Star-planet parans API

For each star and planet the endpoint takes the four angular events (rising, setting, culminating, anticulminating) and asks at which latitude the two happen at the same local sidereal time. Culmination fixes the sidereal time at the body's right ascension; rising and setting move it by the semi-diurnal arc, which is a function of latitude and declination. Each of the twelve event pairs is solved and every root reported, with the latitude, the sidereal time, and the meridian where the pair is angular at this particular chart moment. Meridian against meridian is rejected: that condition has no latitude in it, so it either never holds or holds everywhere, and holding everywhere only means the two share a right ascension. Stars that resolved but produced nothing are named in the response rather than silently dropped, which is what happens to a circumpolar star like Polaris across almost the whole range.

curl -X POST https://api.astroway.info/v1/parans/star \
  -H "X-Api-Key: aw_live_..." \
  -H "Content-Type: application/json" \
  -d '{
  "date": "1990-05-15",
  "time": "14:30:00",
  "timezoneOffset": 3,
  "stars": ["Regulus", "Sirius"],
  "planets": [0, 4]
}'

{
  "ok": true,
  "data": {
    "type": "star-parans",
    "horizon": "geometric",
    "latitudeLimit": 60,
    "count": 16,
    "stars": [
      { "name": "Regulus", "magnitude": 1.36, "rightAscension": 151.9686, "declination": 12.0133 }
    ],
    "parans": [
      {
        "star": "Regulus",
        "starEvent": "rise",
        "planetId": 0,
        "planetName": "Sun",
        "planetEvent": "culminate",
        "latitude": 39.1022,
        "longitude": 6.5735,
        "lst": 51.6
      }
    ]
  }
}

Use this when the fixed-star layer of a chart needs to be more than a conjunction list. A star conjunct a planet by zodiacal longitude is a projection; a paran is the star and the planet actually standing on the angles together, which is the relationship Brady's work is built on and the one that ties a star to a place on the map. In a relocation product the latitudes plot as horizontal bands, and a city sitting on one carries that star-planet pairing. Note the endpoint needs no birth place, only the moment: which latitudes exist is a property of the sky, not of where the person was born.

Solved on hour angles rather than by intersecting map polylines, so the latitude is exact instead of quantised to the polyline step, and the star's actual declination is used rather than the zodiac degree it projects onto. That distinction matters: Vega sits at ecliptic latitude 61 degrees and Sirius at minus 39, so the degree they occupy does not rise anywhere near when they do. Star positions come from the Swiss Ephemeris fixed-star catalogue, and the ecliptic-to-equatorial conversion is checked against the ephemeris itself by running the planets through it. Brady's worked Castor example is reproduced to within a degree; it does not settle whether she used the geometric or the apparent horizon, and since the two differ by about two degrees of paran latitude, that choice is a request parameter instead of a silent default.