skycords (1).ipynb

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    {
     "data": {
      "text/plain": [
       "rad2sec (generic function with 2 methods)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
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    }
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   "source": [
    "using SkyCoords\n",
    "\"\"\"\n",
    "AstroCoordinate represents a point in the sky with flexible input units\n",
    "\"\"\"\n",
    "struct AstroCoordinate{T<:AbstractFloat}\n",
    "    coord::SkyCoords.ICRSCoords\n",
    "\n",
    "    function AstroCoordinate(ra::T, dec::T, units::Symbol=:radians) where T<:AbstractFloat\n",
    "        if units == :radians\n",
    "            new{T}(SkyCoords.ICRSCoords(ra, dec))\n",
    "        elseif units == :hours_degrees\n",
    "            new{T}(SkyCoords.ICRSCoords(ra * π/12.0, deg2rad(dec)))\n",
    "        elseif units == :degrees\n",
    "            new{T}(SkyCoords.ICRSCoords(deg2rad(ra), deg2rad(dec)))\n",
    "        else\n",
    "            throw(ArgumentError(\"units must be :radians, :hours_degrees, or :degrees\"))\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "\"\"\"\n",
    "    gcirc(units, ra1, dec1, ra2, dec2) -> angular_distance\n",
    "\n",
    "### Purpose ###\n",
    "\n",
    "Computes rigorous great circle arc distances using modern Julia astronomical coordinates.\n",
    "\n",
    "### Explanation ###\n",
    "\n",
    "Input positions can be specified in radians, sexagesimal right ascension and declination, \n",
    "or degrees. Uses SkyCoords.jl for precise astronomical calculations.\n",
    "\n",
    "### Arguments ###\n",
    "\n",
    "* `units`: integer, can be either 0, or 1, or 2. Describes units of inputs and output:\n",
    "    * 0: everything (input right ascensions and declinations, and output distance) \n",
    "         is radians\n",
    "    * 1: right ascensions are in decimal hours, declinations in decimal degrees,\n",
    "         output distance in arc seconds\n",
    "    * 2: right ascensions and declinations are in degrees, output distance in arc\n",
    "         seconds\n",
    "* `ra1`: right ascension or longitude of point 1\n",
    "* `dec1`: declination or latitude of point 1\n",
    "* `ra2`: right ascension or longitude of point 2\n",
    "* `dec2`: declination or latitude of point 2\n",
    "\n",
    "Both `ra1` and `dec1`, and `ra2` and `dec2` can be given as 2-tuples `(ra1, dec1)` \n",
    "and `(ra2, dec2)`.\n",
    "\n",
    "### Output ###\n",
    "\n",
    "Angular distance on the sky between points 1 and 2, as an `AbstractFloat`. See\n",
    "`units` argument above for the units.\n",
    "\n",
    "### Method ###\n",
    "\n",
    "Uses SkyCoords.jl's implementation of spherical geometry calculations, which provides\n",
    "high-precision results for astronomical coordinate transformations and distance\n",
    "measurements.\n",
    "\n",
    "### Examples ###\n",
    "\n",
    "```jldoctest\n",
    "julia> using AstroLib\n",
    "\n",
    "julia> gcirc(0, 120, -43, 175, +22)\n",
    "1.590442261600714\n",
    "\n",
    "julia> # Using tuple notation\n",
    "julia> gcirc(1, (12.0, -43.0), (15.0, 22.0))\n",
    "5823.795873591674  # Result in arcseconds\n",
    "\n",
    "julia> # Using \n",
    "\"\"\"\n",
    "function gcirc(units::Integer, ra1::T, dec1::T, ra2::T, dec2::T)::T where {T<:AbstractFloat}\n",
    "    units_sym = if units == 0\n",
    "        :radians\n",
    "    elseif units == 1\n",
    "        :hours_degrees\n",
    "    elseif units == 2\n",
    "        :degrees\n",
    "    else\n",
    "        throw(DomainError(units, \"units must be 0 (radians), 1 (hours, degrees) or 2 (degrees)\"))\n",
