Moon equatorial coordinates

Question

It took some effort, but in the end, I successfully calculated the geographical point of the Sun. I assumed that I could do the same for the Moon.

My plan is:

1. Find RA and declination of the Moon
2. Find GHA of the Moon, using the same math as for the Sun

However, after following this article almost to the letter (except for precession and perturbations), my calculated answer is much different from this site. I've examined the article and my code many times, but can't see an error.

I use Swift programming language, but here it's merely a way to represent my calculations and results.

If anyone would like to try it for yourself, here's my code in text format:

import Foundation

extension Double {
  var radians: Double {
    return self * .pi / 180
  }

  var degrees: Double {
    return self  * 180 / .pi
  }

  var rangedUpTo360: Double {
    let multiples = (self/360).rounded(.down)
    return self - 360*multiples
  }

  var rangedUpTo86400: Double {
    let multiples = (self/86400).rounded(.down)
    return self - 86400*multiples
  }
}

extension Date {
  var greenwich: Date {
    let greenwichDate = self.addingTimeInterval(TimeInterval(-TimeZone.current.secondsFromGMT()))
    return greenwichDate
  }
}

class Astronomy {

  static func julianDays(since: Date) -> Double {
    return since.timeIntervalSince1970 / 86400 + 2_440_587.5
  }

  static func daysSinceJ2000(for date: Date) -> Double {
    return julianDays(since: date) - 2_451_545
  }

  static func sunAxialTilt(for daysSinceJ200: Double) -> Double {
    return 23.4393 - 3.563e-7 * daysSinceJ200
  }

  static func greenwichHourAngle(rightAscension: Double, date: Date) -> Double {
    let greenwichTimeZone = TimeZone(secondsFromGMT: 0)!
    var calendar = Calendar.current
    calendar.timeZone = greenwichTimeZone
    let components = calendar.dateComponents([.hour, .minute, .second], from: date)
    let secondsOfDay = Double(components.hour!)*3600 + Double(components.minute!)*60 + Double(components.second!)

    let centuriesSinceJ200 = daysSinceJ2000(for: date.greenwich) / 36525
    let greenwichSiderealTime = 24110.54841 + 8640184.812866*centuriesSinceJ200 + 0.093104*pow(centuriesSinceJ200, 2) - 0.0000062*pow(centuriesSinceJ200, 3)
    let earthSiderealRotationRate = 1.00273790935 + 5.9e-11*centuriesSinceJ200
    let earthRotation = earthSiderealRotationRate*secondsOfDay
    let gmstSeconds = greenwichSiderealTime + earthRotation
    let gmstSecondsNormalized = gmstSeconds.rangedUpTo86400
    let gmst = gmstSecondsNormalized / 3600 * 15
    return gmst.rangedUpTo360 - rightAscension
  }

  static func moonPosition(on date: Date) -> (declination: Double, RA: Double, distance: Double) {
    date
    // day number
    let d = daysSinceJ2000(for: date)
    // longitude of the ascending node
    var N = 125.1228 - 0.0529538083 * d // have to be normalized
    if N < 0 {
      N += 360
    }
    // inclination to the ecliptic (plane of the Earth's orbit)
    let i = 5.1454
    // argument of perihelion
    var w = 318.0634 + 0.1643573223 * d // have to be normalized
    w = w.rangedUpTo360
    // semi-major axis, or mean distance from Sun
    let a = 60.2666 // (Earth radii)
    // eccentricity (0=circle, 0-1=ellipse, 1=parabola)
    let e = 0.054900
    // mean anomaly (0 at perihelion; increases uniformly with time)
    var M = 115.3654 + 13.0649929509 * d // have to be normalized
    M = M.rangedUpTo360
    // eccentric anomaly
    let E = M + e * sin(M.radians) * (1.0 + e * cos(M.radians))
    let xv = a * (cos(E.radians) - e)
    let yv = a * (sqrt(1.0 - e*e) * sin(E.radians))
    // true anomaly (angle between position and perihelion)
    let v = atan2(yv, xv).degrees
    let r = sqrt(pow(xv, 2) + pow(yv, 2))
    // geocentric ecliptical position
    let xG = r * (cos(N.radians) * cos((v + w).radians) - sin(N.radians) * sin((v + w).radians) * cos(i.radians))
    let yG = r * (sin(N.radians) * cos((v + w).radians) + cos(N.radians) * sin((v + w).radians) * cos(i.radians))
    let zG = r * (sin((v + w).radians) * sin(i.radians))
    // equatorial coordinates
    let ecl = sunAxialTilt(for: d)
    let xE = xG
    let yE = yG * cos(ecl.radians) - zG * sin(ecl.radians)
    let zE = yG * sin(ecl.radians) + zG * cos(ecl.radians)
    //right scension
    var rA = atan2(yE, xE)
    rA = rA.degrees
    // declinatino
    var dec = atan2(zE, sqrt(xE * xE + yE * yE) )
    dec = dec.degrees
    // geocentric distance
    let rG = sqrt(xE * xE + yE * yE + zE * zE)
    return (declination: dec, RA: rA, distance: rG)
  }
}

Astronomy.moonPosition(on: Date().greenwich)