptic ($\\epsilon$) is the term used in astronomy for the angle between the plane of the Earth's orbit and the plane of the Earth's equator.\n",
        "* The annual variation of the Sun's declination is a result of the Earth's axial tilt and its orbit around the Sun. The Sun's declination varies between $-23.44^\\circ$ and $+23.44^\\circ$ over the course of a year. This variation can be approximated by a sinusoidal function because the Earth's orbit is nearly circular and the axial tilt is relatively constant. The annual variation of the declination of the Sun is approximately given:\n",
        "> $\\delta_{SUN} = -23.44^\\circ \\times \\cos\\left(\\frac{360}{365} \\times (D + 10)\\right)$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $D$: the day of the year\n",
        "\n",
        "  $-23.44^\\circ$: minimum solar declination, which occurs at the solstices\n",
        "\n",
        "  or we can use this formula:\n",
        "\n",
        "  > $\\delta_{SUN} = -\\arcsin\\left(\\sin\\left(23.44^\\circ\\right) \\times \\cos\\left(\\frac{360}{365.24} \\times (N+10)\\right)\\right)$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $N$: the difference in days starting from 1st January, so the first day of the year corresponds to $N=0$ and the last day to $N=364$.\n",
        "\n",
        "  $\\frac{360}{365.24}$: the fraction equals the change in the angular position of Earth per day, assuming a circular orbit, this is just the angular velocity ($\\omega$) of Earth’s orbital motion around the Sun in units of degrees per day.\n",
        "* The Sun has zero declination at the equinoxes (intersection points of celestial equator and ecliptic).\n",
        "\n"
      ],
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      "cell_type": "code",
      "source": [
        "import math,numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "plt.style.use(\"dark_background\")"
      ],
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      "execution_count": 1,
      "outputs": []
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      "metadata": {
        "id": "ptsmlVQ1KXtP"
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      "outputs": [],
      "source": [
        "earthAxialTilt = 23.44"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def SunDeclinationFormula1(dayofyear:int)->int or float:\n",
        "  declination = -earthAxialTilt*math.sin(math.radians((360/365.24)*(dayofyear-81)))\n",
        "  return declination"
      ],
      "metadata": {
        "id": "xs_Vov6wX59Y"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# this formula should return a positive value, which is correct for the time near the summer solstice.\n",
        "def SunDeclinationFormula2(dayofyear:int)->int or float:\n",
        "  angularVelocity = 2*math.pi/365.24  # angular velocity in rad/day\n",
        "  obliquity = math.radians(earthAxialTilt)\n",
        "  declination = -math.asin(math.sin(obliquity)*math.cos(angularVelocity*(dayofyear+10)))\n",
        "  return math.degrees(declination)"
      ],
      "metadata": {
        "id": "sV-VVZ3AYf5z"
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      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "dayofyear = 171 # day of 1st solstice, around June 20th, close to the summer solstice\n",
        "declinationResult1 = SunDeclinationFormula1(dayofyear)\n",
        "declinationResult2 = SunDeclinationFormula2(dayofyear)\n",
        "print(f\"Declination Result-1: {declinationResult1}\")\n",
        "print(f\"Declination Result-2: {declinationResult2}\")"
      ],
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          "base_uri": "https://localhost:8080/"
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        "id": "jp2u6rgjY_Y1",
        "outputId": "c80ebf6f-7a8b-4687-f8bf-b8fc16793c97"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Declination Result-1: -23.434048110067284\n",
            "Declination Result-2: 23.43035418879223\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dayofyear = 2 # January 2nd.\n",
        "declinationResult1 = SunDeclinationFormula1(dayofyear)\n",
        "declinationResult2 = SunDeclinationFormula2(dayofyear)\n",
        "print(f\"Declination Result-1: {declinationResult1}\")\n",
        "print(f\"Declination Result-2: {declinationResult2}\")"
      ],
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        "colab": {
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      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Declination Result-1: 22.916371633940802\n",
            "Declination Result-2: -22.91360189235458\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# equinoxes and solstices in 2020\n",
        "equinoxesAndSolsticesin2022 = np.array([79,171,265,355])"
      ],
      "metadata": {
        "id": "Wr_3xKnDZ33D"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for day in equinoxesAndSolsticesin2022:\n",
        "  print(f\"Declination: {SunDeclinationFormula2(day)} for Day: {day}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pZyL2Z6gaQ2K",
        "outputId": "2eb38cb6-b43e-40df-879f-1166ce081a30"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Declination: -0.9055076998096332 for Day: 79\n",
