Astropy

# Astronomical Coordinates (astropy.coordinates)

The `astropy.coordinates` package provides tools for representing celestial coordinates and transforming between different coordinate systems.

## Creating Coordinates with SkyCoord

The high-level `SkyCoord` class is the recommended interface:

```python
from astropy import units as u
from astropy.coordinates import SkyCoord

# Decimal degrees
c = SkyCoord(ra=10.625*u.degree, dec=41.2*u.degree, frame='icrs')

# Sexagesimal strings
c = SkyCoord(ra='00h42m30s', dec='+41d12m00s', frame='icrs')

# Mixed formats
c = SkyCoord('00h42.5m +41d12m', unit=(u.hourangle, u.deg))

# Galactic coordinates
c = SkyCoord(l=120.5*u.degree, b=-23.4*u.degree, frame='galactic')
```

## Array Coordinates

Process multiple coordinates efficiently using arrays:

```python
# Create array of coordinates
coords = SkyCoord(ra=[10, 11, 12]*u.degree,
                  dec=[41, -5, 42]*u.degree)

# Access individual elements
coords[0]
coords[1:3]

# Array operations
coords.shape
len(coords)
```

## Accessing Components

```python
c = SkyCoord(ra=10.68*u.degree, dec=41.27*u.degree, frame='icrs')

# Access coordinates
c.ra        # <Longitude 10.68 deg>
c.dec       # <Latitude 41.27 deg>
c.ra.hour   # Convert to hours
c.ra.hms    # Hours, minutes, seconds tuple
c.dec.dms   # Degrees, arcminutes, arcseconds tuple
```

## String Formatting

```python
c.to_string('decimal')      # '10.68 41.27'
c.to_string('dms')          # '10d40m48s 41d16m12s'
c.to_string('hmsdms')       # '00h42m43.2s +41d16m12s'

# Custom formatting
c.ra.to_string(unit=u.hour, sep=':', precision=2)
```

## Coordinate Transformations

Transform between reference frames:

```python
c_icrs = SkyCoord(ra=10.68*u.degree, dec=41.27*u.degree, frame='icrs')

# Simple transformations (as attributes)
c_galactic = c_icrs.galactic
c_fk5 = c_icrs.fk5
c_fk4 = c_icrs.fk4

# Explicit transformations
c_icrs.transform_to('galactic')
c_icrs.transform_to(FK5(equinox='J1975'))  # Custom frame parameters
```

## Common Coordinate Frames

### Celestial Frames
- **ICRS**: International Celestial Reference System (default, most common)
- **FK5**: Fifth Fundamental Catalogue (equinox J2000.0 by default)
- **FK4**: Fourth Fundamental Catalogue (older, requires equinox specification)
- **GCRS**: Geocentric Celestial Reference System
- **CIRS**: Celestial Intermediate Reference System

### Galactic Frames
- **Galactic**: IAU 1958 galactic coordinates
- **Supergalactic**: De Vaucouleurs supergalactic coordinates
- **Galactocentric**: Galactic center-based 3D coordinates

### Horizontal Frames
- **AltAz**: Altitude-azimuth (observer-dependent)
- **HADec**: Hour angle-declination

### Ecliptic Frames
- **GeocentricMeanEcliptic**: Geocentric mean ecliptic
- **BarycentricMeanEcliptic**: Barycentric mean ecliptic
- **HeliocentricMeanEcliptic**: Heliocentric mean ecliptic

## Observer-Dependent Transformations

For altitude-azimuth coordinates, specify observation time and location:

```python
from astropy.time import Time
from astropy.coordinates import EarthLocation, AltAz

# Define observer location
observing_location = EarthLocation(lat=40.8*u.deg, lon=-121.5*u.deg, height=1060*u.m)
# Or use named observatory
observing_location = EarthLocation.of_site('Apache Point Observatory')

# Define observation time
observing_time = Time('2023-01-15 23:00:00')

# Transform to alt-az
aa_frame = AltAz(obstime=observing_time, location=observing_location)
aa = c_icrs.transform_to(aa_frame)

print(f"Altitude: {aa.alt}")
print(f"Azimuth: {aa.az}")
```

## Working with Distances

Add distance information for 3D coordinates:

```python
# With distance
c = SkyCoord(ra=10*u.degree, dec=9*u.degree, distance=770*u.kpc, frame='icrs')

# Access 3D Cartesian coordinates
c.cartesian.x
c.cartesian.y
c.cartesian.z

# Distance from origin
c.distance

# 3D separation
c1 = SkyCoord(ra=10*u.degree, dec=9*u.degree, distance=10*u.pc)
c2 = SkyCoord(ra=11*u.degree, dec=10*u.degree, distance=11.5*u.pc)
sep_3d =