[
  {
    "$project": {
      "_id": 0,
      "watchlist": [
        {
          "name": "my_favorite_spot",
          "ra": 134.0779551,
          "dec": -0.4421303
        },
        {
          "name": "my_star",
          "ra": 14.5551,
          "dec": 37.4451303
        }
      ],
      "max_distance_arcsec": {
        "$literal": 2.0
      },
      "ra": {
        "$degreesToRadians": "$candidate.ra"
      },
      "dec": {
        "$degreesToRadians": "$candidate.dec"
      }
    }
  },
  {
    "$project": {
      "watchlist": 1,
      "max_distance_arcsec": 1,
      "dec": 1,
      "dra_dec": {
        "$zip": {
          "inputs": [
            {
              "$map": {
                "input": "$watchlist",
                "as": "object",
                "in": {
                  "$subtract": [
                    "$ra", {
                      "$degreesToRadians": "$$object.ra"
                    }
                  ]
                }
              }
            }, {
              "$map": {
                "input": "$watchlist",
                "as": "object",
                "in": {
                  "$degreesToRadians": "$$object.dec"
                }
              }
            }
          ]
        }
      }
    }
  },
  {
    "$project": {
      "watchlist": 1,
      "max_distance_arcsec": 1,
      "distances_arcsec": {
        "$map": {
          "input": "$dra_dec",
          "as": "s",
          "in": {
            "$multiply": [
              3600.0, {
                "$radiansToDegrees": {
                  "$atan2": [
                    {
                      "$sqrt": {
                        "$add": [
                          {
                            "$pow": [
                              {
                                "$multiply": [
                                  {
                                    "$cos": "$dec"
                                  }, {
                                    "$sin": {
                                      "$arrayElemAt": [
                                        "$$s", 0
                                      ]
                                    }
                                  }
                                ]
                              }, 2
                            ]
                          }, {
                            "$pow": [
                              {
                                "$subtract": [
                                  {
                                    "$multiply": [
                                      {
                                        "$cos": {
                                          "$arrayElemAt": [
                                            "$$s", 1
                                          ]
                                        }
                                      }, {
                                        "$sin": "$dec"
                                      }
                                    ]
                                  }, {
                                    "$multiply": [
                                      {
                                        "$sin": {
                                          "$arrayElemAt": [
                                            "$$s", 1
                                          ]
                                        }
                                      }, {
                                        "$cos": "$dec"
                                      }, {
                                        "$cos": {
                                          "$arrayElemAt": [
                                            "$$s", 0
                                          ]
                                        }
                                      }
                                    ]
                                  }
                                ]
                              }, 2
                            ]
                          }
                        ]
                      }
                    }, {
                      "$add": [
                        {
                          "$multiply": [
                            {
                              "$sin": {
                                "$arrayElemAt": [
                                  "$$s", 1
                                ]
                              }
                            }, {
                              "$sin": "$dec"
                            }
                          ]
                        }, {
                          "$multiply": [
                            {
                              "$cos": {
                                "$arrayElemAt": [
                                  "$$s", 1
                                ]
                              }
                            }, {
                              "$cos": "$dec"
                            }, {
                              "$cos": {
                                "$arrayElemAt": [
                                  "$$s", 0
                                ]
                              }
                            }
                          ]
                        }
                      ]
                    }
                  ]
                }
              }
            ]
          }
        }
      }
    }
  },
  {
    "$project": {
      "watchlist": 1,
      "distances_arcsec": 1,
      "nearest_index": {
        "$indexOfArray": [
          "$distances_arcsec", {
            "$min": "$distances_arcsec"
          }
        ]
      },
      "bingo": {
        "$filter": {
          "input": {
            "$zip": {
              "inputs": [
                "$watchlist", "$distances_arcsec"
              ]
            }
          },
          "as": "item",
          "cond": {
            "$lte": [
              {
                "$arrayElemAt": [
                  "$$item", 1
                ]
              }, "$max_distance_arcsec"
            ]
          }
        }
      }
    }
  },
  {
    "$match": {
      "bingo.0": {
        "$exists": true
      }
    }
  },
  {
    "$project": {
      "annotations.nearest_name": {
        "$arrayElemAt": [
          "$watchlist.name", "$nearest_index"
        ]
      },
      "annotations.nearest_distance_arcsec": {
        "$round": [
          {
            "$arrayElemAt": [
              "$distances_arcsec", "$nearest_index"
            ]
          }, 3
        ]
      },
      "annotations.matches": {
        "$map": {
          "input": "$bingo",
          "as": "item",
          "in": {
            "$arrayElemAt": [
              "$$item", 0
            ]
          }
        }
      },
      "annotations.distances_arcsec": {
        "$map": {
          "input": "$bingo",
          "as": "item",
          "in": {
            "$round": [
              {
                "$arrayElemAt": [
                  "$$item", 1
                ]
              }, 3
            ]
          }
        }
      }
    }
  }
]