            "Declination: 23.43035418879223 for Day: 171\n",
            "Declination: -0.4195073085061084 for Day: 265\n",
            "Declination: -23.439788273994935 for Day: 355\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "declinationValues = [SunDeclinationFormula2(day) for day in range(1,366)]"
      ],
      "metadata": {
        "id": "3s3wXu7dxp-8"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10,5))\n",
        "plt.plot(range(1,366),declinationValues,label=\"Sun Declination\")\n",
        "plt.xlabel(\"Days\")\n",
        "plt.ylabel(\"Sun Declination (degrees)\")\n",
        "plt.title(\"Sun Declination Over a Year\")\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "N0pH9BCkxycH",
        "outputId": "e86a8ad1-e54a-4c9b-eac1-8dc5473110b2"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Diurnal Arc\n",
        "\n",
        "* From the viewpoint of an observer on Earth, the apparent motion of an object on the celestial sphere follows an arc above the horizon, which is called **diurnal arc**. The time-dependent horizontal position of the object is measured by its hour angle $h$.\n",
        "*  For an observer at a given latitude on Earth, it's the angle through which a star (or any celestial object) appears to move above the horizon during the course of a night.\n",
        "* The formula for the diurnal arc depends on the declination of the celestial object ($\\delta$) and the latitude of the observer ($\\phi$).\n",
        "  > $\\cos(H) = \\frac{-\\sin(h) + \\sin(\\phi) \\sin(\\delta)}{\\cos(\\phi) \\cos(\\delta)}$\n",
        "\n",
        "  where:\n",
        "\n",
        "  $\\delta$: the declination of the object\n",
        "\n",
        "  $\\phi$: the latitude of the observer’s position on Earth\n",
        "\n",
        "  $H$: is the hour angle at either rising or setting of the celestial object\n",
        "\n",
        "  $h$: is the altitude of the celestial object at either rising or setting typically set to 0 for the object just on the horizon\n",
        "* An hour angle of $24^{h}$ corresponds to a full circle of $360^\\circ$ parallel to the celestial equator. This is because the celestial sphere appears to rotate $360^\\circ$ around the Earth in 24 hours, corresponding to the Earth's rotation period. For this reason, $h$ is can be equivalently expressed in degrees or radians. By definition the hour angle is zero when the object reaches the highest altitude above the horizon. The hour angle corresponding to the setting time, when the object just vanishes beneath the horizon is given by:\n",
        "  > $cos{h_{set}} = -tan{\\delta} \\times tan{\\phi}$\n",
        "  \n",
        "  where:\n",
        "\n",
        "  $\\delta$: the declination of the object\n",
        "\n",
        "  $\\phi$: the latitude of the observer’s position on Earth\n",
        "* One hour of time is equivalent to $15^\\circ$ of rotation ($\\frac{360^\\circ}{24} = 15^\\circ$)\n",
        "* As a consequence, the variable $T = 2 \\times h_{set}$ measures the so-called sidereal time for which the object is in principle visible on the sky (stars are of course outshined by the Sun during daytime)."
      ],
      "metadata": {
        "id": "57QW7Sdjt3Md"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        "!pip install astropy"
      ],
      "metadata": {
        "id": "ggVPVgEfthti"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from astropy.coordinates import SkyCoord,EarthLocation\n",
        "import astropy.units as u"
      ],
      "metadata": {
        "id": "pkGDjta2zTFI"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# For example, let us consider the star Betelgeuse in the constellation of Orion.\n",
        "# It is a red giant that is among the brightest stars on the sky.\n",
        "betelgeuse = SkyCoord.from_name(\"betelgeuse\")\n",
        "print(f\"Right Ascension of Betelgeuse:\\n{betelgeuse.ra}\")\n",
        "print(f\"Declination of Betelgeuse:\\n{betelgeuse.dec}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SY6AbCCEyyyZ",
        "outputId": "409df72a-1774-41b9-c0ee-dcbe0c06391e"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Right Ascension of Betelgeuse:\n",
            "88.792938991 deg\n",
            "Declination of Betelgeuse:\n",
            "7.407063995 deg\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Translate as degrees (d), arc minutes (m) and arc seconds (s)**:\n",
        "\n",
        "For example: 7.407063995\n",
        "\n",
        "* Degrees (d): 7 (since 7.407063995 has a whole number part of 7)\n",
        "* Arc Minutes (m):\n",
        "  - Decimal part is 0.407063995.\n",
        "  - Multiply this by 60: $0.407063995 \\times 60 = 24.4238397$\n",
        "  - The whole number part is 24 arc minutes.\n",
        "* Arc Seconds (s):\n",
        "  - The decimal part of arc minutes is approximately 0.4238397.\n",
        "  - Multiply this by 60: $0.4238397 \\times 60 = 25.43$\n",
        "  - Approximately 25.43 arc seconds.\n",
        "So, **7.407063995 degrees** can be expressed as **7 degrees,24 arc minutes,25.43 arc seconds**, or \"$07^\\circ$ $24^{'}$ $25^{''}$\"."