    "    end\n",
    "    \n",
    "    coord1 = AstroCoordinate(ra1, dec1, units_sym)\n",
    "    coord2 = AstroCoordinate(ra2, dec2, units_sym)\n",
    "    \n",
    "    distance = SkyCoords.separation(coord1.coord, coord2.coord)\n",
    "    \n",
    "    return units == 0 ? distance : rad2sec(distance)\n",
    "end\n",
    "\n",
    "# Type promotion for mixed Real inputs\n",
    "function gcirc(units::Integer, ra1::Real, dec1::Real, ra2::Real, dec2::Real)\n",
    "    T = promote_type(float(typeof(ra1)), float(typeof(dec1)), \n",
    "                    float(typeof(ra2)), float(typeof(dec2)))\n",
    "    return gcirc(units, T(ra1), T(dec1), T(ra2), T(dec2))\n",
    "end\n",
    "\n",
    "# Tuple input handlers\n",
    "function gcirc(units::Integer, radec1::Tuple{Real,Real}, ra2::Real, dec2::Real)\n",
    "    T = promote_type(float(typeof(radec1[1])), float(typeof(radec1[2])), \n",
    "                    float(typeof(ra2)), float(typeof(dec2)))\n",
    "    return gcirc(units, T(radec1[1]), T(radec1[2]), T(ra2), T(dec2))\n",
    "end\n",
    "\n",
    "function gcirc(units::Integer, ra1::Real, dec1::Real, radec2::Tuple{Real,Real})\n",
    "    T = promote_type(float(typeof(ra1)), float(typeof(dec1)), \n",
    "                    float(typeof(radec2[1])), float(typeof(radec2[2])))\n",
    "    return gcirc(units, T(ra1), T(dec1), T(radec2[1]), T(radec2[2]))\n",
    "end\n",
    "\n",
    "function gcirc(units::Integer, radec1::Tuple{Real,Real}, radec2::Tuple{Real,Real})\n",
    "    T = promote_type(float(typeof(radec1[1])), float(typeof(radec1[2])), \n",
    "                    float(typeof(radec2[1])), float(typeof(radec2[2])))\n",
    "    return gcirc(units, T(radec1[1]), T(radec1[2]), T(radec2[1]), T(radec2[2]))\n",
    "end\n",
    "\n",
    "# Updated broadcasting implementation\n",
    "function Base.Broadcast.broadcasted(::typeof(gcirc), units::Integer, \n",
    "                                  ra1::AbstractArray, dec1::AbstractArray, \n",
    "                                  ra2::AbstractArray, dec2::AbstractArray)\n",
    "    T = promote_type(float(eltype(ra1)), float(eltype(dec1)), \n",
    "                    float(eltype(ra2)), float(eltype(dec2)))\n",
    "    return T[gcirc(units, r1, d1, r2, d2) for (r1, d1, r2, d2) in zip(ra1, dec1, ra2, dec2)]\n",
    "end\n",
    "\n",
    "function Base.Broadcast.broadcasted(::typeof(gcirc), units::Integer, \n",
    "                                  ra1::AbstractArray, dec1::AbstractArray, \n",
    "                                  ra2::Number, dec2::Number)\n",
    "    T = promote_type(float(eltype(ra1)), float(eltype(dec1)), \n",
    "                    float(typeof(ra2)), float(typeof(dec2)))\n",
    "    return T[gcirc(units, r1, d1, T(ra2), T(dec2)) for (r1, d1) in zip(ra1, dec1)]\n",
    "end\n",
    "\n",
    "function Base.Broadcast.broadcasted(::typeof(gcirc), units::Integer, \n",
    "                                  ra1::Number, dec1::Number,\n",
    "                                  ra2::AbstractArray, dec2::AbstractArray)\n",
    "    T = promote_type(float(typeof(ra1)), float(typeof(dec1)), \n",
    "                    float(eltype(ra2)), float(eltype(dec2)))\n",
    "    return T[gcirc(units, T(ra1), T(dec1), r2, d2) for (r2, d2) in zip(ra2, dec2)]\n",
    "end\n",
    "\n",
    "# Helper function for converting radians to arcseconds\n",
    "rad2sec(x::T) where T<:AbstractFloat = x * T(206264.8062470963)"
   ]
  },
  {
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     "text": [
      "\u001b[0m\u001b[1mTest Summary:                   | \u001b[22m\u001b[32m\u001b[1mPass  \u001b[22m\u001b[39m\u001b[36m\u001b[1mTotal  \u001b[22m\u001b[39m\u001b[0m\u001b[1mTime\u001b[22m\n",
