SwiftAstro

A Swift package for astronomy.

About SwiftAstro.

SwiftAstro is a Swift package that provides:

• A swifty interface for the Yale Bright Star Catalog of 9,110 stars that are considered visible to the naked eye.
• Computation of the motion of the planets using the VSOP87 theory.
• Data structures to represent quantities of distance, time, and angles for astronomical calculations.

Yale Bright Star Catalog.

The SwiftAstro.brightStarCatalog property provides access to a BrightStarCatalog instance.

The stars property provides access to all stars in the catalog. The catalog can also be subscripted with the Harvard Revised Star Number (HR).

Example: Find the visual magnitude of Vega, HR number 7001.

if let vega = SwiftAstro.brightStarCatalog[7001] {
  print(vega.visualMagnitude).        // 0.03
}

Example: Find all stars with a visual magnitude of 1.0 or lower.

let brightest = SwiftAstro.brightStarCatalog.stars.filter {
  star in

  guard let magnitude = star.visualMagnitude else {
    return false
  }
            
  return magnitude <= 1.0
}

Astronomical calculations.

Heliocentric position of the planets.

The planets are enumerated by the Planet enum. The heliocentricPosition function returns the heliocentric position of a planet for a given Julian day. The algorithm sums terms from the VSOP87B theory, the result is given in spherical coordinates.

Example: Calculate the position of Mars on Julian Day 2460156.0 (noon on 30th July 2023).

let t = SwiftAstro.Time(julianDays: 2460156.0)
let posn = SwiftAstro.Planet.mars.heliocentricPosition(t: t)

Gives longitude -3.0927667317253196 radians, latitude 0.023473327404147742 radians, and radius 1.6478994217781984 astronomical units (the distance between Mars and the Sun).

Geocentric position of the planets.

Calculates the apparent geocentric position of a planet when viewed from Earth against the background of the stars.

Example: Calculate the position of Venus on 10th February 2024 at 19:00 UTC.

let t = SwiftAstro.Time(2024, 02, 10, 19, 0, 0)
let (lon, lat) = SwiftAstro.Planet.venus.geocentricPosition(t: t)

print(lon.rightAscension.description, lat.degreesMinutesSeconds)

Gives the planet's 'right ascension as 19h 36m 37.569s, and declination as -021° 25' 22.986".

Compare with 19h 36m 39.41s and -21° 25' 21.2" computed by JPL Horizons (https://ssd.jpl.nasa.gov/horizons/).

Geocentric position of the Moon and Sun.

Calculate the apparent geocentric position of the Moon or the Sun when viewed from Earth against the background of the stars.

Example: Calculate the position of the Moon and Sun on 1st July 2024 at 15:00 UTC.

let t = SwiftAstro.Time(2024, 7, 1, 15, 0, 0)

let (raSun, declSun) = SwiftAstro.sun.geocentricPosition(t: t)
print(raSun.rightAscension)            // 06h 43m 08.592s
print(declSun.degreesMinutesSeconds)   // 023° 03' 53.911"

let (raMoon, declMoon) = SwiftAstro.moon.geocentricPosition(t: t)
print(raMoon.rightAscension)          // 02h 49m 21.979s
print(declMoon.degreesMinutesSeconds) // 019° 14' 35.610"

For comparison JPL Horizons gives:

• For the Sun: 6h 43m 10.49s, 23º 03' 55.0"
• For the Moon: 2h 48m 02.59s, 19º 08' 45.1"

Pluto.

The heliocentric and geocentric positions of Pluto are available from the SwiftAstro.pluto struct.

Data structures.

Distance.

The SwiftAstro.Distance data structure represents an astronomical distance. The underlying unit of measurement is the astronomical unit. Initialisers and accessors are also available for light years, light minutes, light seconds, meters, and parsecs.

Example: For a distance of 1 light year, find the corresponding distance in astronomical units and parsecs.

let distance = SwiftAstro.Distance(lightYears: 1.0)
let au = distance.astronomicalUnits    // 63241.07708426628
let pc = distance.parsecs              // 0.30660139378555057

Angle.

The SwiftAstro.Angle data structure represents an angular measurement. The underlying unit is the radian. Accessors and initialisers are also available for degrees and arc seconds. Additionally, the SwiftAstro.Angle.RightAscension property provides a view of an angle as a right ascension. Similarly, the SwiftAstro.Angle.DegreesMinutesSeconds property provides a view of an angle in DMS form. Angles may also be initialised using right ascension and DMS values.

Example: Find the right ascension and declination of Sirius, star number 2491 in the Yale Bright Star Catalog.

if let sirius = SwiftAstro.brightStarCatalog[2491],
   let ra = sirius.rightAscension?.rightAscension,
   let dec = sirius.declination?.degreesMinutesSeconds
{
  print (ra)               // 06h 45m 08.900s
  print (dec)              // -016° 42' 58.000"
}

Time.

The 'SwiftAstro.Time` data structure represents a moment in time. The underlying unit is the Julian Day, which measures the number of continuous days since noon on 1st January -4713.

Accessors and initialisers are also available for the corresponding Foundation Date and for the timeIntervalSinceReferenceDate.

A convenience initialiser is provided for date/time in UTC in the Gregorian calendar: SwiftAstro.Date(2024, 5,29, 18, 30, 0) initialises as 29th May 2024, 18:30 UTC.

Nutation.

The nutation instance method returns a pair of SwiftAstro.Angle values. The first value represents the nutation in longitude for the instance time, the second value represents the nutation in obliquity. The method of calculation is Meeus' abridged version of the '1980 IAU Theory of Nutation' omitting small terms (see Meeus, 1991, p. 132).

Obliquity of the ecliptic.

The meanObliquityOfTheEcliptic instance method returns a SwiftAstro.Angle representing the mean obliquity of the ecliptic for the instance time. The method of calculation is due to Laskar (1986), cited in Meeus, 1991, p. 135.

Spherical position.

The SphericalPosition struct represents the relative spherical coordinates of an object in terms of longitude, latitude, and radius (distance to the origin).

Physical constants.

Distances.

SwiftAstro.Distance.metersPerAstronomicalUnit SwiftAstro.Distance.metersPerLightYear SwiftAstro.Distance.metersPerLightMinute SwiftAstro.Distance.metersPerLightSecond SwiftAstro.Distance.astronomicalUnitsPerParsec SwiftAstro.Distance.astronomicalUnitsPerLightYear

Durations of time.

SwiftAstro.Distance.lightSecondsPerLightYear SwiftAstro.Distance.lightSecondsPerAstronomicalUnit

Angles.

SwiftAstro.Angle.meanObliquityOfEclipticAtJ2000

Sources.

Bretagnon, P. and Francou, G. (1988) 'Planetary Solutions VSOP87', Astronomy and Astrophysics, vol. 202(309B).

Meeus, J. (1991) 'Astronomical Algorithms', Willmann-Bell: Viriginia, USA.

Hoffleit, D. and Warren Jr, W. H. (1991) 'Yale Bright Star Catalog: 5th Revised Edition', Available at http://cdsarc.u-strasbg.fr/viz-bin/cat/V/50