      ],
      "metadata": {
        "id": "OaEBIQyd05o0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# In addition to the star’s declination, we need the position of the observer.\n",
        "observerCoordinate = EarthLocation(\n",
        "    lat=53*u.deg+28*u.arcmin+49*u.arcsec,\n",
        "    lon=10*u.deg+14*u.arcmin+23*u.arcsec\n",
        ") # Hamburg Observatory\n",
        "print(f\"Observer Coordinate: {observerCoordinate}\")\n",
        "print(f\"Observer Latitude: {observerCoordinate.lat}\")\n",
        "print(f\"Observer Longitude: {observerCoordinate.lon}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rdxWXsQQz-5Q",
        "outputId": "fcbeefff-078d-459a-f512-ba961a9428d1"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Observer Coordinate: (3743272.38675498, 676200.50846503, 5102531.52113739) m\n",
            "Observer Latitude: 53.48027777777777 deg\n",
            "Observer Longitude: 10.239722222222222 deg\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def DiurnalArc(latitude:int or float,declination:int or float)->int or float:\n",
        "  \"\"\"\n",
        "    Calculate the diurnal arc for a given latitude and declination.\n",
        "\n",
        "    Parameters:\n",
        "    latitude (float): The observer's latitude in degrees.\n",
        "    declination (float): The declination of the celestial object in degrees.\n",
        "\n",
        "    Returns:\n",
        "    float: The diurnal arc in degrees, or None if the object never rises or sets.\n",
        "  \"\"\"\n",
        "  # Convert latitude and declination to radians\n",
        "  latRad = math.radians(latitude)\n",
        "  decRad = math.radians(declination)\n",
        "  try:\n",
        "    cosH = (-math.sin(0)+math.sin(latRad)*math.sin(decRad))/(math.cos(latRad)*math.cos(decRad))\n",
        "    # If cos_h is outside the range -1 to 1, the object never rises or sets\n",
        "    if (cosH < -1) or (cosH > 1):\n",
        "      return None\n",
        "    # Calculate the hour angle in degrees\n",
        "    Hvalue = math.degrees(math.acos(cosH))\n",
        "    # The diurnal arc is twice the hour angle (from rising to setting)\n",
        "    return 2*Hvalue\n",
        "  except ValueError:\n",
        "    # This occurs if the math.acos() function receives an input outside its domain [-1, 1]\n",
        "    # Which means the object is circumpolar (always above the horizon) or never rises\n",
        "    raise None"
      ],
      "metadata": {
        "id": "c6hCY1w-2wEv"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def HourAngleAtSet(latitude:int or float,declination:int or float)->int or float:\n",
        "  \"\"\"\n",
        "    Calculate the hour angle at the setting time of a celestial object.\n",
        "\n",
        "    Parameters:\n",
        "    latitude (float): The observer's latitude in degrees.\n",
        "    declination (float): The declination of the celestial object in degrees.\n",
        "\n",
        "    Returns:\n",
        "    float: The hour angle at set time in degrees, or None if the object doesn't set.\n",
        "  \"\"\"\n",
        "  # Convert latitude and declination to radians\n",
        "  latRad = math.radians(latitude)\n",
        "  decRad = math.radians(declination)\n",
        "  try:\n",
        "    tanDec = math.tan(decRad)\n",
        "    tanLat = math.tan(latRad)\n",
        "    cosHSet = -tanDec*tanLat\n",
        "    # If cos_h_set is outside the range -1 to 1, the object never sets\n",
        "    if cosHSet < -1 or cosHSet > 1:\n",
        "      return None\n",
        "    # Calculate the hour angle in degrees\n",
        "    hSet = math.degrees(math.acos(cosHSet))\n",
        "    return hSet\n",
        "  except ValueError:\n",
        "    # This occurs if the math.acos() function receives an input outside its domain [-1, 1]\n",
        "    # Which means the object is circumpolar (always above the horizon) or never sets\n",
        "    return None"
      ],
      "metadata": {
        "id": "Z_W8IrT74a8K"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "h = math.acos(-math.tan(betelgeuse.dec.radian) * math.tan(observerCoordinate.lat.radian))\n",
        "print(h)\n",
        "T = (math.degrees(2*h)/360)*u.sday\n",
        "print(\"T = {:.2f}\".format(T.to(u.h)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rpZkzCvWAhtl",
        "outputId": "a2130d75-bdcb-4fa1-a41b-91b49090dc32"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.7472730763094302\n",