      "AstroCoordinate and gcirc tests | \u001b[32m  15  \u001b[39m\u001b[36m   15  \u001b[39m\u001b[0m0.5s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Test.DefaultTestSet(\"AstroCoordinate and gcirc tests\", Any[], 15, false, false, true, 1.74319942435e9, 1.743199424839e9, false, \"In[21]\")"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Test\n",
    "using SkyCoords\n",
    "\n",
    "@testset \"AstroCoordinate and gcirc tests\" begin\n",
    "    # Test AstroCoordinate constructor with invalid units\n",
    "    @test_throws ArgumentError AstroCoordinate(1.0, 1.0, :invalid_units)\n",
    "    \n",
    "    # Original tests for basic functionality\n",
    "    @test gcirc(0, 2.0, -0.75, 3.0, 0.4) ≈ \n",
    "          SkyCoords.separation(\n",
    "              SkyCoords.ICRSCoords(2.0, -0.75),\n",
    "              SkyCoords.ICRSCoords(3.0, 0.4))\n",
    "    \n",
    "    # Test AstroCoordinate constructor with all valid units\n",
    "    @test isa(AstroCoordinate(1.0, 1.0, :radians), AstroCoordinate)\n",
    "    @test isa(AstroCoordinate(1.0, 1.0, :hours_degrees), AstroCoordinate)\n",
    "    @test isa(AstroCoordinate(1.0, 1.0, :degrees), AstroCoordinate)\n",
    "    \n",
    "    # Test hours/degrees input (units = 1)\n",
    "    ra1_hours, dec1_deg = 12.0, -43.0\n",
    "    ra2_hours, dec2_deg = 15.0, 22.0\n",
    "    result1 = gcirc(1, ra1_hours, dec1_deg, ra2_hours, dec2_deg)\n",
    "    expected1 = rad2sec(SkyCoords.separation(\n",
    "        SkyCoords.ICRSCoords(ra1_hours * π/12.0, deg2rad(dec1_deg)),\n",
    "        SkyCoords.ICRSCoords(ra2_hours * π/12.0, deg2rad(dec2_deg))))\n",
    "    @test result1 ≈ expected1\n",
    "    \n",
    "    # Comprehensive tests from original implementation\n",
    "    @test gcirc.(0, [0,1,2], [1,2,3], [2,3,4], [3,4,5]) ≈\n",
    "        [1.222450611061632, 2.500353926443337, 1.5892569925227757]\n",
    "    \n",
    "    @test @inferred(gcirc(0, 120, -43, 175, +22)) ≈ 1.590442261600714\n",
    "    @test @inferred(gcirc(1, (120, -43), 175, +22)) ≈ 415908.56615322345\n",
    "    @test @inferred(gcirc(2, 120, -43, (175, +22))) ≈ 296389.3666794745\n",
    "    @test @inferred(gcirc(0, (120, -43), (175, +22))) ≈ 1.590442261600714\n",
    "    \n",
    "    @test gcirc.(1, [120], [-43], 175, +22) ≈ [415908.56615322345]\n",
    "    @test gcirc.(2, 120, -43, [175], [+22]) ≈ [296389.3666794745]\n",
    "    \n",
    "    # Test error conditions\n",
    "    @test_throws DomainError gcirc(3, 120.0, -43.0, 175.0, 22.0)\n",
    "    @test_throws DomainError @inferred(gcirc(3, 0, 0, 0, 0))\n",
    "end"
   ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Angular distances between astronomical objects:\n",
      "Andromeda to Pleiades: 150825.7657184823 arcseconds\n",
      "Pleiades to Orion: 132950.90651285887 arcseconds\n",
      "Orion to Omega Centauri: 384869.3303342714 arcseconds\n",
      "\n",
      "Survey field coverage analysis:\n",
      "Points 1 and 2 are separated by 0.5000000000000093 degrees\n",
      "Points 1 and 6 are separated by 0.24621118823618268 degrees\n",
      "Points 1 and 7 are separated by 0.5581697159663188 degrees\n",
      "Points 1 and 11 are separated by 0.49241882556309147 degrees\n",
      "Points 1 and 12 are separated by 0.7044218862748391 degrees\n",
      "Points 1 and 16 are separated by 0.7386193609915382 degrees\n",
      "Points 1 and 17 are separated by 0.8966379904138547 degrees\n",
      "Points 1 and 21 are separated by 0.9848092433724535 degrees\n",
      "Points 2 and 3 are separated by 0.49999999999999345 degrees\n",
      "Points 2 and 4 are separated by 0.9999999999999873 degrees\n",
      "Points 2 and 6 are separated by 0.5581697159663171 degrees\n",
