# `AstroUtils.Coordinates`
[🔗](https://github.com/jakedjohnson/astro_utils/blob/v0.1.0/lib/astro_utils/coordinates.ex#L1)

Coordinate-system transforms on the sphere.

These functions implement spherical trigonometry identities with no
ephemeris data, process state, or I/O.

# `ecliptic_to_horizontal`

```elixir
@spec ecliptic_to_horizontal(number(), number(), number(), number()) ::
  {float(), float()}
```

Convert an ecliptic longitude (on the ecliptic plane, lat = 0) to local
horizontal coordinates (altitude, azimuth).

Uses standard spherical trigonometry:

1. ecliptic → equatorial via obliquity rotation
2. equatorial → hour-angle via local sidereal time
3. hour-angle + declination → altitude / azimuth

All inputs and outputs are in **degrees**.  Azimuth convention: 0° = North,
90° = East, increasing clockwise (standard astronomical/navigational
convention).

The result is the geometric direction. Ecliptic latitude is assumed to be
zero, and no correction is applied for atmospheric refraction, parallax, or
observer elevation.

## Parameters

  * `ecl_lon_deg` — ecliptic longitude in degrees (0–360; other values are
    handled by the trigonometry and need not be normalized)
  * `obliquity_deg` — obliquity of the ecliptic in degrees (~23.44 currently)
  * `lst_deg` — local sidereal time in degrees (0–360); multiply sidereal
    hours by 15 to get degrees
  * `lat_deg` — observer geographic latitude in degrees (−90 to 90, north
    positive)

## Returns

  `{altitude_deg, azimuth_deg}` where altitude ∈ [-90, 90] and
  azimuth ∈ [0, 360). Azimuth is not meaningful at the zenith and nadir,
  where it degenerates to `0.0`.

## Examples

Seen from the equator with the vernal equinox on the meridian, the
summer-solstice point (ecliptic longitude 90°) sits on the eastern horizon,
north of due east by the obliquity:

    iex> {alt, az} = AstroUtils.Coordinates.ecliptic_to_horizontal(90.0, 23.44, 0.0, 0.0)
    iex> {Float.round(alt, 6), Float.round(az, 6)}
    {0.0, 66.56}

---

*Consult [api-reference.md](api-reference.md) for complete listing*