            "T = 13.31 h\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def DegreeToHour(degree:int or float)->int or float:\n",
        "  \"\"\"\n",
        "    Convert degrees to hours.\n",
        "\n",
        "    Parameters:\n",
        "    degrees (float): Angle in degrees.\n",
        "\n",
        "    Returns:\n",
        "    float: Equivalent angle in hours.\n",
        "  \"\"\"\n",
        "  return degree/15"
      ],
      "metadata": {
        "id": "LM_w0sxX79QL"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "decBetelgeuse = betelgeuse.dec.to_value() #delta\n",
        "latObserver = observerCoordinate.lat.to_value() #phi\n",
        "hSet = HourAngleAtSet(latitude=latObserver,declination=decBetelgeuse)\n",
        "dArc = DiurnalArc(latitude=latObserver,declination=decBetelgeuse)\n",
        "print(f\"Hour Angle in Degree for Betelgeuse on Hamburg Observatory: {hSet} deg or Hour: {DegreeToHour(hSet*2)} h\")\n",
        "print(f\"Diurnal-Arc for Betelgeuse on Hamburg Observatory: {dArc} deg or Hour: {DegreeToHour(dArc*2)} h\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yMTul3Hs6DCz",
        "outputId": "1ac824b0-bf96-4cba-a837-9476a5d526c5"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Hour Angle in Degree for Betelgeuse on Hamburg Observatory: 100.11137292937018 deg or Hour: 13.348183057249356 h\n",
            "Diurnal-Arc for Betelgeuse on Hamburg Observatory: 159.77725414125965 deg or Hour: 21.303633885501288 h\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def HourAngleOtherMethod(latitude:u,declination:u)->int or float:\n",
        "  hSet = math.acos(-math.tan(declination.radian)*math.tan(latitude.radian))\n",
        "  # By doubling this angle, you effectively calculate the total angular distance the object travels in the sky from rising to setting\n",
        "  degreeHSet = (math.degrees(2*hSet)/360)*u.sday # in sidereal days, calculates the time duration (in hours) that the object is above the horizon\n",
        "  return degreeHSet.to(u.h) # hour"
      ],
      "metadata": {
        "id": "F4BAjicwGK8B"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "hSet = HourAngleOtherMethod(latitude=observerCoordinate.lat,declination=betelgeuse.dec)\n",
        "print(f\"Betelgeuse could be seen : {hSet} at the Observatory\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hTAJIg5U61O0",
        "outputId": "6b3417b1-e51a-4ae5-b118-9638a93d9848"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Betelgeuse could be seen : 13.311736728655621 h at the Observatory\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**if it were not for the Sun, Betelgeuse could be seen 13 h at the Observatory**"
      ],
      "metadata": {
        "id": "2_69HY-Z8nx7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Day Length Example"
      ],
      "metadata": {
        "id": "Yjyo17C1IGSp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "days = np.arange(365)\n",
        "angularVelocityofEarth = 2*math.pi/365.24\n",
        "obliquity = math.radians(23.44)\n",
        "declinationsOfSun = -np.arcsin(math.sin(obliquity)*np.cos(angularVelocityofEarth*(days+10))) # delta, declination of the Sun for all days of the year"
      ],
      "metadata": {
        "id": "8R-rxyS6HHVD"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "dayLengths = np.arccos(-np.tan(declinationsOfSun)*math.tan(observerCoordinate.lat.radian)) # depends on Hamburg Observatory\n",
        "hSets = (np.degrees(2*dayLengths)/360)*u.sday.to(u.h)"
      ],
      "metadata": {
        "id": "6jcy0wKCInsL"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10,5))\n",
        "plt.plot(days,hSets)\n",
        "plt.title(\"Day Length\")\n",
        "plt.xlabel(\"Days\")\n",
        "plt.ylabel(\"Day Length [hr]\")\n",
        "plt.grid(True)\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "6S25IxRiJFmU",
        "outputId": "56747966-aae7-40ce-a9c2-63651fae346b"
      },
      "execution_count": 24,
      "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": [
        "print(f\"Minimum Day Length: {hSets.min()} hours\")\n",
        "print(f\"Maximum Day Length: {hSets.max()} hours\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "coRTYcmUJl5H",
        "outputId": "3d1ceda7-b821-47ff-f766-a2c112a93723"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Minimum Day Length: 7.201786110785734 hours\n",
            "Maximum Day Length: 16.732599523096972 hours\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**The difference between minimal and maximal day length increases with latitude**"
      ],