      "Points 2 and 7 are separated by 0.24999940504339124 degrees\n",
      "Points 2 and 8 are separated by 0.5598596254100974 degrees\n",
      "Points 2 and 11 are separated by 0.704421886274836 degrees\n",
      "Points 2 and 12 are separated by 0.4999952403301562 degrees\n",
      "Points 2 and 13 are separated by 0.7097658735722852 degrees\n",
      "Points 2 and 16 are separated by 0.8966379904138545 degrees\n",
      "Points 2 and 17 are separated by 0.7499839360187311 degrees\n",
      "Points 2 and 18 are separated by 0.9060703997249829 degrees\n",
      "Points 2 and 22 are separated by 0.9999619220976234 degrees\n",
      "Points 3 and 4 are separated by 0.49999999999999345 degrees\n",
      "Points 3 and 7 are separated by 0.5598596254100954 degrees\n",
      "Points 3 and 8 are separated by 0.25376858366962285 degrees\n",
      "Points 3 and 9 are separated by 0.5615611440373289 degrees\n",
      "Points 3 and 12 are separated by 0.7097658735722845 degrees\n",
      "Points 3 and 13 are separated by 0.5075335804568828 degrees\n",
      "Points 3 and 14 are separated by 0.7151223658570284 degrees\n",
      "Points 3 and 17 are separated by 0.9060703997249837 degrees\n",
      "Points 3 and 18 are separated by 0.7612914033894037 degrees\n",
      "Points 3 and 19 are separated by 0.9154977943682893 degrees\n",
      "Points 4 and 5 are separated by 0.5000000000000092 degrees\n",
      "Points 4 and 8 are separated by 0.5615611440373297 degrees\n",
      "Points 4 and 9 are separated by 0.25751843707724975 degrees\n",
      "Points 4 and 10 are separated by 0.56327365070674 degrees\n",
      "Points 4 and 13 are separated by 0.715122365857028 degrees\n",
      "Points 4 and 14 are separated by 0.5150332718688246 degrees\n",
      "Points 4 and 15 are separated by 0.7204894708657125 degrees\n",
      "Points 4 and 18 are separated by 0.9154977943682896 degrees\n",
      "Points 4 and 19 are separated by 0.7725409019939161 degrees\n",
      "Points 4 and 20 are separated by 0.9249175001268816 degrees\n",
      "Points 5 and 9 are separated by 0.5632736507067414 degrees\n",
      "Points 5 and 10 are separated by 0.2612486797001686 degrees\n",
      "Points 5 and 14 are separated by 0.720489470865712 degrees\n",
      "Points 5 and 15 are separated by 0.5224937434334596 degrees\n",
      "Points 5 and 19 are separated by 0.9249175001268821 degrees\n",
      "Points 5 and 20 are separated by 0.7837315751327051 degrees\n",
      "Points 6 and 7 are separated by 0.5000000000000093 degrees\n",
      "Points 6 and 11 are separated by 0.24621118823618268 degrees\n",
      "Points 6 and 12 are separated by 0.5581697159663188 degrees\n",
      "Points 6 and 16 are separated by 0.49241882556310396 degrees\n",
      "Points 6 and 17 are separated by 0.7044218862748481 degrees\n",
      "Points 6 and 21 are separated by 0.7386193609915382 degrees\n",
      "Points 6 and 22 are separated by 0.8966379904138547 degrees\n",
      "Points 7 and 8 are separated by 0.49999999999999345 degrees\n",
      "Points 7 and 9 are separated by 0.9999999999999873 degrees\n",
      "Points 7 and 11 are separated by 0.5581697159663171 degrees\n",
      "Points 7 and 12 are separated by 0.24999940504339124 degrees\n",
      "Points 7 and 13 are separated by 0.5598596254100974 degrees\n",
      "Points 7 and 16 are separated by 0.7044218862748448 degrees\n",
      "Points 7 and 17 are separated by 0.4999952403301689 degrees\n",
      "Points 7 and 18 are separated by 0.7097658735722946 degrees\n",
      "Points 7 and 21 are separated by 0.8966379904138545 degrees\n",
      "Points 7 and 22 are separated by 0.7499839360187311 degrees\n",
      "Points 7 and 23 are separated by 0.9060703997249829 degrees\n",