      "metadata": {
        "id": "nX9onLcoJ5eC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "that the range of the declination of the\n",
        "Sun is: $-\\epsilon_{0} \\leq \\delta_{SUN} \\leq \\epsilon_{0}$,\n",
        "\n",
        "this corresponds to the polar night or polar day during which the Sun never rises or sets"
      ],
      "metadata": {
        "id": "p2hNEXxdKG1M"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "newyorkCoordinateLat = 40+43/60 # deg\n",
        "bangkokCoordinateLat = 13+45/60 # deg\n",
        "ankaraCoordinateLat = 39+56/60 # deg"
      ],
      "metadata": {
        "id": "b6YMH0hIJyxf"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "coordinates = {\"NewYork\":math.radians(newyorkCoordinateLat),\n",
        "               \"Bangkok\": math.radians(bangkokCoordinateLat),\n",
        "               \"Ankara\":math.radians(ankaraCoordinateLat)}"
      ],
      "metadata": {
        "id": "W39KID9-LTUA"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "coordinates[\"Hamburg\"] = observerCoordinate.lat.radian"
      ],
      "metadata": {
        "id": "cSYih1QCNBB8"
      },
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for city,coorLat in coordinates.items():\n",
        "  print(f\"Degree of {city} is {math.degrees(coorLat)} deg - As radian: {coorLat} rad\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NGEJ_HoZLtTu",
        "outputId": "80c01d15-7688-4b6c-acfd-d191920a20bc"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Degree of NewYork is 40.71666666666667 deg - As radian: 0.7106398937703579 rad\n",
            "Degree of Bangkok is 13.75 deg - As radian: 0.2399827721492203 rad\n",
            "Degree of Ankara is 39.93333333333333 deg - As radian: 0.6969681479630688 rad\n",
            "Degree of Hamburg is 53.48027777777777 deg - As radian: 0.9334069321033784 rad\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10,5))\n",
        "for city,coorLat in coordinates.items():\n",
        "  hSets = np.arccos(np.clip(-np.tan(declinationsOfSun)*math.tan(coorLat),-1.0,1.0))\n",
        "  dayLengths = (np.degrees(2*hSets/360))*u.sday.to(u.h)\n",
        "  plt.plot(days,dayLengths,label=city)\n",
        "plt.xlabel(\"Days\")\n",
        "plt.ylabel(\"Day Length [hr]\")\n",
        "plt.xlim(0,364)\n",
        "plt.ylim(0,24)\n",
        "plt.legend(loc=\"upper right\")\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "F_sdVqhzMBvn",
        "outputId": "37bf5246-e2ac-4f26-8a9b-dab02f8b9f35"
      },
      "execution_count": 30,
      "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": [
        "**in Bangkok, which is in the tropics, experience a day length around 12 h over the whole year**"
      ],
      "metadata": {
        "id": "q4RjzDmxNTfy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Observation of Celestial Objects\n",
        "\n",
        "* While it is important to be able to specify the positions of celestial objects in a coordinate system that is independent of time and the observer’s location, at the end of the day you want to know where on the sky you can find the object. To that end, the so-called horizontal coordinate system is used, which is based on an imaginary plane that is oriented tangential to the surface of Earth at the location of the observer.\n",
        "* The angular position measured in normal direction from the horizon is the **altitude** $a$ and the angular separation from some reference direction (usually, the North direction) parallel to the horizon is the **azimuth** of the object. Azimuth is a common term in astronomy and navigation that refers to the angle between the direction of a celestial object and the direction of north, measured along the horizon. The azimuth measured from North corresponds to the compass direction. This is why the horizontal system also goes under the name of **alt-azimuth system**.\n",
        "* Imagine you are standing outside and looking at the sky. If you look directly towards the north, the azimuth of the point on the horizon you're looking at is 0 degrees. If you turn to your right and face east, you're now looking at a point on the horizon with an azimuth of 90 degrees. If you continue turning to face south, the azimuth is 180 degrees, and if you face west, it's 270 degrees. For instance, if you're observing the Sun at a certain time and location, and it's located due south from your position, it would have an azimuth of approximately 180 degrees. If it's rising and you're facing it, its azimuth is approximately 90 degrees (east)."