      "Points 8 and 9 are separated by 0.49999999999999345 degrees\n",
      "Points 8 and 12 are separated by 0.5598596254100954 degrees\n",
      "Points 8 and 13 are separated by 0.25376858366962285 degrees\n",
      "Points 8 and 14 are separated by 0.5615611440373289 degrees\n",
      "Points 8 and 17 are separated by 0.7097658735722934 degrees\n",
      "Points 8 and 18 are separated by 0.5075335804568957 degrees\n",
      "Points 8 and 19 are separated by 0.7151223658570378 degrees\n",
      "Points 8 and 22 are separated by 0.9060703997249837 degrees\n",
      "Points 8 and 23 are separated by 0.7612914033894037 degrees\n",
      "Points 8 and 24 are separated by 0.9154977943682893 degrees\n",
      "Points 9 and 10 are separated by 0.5000000000000092 degrees\n",
      "Points 9 and 13 are separated by 0.5615611440373297 degrees\n",
      "Points 9 and 14 are separated by 0.25751843707724975 degrees\n",
      "Points 9 and 15 are separated by 0.56327365070674 degrees\n",
      "Points 9 and 18 are separated by 0.7151223658570373 degrees\n",
      "Points 9 and 19 are separated by 0.5150332718688376 degrees\n",
      "Points 9 and 20 are separated by 0.7204894708657221 degrees\n",
      "Points 9 and 23 are separated by 0.9154977943682896 degrees\n",
      "Points 9 and 24 are separated by 0.7725409019939161 degrees\n",
      "Points 9 and 25 are separated by 0.9249175001268816 degrees\n",
      "Points 10 and 14 are separated by 0.5632736507067414 degrees\n",
      "Points 10 and 15 are separated by 0.2612486797001686 degrees\n",
      "Points 10 and 19 are separated by 0.7204894708657215 degrees\n",
      "Points 10 and 20 are separated by 0.522493743433473 degrees\n",
      "Points 10 and 24 are separated by 0.9249175001268821 degrees\n",
      "Points 10 and 25 are separated by 0.7837315751327051 degrees\n",
      "Points 11 and 12 are separated by 0.5000000000000093 degrees\n",
      "Points 11 and 16 are separated by 0.2462111882361952 degrees\n",
      "Points 11 and 17 are separated by 0.5581697159663245 degrees\n",
      "Points 11 and 21 are separated by 0.49241882556310396 degrees\n",
      "Points 11 and 22 are separated by 0.7044218862748481 degrees\n",
      "Points 12 and 13 are separated by 0.49999999999999345 degrees\n",
      "Points 12 and 14 are separated by 0.9999999999999873 degrees\n",
      "Points 12 and 16 are separated by 0.5581697159663226 degrees\n",
      "Points 12 and 17 are separated by 0.24999940504340398 degrees\n",
      "Points 12 and 18 are separated by 0.5598596254101033 degrees\n",
      "Points 12 and 21 are separated by 0.7044218862748448 degrees\n",
      "Points 12 and 22 are separated by 0.4999952403301689 degrees\n",
      "Points 12 and 23 are separated by 0.7097658735722946 degrees\n",
      "Points 13 and 14 are separated by 0.49999999999999345 degrees\n",
      "Points 13 and 17 are separated by 0.5598596254101011 degrees\n",
      "Points 13 and 18 are separated by 0.2537685836696358 degrees\n",
      "Points 13 and 19 are separated by 0.5615611440373349 degrees\n",
      "Points 13 and 22 are separated by 0.7097658735722934 degrees\n",
      "Points 13 and 23 are separated by 0.5075335804568957 degrees\n",
      "Points 13 and 24 are separated by 0.7151223658570378 degrees\n",
      "Points 14 and 15 are separated by 0.5000000000000092 degrees\n",
      "Points 14 and 18 are separated by 0.5615611440373355 degrees\n",
      "Points 14 and 19 are separated by 0.2575184370772629 degrees\n",
      "Points 14 and 20 are separated by 0.5632736507067461 degrees\n",
      "Points 14 and 23 are separated by 0.7151223658570373 degrees\n",
      "Points 14 and 24 are separated by 0.5150332718688376 degrees\n",
      "Points 14 and 25 are separated by 0.7204894708657221 degrees\n",
      "Points 15 and 19 are separated by 0.5632736507067473 degrees\n",
      "Points 15 and 20 are separated by 0.2612486797001819 degrees\n",
      "Points 15 and 24 are separated by 0.7204894708657215 degrees\n",
      "Points 15 and 25 are separated by 0.522493743433473 degrees\n",
      "Points 16 and 17 are separated by 0.5000000000000093 degrees\n",
      "Points 16 and 21 are separated by 0.24621118823618268 degrees\n",
      "Points 16 and 22 are separated by 0.5581697159663188 degrees\n",
      "Points 17 and 18 are separated by 0.49999999999999345 degrees\n",
      "Points 17 and 19 are separated by 0.9999999999999873 degrees\n",
      "Points 17 and 21 are separated by 0.5581697159663171 degrees\n",
      "Points 17 and 22 are separated by 0.24999940504339124 degrees\n",
      "Points 17 and 23 are separated by 0.5598596254100974 degrees\n",
      "Points 18 and 19 are separated by 0.49999999999999345 degrees\n",
      "Points 18 and 22 are separated by 0.5598596254100954 degrees\n",
      "Points 18 and 23 are separated by 0.25376858366962285 degrees\n",
      "Points 18 and 24 are separated by 0.5615611440373289 degrees\n",
      "Points 19 and 20 are separated by 0.5000000000000092 degrees\n",
      "Points 19 and 23 are separated by 0.5615611440373297 degrees\n",
      "Points 19 and 24 are separated by 0.25751843707724975 degrees\n",
      "Points 19 and 25 are separated by 0.56327365070674 degrees\n",
      "Points 20 and 24 are separated by 0.5632736507067414 degrees\n",
      "Points 20 and 25 are separated by 0.2612486797001686 degrees\n",
      "Points 21 and 22 are separated by 0.5000000000000093 degrees\n",
      "Points 22 and 23 are separated by 0.49999999999999345 degrees\n",
      "Points 22 and 24 are separated by 0.9999999999999873 degrees\n",
      "Points 23 and 24 are separated by 0.49999999999999345 degrees\n",
      "Points 24 and 25 are separated by 0.5000000000000092 degrees\n",
      "\n",
      "Asteroid tracking:\n",
      "Total distance traveled: 2.6831246425616166 degrees\n",
      "\n",
      "Telescope selection:\n",
      "Best telescope for observation is telescope 3\n",
      "Distances from each telescope to target (arcseconds):\n",
      "Telescope 1: 289965.8459651378\n",
      "Telescope 2: 167308.35492649037\n",
      "Telescope 3: 107741.68246596894\n",
      "Telescope 4: 345380.54950435314\n",
      "\n",
      "Field overlap analysis:\n",
      "One field completely inside the other. Area: 1.0178760197630929e7\n"
     ]
    }
   ],
   "source": [
    "### Example 1: Calculate separation between famous astronomical objects ###\n",
    "\n",
    "# Coordinates of some famous objects (RA in hours, Dec in degrees)\n",
    "andromeda = (0.712500, 41.269167)    # Andromeda Galaxy (M31)\n",
    "pleiades = (3.791667, 24.105000)     # Pleiades Cluster (M45)\n",
    "orion = (5.588333, -1.942222)        # Orion Nebula (M42)\n",
    "omega_centauri = (13.446667, -47.478333)  # Omega Centauri (NGC 5139)\n",
    "\n",
    "# Calculate angular distances between objects (output in arcseconds)\n",
    "println(\"Angular distances between astronomical objects:\")\n",
    "println(\"Andromeda to Pleiades: \", gcirc(1, andromeda, pleiades), \" arcseconds\")\n",
    "println(\"Pleiades to Orion: \", gcirc(1, pleiades, orion), \" arcseconds\")\n",
    "println(\"Orion to Omega Centauri: \", gcirc(1, orion, omega_centauri), \" arcseconds\")\n",
    "\n",
    "### Example 2: Survey field coverage analysis ###\n",
    "\n",
    "# Create a grid of observations (RA and Dec in degrees)\n",
    "function create_survey_grid(center_ra, center_dec, width, height, n_points)\n",
    "    ras = range(center_ra - width/2, center_ra + width/2, length=n_points)\n",