      ],
      "metadata": {
        "id": "Yp5e_6ujNaTx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import astropy.units as u\n",
        "from astropy.coordinates import SkyCoord,EarthLocation,AltAz,get_sun\n",
        "from astropy.time import Time # By default, sets the coordinated universal time (UTC).\n",
        "import numpy as np"
      ],
      "metadata": {
        "id": "QBT2rr3kM9mL"
      },
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "observerLocation = EarthLocation(\n",
        "    lat=53*u.deg+28*u.arcmin+49*u.arcsec,\n",
        "    lon=10*u.deg+14*u.arcmin+23*u.arcsec\n",
        ")"
      ],
      "metadata": {
        "id": "p9RlQUWaV0Iv"
      },
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "observerLat = observerLocation.lat # phi\n",
        "observerLon = observerLocation.lon\n",
        "print(f\"Observer Latitude: {observerLat}\")\n",
        "print(f\"Observer Longitude: {observerLon}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7QvPoSfbWDZp",
        "outputId": "89f28008-d3e9-4d64-f651-51829e49aa93"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Observer Latitude: 53.48027777777777 deg\n",
            "Observer Longitude: 10.239722222222222 deg\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# CEST stands for Central European Summer Time.\n",
        "utcShift = 2*u.hour # CEST time zone (+2h)\n",
        "noonCEST = Time(\"2020-07-31 12:00:00\")-utcShift\n",
        "print(f\"Noon Time for CEST: {noonCEST}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tAgMcq-1WOvG",
        "outputId": "e31846ad-c37b-42c1-af1d-bfef30f1bcb1"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Noon Time for CEST: 2020-07-31 10:00:00.000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Since altitude and azimuth are time dependent, we need to create a sequence of frames covering a whole day\n",
        "# The coordinated universal time (UTC) is an international standard for time.\n",
        "elapsed = np.arange(0,24*60,5)*u.min\n",
        "time = noonCEST+elapsed"
      ],
      "metadata": {
        "id": "obOosKAKWplz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# sequence of horizontal frames\n",
        "frameLocal24h = AltAz(obstime=time,location=observerLocation)"
      ],
      "metadata": {
        "id": "l0xAj8LVXM2Y"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "aldebaran = SkyCoord.from_name(\"aldebaran\")"
      ],
      "metadata": {
        "id": "KLDFxmE0YCeZ"
      },
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "decAldebaran = aldebaran.dec\n",
        "raAldebaran = aldebaran.ra\n",
        "print(f\"Declination of Aldebaran: {decAldebaran}\")\n",
        "print(f\"Right Ascension of Aldebara: {raAldebaran}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ddv2JTXGYcA5",
        "outputId": "764a2a44-a009-4a2a-a12a-021cc4c984c5"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Declination of Aldebaran: 16.509302351 deg\n",
            "Right Ascension of Aldebara: 68.98016279 deg\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# turns the declination and right ascension of the star into altitudes and azimuths for the time sequence of frames\n",
        "# Modern telescopes are controlled by software, making it relatively easy for the observer to direct a telescope to a specific celestial object\n",
        "aldebaranLocal = aldebaran.transform_to(frameLocal24h)"
      ],
      "metadata": {
        "id": "pU6b6JchYkQ9"
      },
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# time-dependent coordinates of the Sun in equatorial system\n",
        "sun = get_sun(time)\n",
        "sunLocal = sun.transform_to(frameLocal24h)"
      ],
      "metadata": {
        "id": "szPvHy1GZTKx"
      },
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "elapsedNight = elapsed[np.where(sunLocal.alt<0)]\n",
        "aldebaranNight = aldebaranLocal.alt[np.where(sunLocal.alt<0)]"
      ],
      "metadata": {