    "    decs = range(center_dec - height/2, center_dec + height/2, length=n_points)\n",
    "    return [(ra, dec) for ra in ras for dec in decs]\n",
    "end\n",
    "\n",
    "# Create a survey grid centered on the Carina Nebula\n",
    "carina_grid = create_survey_grid(160.5, -59.5, 2.0, 2.0, 5)\n",
    "\n",
    "# Calculate separations between all points in the grid\n",
    "println(\"\\nSurvey field coverage analysis:\")\n",
    "for i in 1:length(carina_grid)\n",
    "    for j in (i+1):length(carina_grid)\n",
    "        sep = gcirc(2, carina_grid[i], carina_grid[j])\n",
    "        if sep < 3600.0  # If separation is less than 1 degree\n",
    "            println(\"Points $i and $j are separated by $(sep/3600.0) degrees\")\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "### Example 3: Time series observation planning ###\n",
    "\n",
    "# Simulate object movement over time\n",
    "function simulate_object_motion(start_ra, start_dec, hours, speed_ra, speed_dec)\n",
    "    times = range(0, hours, length=24)\n",
    "    ras = start_ra .+ speed_ra .* times\n",
    "    decs = start_dec .+ speed_dec .* times\n",
    "    return collect(zip(ras, decs))\n",
    "end\n",
    "\n",
    "# Simulate a moving object (like an asteroid)\n",
    "asteroid_positions = simulate_object_motion(180.0, 0.0, 24, 0.1, 0.05)\n",
    "\n",
    "# Calculate total angular distance traveled\n",
    "total_distance = 0.0\n",
    "for i in 1:(length(asteroid_positions)-1)\n",
    "    total_distance += gcirc(2, asteroid_positions[i], asteroid_positions[i+1])\n",
    "end\n",
    "\n",
    "println(\"\\nAsteroid tracking:\")\n",
    "println(\"Total distance traveled: $(total_distance/3600.0) degrees\")\n",
    "\n",
    "### Example 4: Multi-telescope observation planning ###\n",
    "\n",
    "# Define telescope locations (RA, Dec in degrees)\n",
    "telescopes = [\n",
    "    (245.0, 31.0),  # Apache Point\n",
    "    (155.5, 19.8),  # Mauna Kea\n",
    "    (149.1, -31.3), # Siding Spring\n",
    "    (70.7, -29.3)   # La Silla\n",
    "]\n",
    "\n",
    "# Target object\n",
    "target = (180.0, -20.0)\n",
    "\n",
    "# Calculate which telescope is closest to the target\n",
    "distances = [gcirc(2, tel, target) for tel in telescopes]\n",
    "best_telescope = argmin(distances)\n",
    "\n",
    "println(\"\\nTelescope selection:\")\n",
    "println(\"Best telescope for observation is telescope $best_telescope\")\n",
    "println(\"Distances from each telescope to target (arcseconds):\")\n",
    "for (i, dist) in enumerate(distances)\n",
    "    println(\"Telescope $i: $dist\")\n",
    "end\n",
    "\n",
    "### Example 5: Field overlap calculation ###\n",
    "\n",
    "function calculate_field_overlap(field1_center, field1_radius, field2_center, field2_radius)\n",
    "    separation = gcirc(2, field1_center, field2_center)\n",
    "    \n",
    "    if separation > (field1_radius + field2_radius)\n",
    "        return \"Fields do not overlap\"\n",
    "    elseif separation < abs(field1_radius - field2_radius)\n",
    "        smaller_radius = min(field1_radius, field2_radius)\n",
    "        return \"One field completely inside the other. Area: $(π * smaller_radius^2)\"\n",
    "    else\n",
    "        return \"Fields partially overlap\"\n",
    "    end\n",
    "end\n",
    "\n",
    "# Example fields (centers in degrees, radii in arcseconds)\n",
    "field1 = ((180.0, 0.0), 1800.0)  # 0.5 degree radius\n",
    "field2 = ((180.1, 0.1), 3600.0)  # 1.0 degree radius\n",
    "\n",
    "println(\"\\nField overlap analysis:\")\n",
    "println(calculate_field_overlap(field1[1], field1[2], field2[1], field2[2]))"
   ]
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