        "id": "sqS7IDSgbDoA"
      },
      "execution_count": 53,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(10,5))\n",
        "plt.title(\"Aldebaran-Time\")\n",
        "plt.plot(elapsed.to(u.h),sunLocal.alt,color=\"orange\",label=\"Sun\")\n",
        "plt.plot(elapsed.to(u.h),aldebaranLocal.alt,color=\"green\",label=\"Aldebaran (DayLight)\",linestyle=\":\")\n",
        "plt.plot(elapsedNight.to(u.h),aldebaranNight,color=\"red\",label=\"Aldebaran (Night)\",linestyle=\"--\")\n",
        "plt.xlabel(\"Time From Noon [h]\")\n",
        "plt.ylabel(\"Altitude [deg]\")\n",
        "plt.xlim(0,24)\n",
        "plt.ylim(0,60)\n",
        "plt.xticks(np.arange(13)*2)\n",
        "plt.legend(loc=\"upper center\")\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "EMuCZPZ2Zr11",
        "outputId": "3b40c24c-a6fc-4696-83a4-f4dbcb779c7d"
      },
      "execution_count": 57,
      "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": [
        "**Since objects with negative altitude are invisible for the observer, only positive values are shown**"
      ],
      "metadata": {
        "id": "I2ybDzS-bgCM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def CalculateAltAz(observerLocation:tuple,objectCoordinate:tuple,observationTime:str)->tuple:\n",
        "  location = EarthLocation(\n",
        "      lat=observerLocation[0]*u.deg,\n",
        "      lon = observerLocation[1]*u.deg\n",
        "  )\n",
        "  time = Time(observationTime)\n",
        "  skyCoord = SkyCoord(\n",
        "      ra=objectCoordinate[0]*u.deg,\n",
        "      dec=objectCoordinate[1]*u.deg,\n",
        "      frame=\"icrs\"\n",
        "  )\n",
        "  altAz = AltAz(obstime=time,location=location)\n",
        "  altAzCoordinate = skyCoord.transform_to(altAz)\n",
        "  altitude = altAzCoordinate.alt.deg # degree\n",
        "  azimuth = altAzCoordinate.az.deg # degree\n",
        "  return (altitude,azimuth)"
      ],
      "metadata": {
        "id": "vk4ytsm8bHTA"
      },
      "execution_count": 63,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "polarisCoordinate = SkyCoord.from_name(\"polaris\")\n",
        "print(f\"Polaris RA: {polarisCoordinate.ra}\")\n",
        "print(f\"Polaris DEC: {polarisCoordinate.dec}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9fb7P4Z2diSh",
        "outputId": "3a385a65-322a-47d7-a2a3-1c6ef97c8def"
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Polaris RA: 37.946143 deg\n",
            "Polaris DEC: 89.264138 deg\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "newyorkCoord = (40.7128,-74.0060)"
      ],
      "metadata": {
        "id": "pKTtjkaBd8Ns"
      },
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "observationTime = \"2023-12-09 12:00:00\""
      ],
      "metadata": {
        "id": "0Iixnx8eeQh_"
      },
      "execution_count": 61,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "altitude,azimuth = CalculateAltAz(observerLocation=newyorkCoord,\n",
        "                                  objectCoordinate=(polarisCoordinate.ra.to_value(),\n",
        "                                                    polarisCoordinate.dec.to_value()),\n",
        "                                  observationTime=observationTime)"
      ],
      "metadata": {
        "id": "8lRDMtDcdzPM"
      },
      "execution_count": 64,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"Altitude of Polaris for {observationTime}: {altitude} deg\")\n",
        "print(f\"Azimuth of Polaris for {observationTime}: {azimuth} deg\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bLU01gikeVfn",
        "outputId": "285e5f89-de8e-4e58-a3b2-131186f5c3b1"
      },
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Altitude of Polaris for 2023-12-09 12:00:00: 40.24138987130087 deg\n",
            "Azimuth of Polaris for 2023-12-09 12:00:00: 359.44648245374805 deg\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "C5GEiOYsesCz"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}