Class: Ephemeris

Inherits:
Object
  • Object
show all
Defined in:
lib/ephemeris.rb

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(date, lat, lon, tz) ⇒ Ephemeris

Returns a new instance of Ephemeris.



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# File 'lib/ephemeris.rb', line 165

def initialize (date, lat, lon, tz)
  pi      = Math::PI

  def get_vars(body) # GET VARIABLES FOR THE BODY
    b = @body[body]
    return b["N"], b["i"], b["w"], b["a"], b["e"], b["M"]
  end

  def body_calc(body) # CALCULATE FOR THE BODY
    pi      = Math::PI
    n_b, i_b, w_b, a_b, e_b, m_b = self.get_vars(body)
    w_b     = (w_b + 360) % 360
    m_b     = m_b % 360
    e1      = m_b + (180/pi) * e_b * Math.sin(m_b.deg) * (1 + e_b*Math.cos(m_b.deg))
    e0      = 0
    while (e1 - e0).abs > 0.0005
      e0    = e1
      e1    = e0 - (e0 - (180/pi) * e_b * Math.sin(e0.deg) - m_b) / (1 - e_b * Math.cos(e0.deg))
    end
    e       = e1
    x       = a_b * (Math.cos(e.deg) - e_b)
    y       = a_b * Math.sqrt(1 - e_b*e_b) * Math.sin(e.deg)
    r       = Math.sqrt(x*x + y*y)
    v       = (Math.atan2(y, x)*180/pi + 360) % 360
    xeclip  = r * (Math.cos(n_b.deg) * Math.cos((v+w_b).deg) - Math.sin(n_b.deg) * Math.sin((v+w_b).deg) * Math.cos(i_b.deg))
    yeclip  = r * (Math.sin(n_b.deg) * Math.cos((v+w_b).deg) + Math.cos(n_b.deg) * Math.sin((v+w_b).deg) * Math.cos(i_b.deg))
    zeclip  = r * Math.sin((v+w_b).deg) * Math.sin(i_b.deg)
    lon     =  (Math.atan2(yeclip, xeclip)*180/pi + 360) % 360
    lat     =  Math.atan2(zeclip, Math.sqrt(xeclip*xeclip + yeclip*yeclip))*180/pi
    r_b     =  Math.sqrt(xeclip*xeclip + yeclip*yeclip + zeclip*zeclip)
    m_J     = @body["jupiter"]["M"] 
    m_S     = @body["saturn"]["M"] 
    m_U     = @body["uranus"]["M"] 
    plon    = 0
    plat    = 0
    pdist   = 0
    case body
    when "moon"
      lb     = (n_b + w_b + m_b) % 360
      db     = (lb - @ls + 360) % 360
      fb     = (lb - n_b + 360) % 360
      plon  += -1.274 * Math.sin((m_b - 2*db).deg)
      plon  +=  0.658 * Math.sin((2*db).deg)
      plon  += -0.186 * Math.sin(@ms.deg)
      plon  += -0.059 * Math.sin((2*m_b - 2*db).deg)
      plon  += -0.057 * Math.sin((m_b - 2*db + @ms).deg)
      plon  +=  0.053 * Math.sin((m_b + 2*db).deg)
      plon  +=  0.046 * Math.sin((2*db - @ms).deg)
      plon  +=  0.041 * Math.sin((m_b - @ms).deg)
      plon  += -0.035 * Math.sin(db.deg)
      plon  += -0.031 * Math.sin((m_b + @ms).deg)
      plon  += -0.015 * Math.sin((2*fb - 2*db).deg)
      plon  +=  0.011 * Math.sin((m_b - 4*db).deg)
      plat  += -0.173 * Math.sin((fb - 2*db).deg)
      plat  += -0.055 * Math.sin((m_b - fb - 2*db).deg)
      plat  += -0.046 * Math.sin((m_b + fb - 2*db).deg)
      plat  +=  0.033 * Math.sin((fb + 2*db).deg)
      plat  +=  0.017 * Math.sin((2*m_b + fb).deg)
      pdist += -0.58  * Math.cos((m_b - 2*db).deg)
      pdist += -0.46  * Math.cos(2*db.deg)
    when "jupiter"
      plon  += -0.332 * Math.sin((2*m_J - 5*m_S - 67.6).deg)
      plon  += -0.056 * Math.sin((2*m_J - 2*m_S + 21).deg)
      plon  +=  0.042 * Math.sin((3*m_J - 5*m_S + 21).deg)
      plon  += -0.036 * Math.sin((m_J - 2*m_S).deg)
      plon  +=  0.022 * Math.cos((m_J - m_S).deg)
      plon  +=  0.023 * Math.sin((2*m_J - 3*m_S + 52).deg)
      plon  += -0.016 * Math.sin((m_J - 5*m_S - 69).deg)
    when "saturn"
      plon  +=  0.812 * Math.sin((2*m_J - 5*m_S - 67.6).deg)
      plon  += -0.229 * Math.cos((2*m_J - 4*m_S - 2).deg)
      plon  +=  0.119 * Math.sin((m_J - 2*m_S - 3).deg)
      plon  +=  0.046 * Math.sin((2*m_J - 6*m_S - 69).deg)
      plon  +=  0.014 * Math.sin((m_J - 3*m_S + 32).deg)
      plat  += -0.020 * Math.cos((2*m_J - 4*m_S - 2).deg)
      plat  +=  0.018 * Math.sin((2*m_J - 6*m_S - 49).deg)
    when "uranus"
      plon  +=  0.040 * Math.sin((m_S - 2*m_U + 6).deg)
      plon  +=  0.035 * Math.sin((m_S - 3*m_U + 33).deg)
      plon  += -0.015 * Math.sin((m_J - m_U + 20).deg)
    end
    lon   += plon
    lat   += plat
    r_b   += pdist
    if body == "moon"
      xeclip  = Math.cos(lon.deg) * Math.cos(lat.deg)
      yeclip  = Math.sin(lon.deg) * Math.cos(lat.deg)
      zeclip  = Math.sin(lat.deg)
    else
      xeclip += @xs
      yeclip += @ys
    end
    xequat  = xeclip
    yequat  = yeclip * Math.cos(@ecl.deg) - zeclip * Math.sin(@ecl.deg)
    zequat  = yeclip * Math.sin(@ecl.deg) + zeclip * Math.cos(@ecl.deg)
    ra      = (Math.atan2(yequat, xequat)*180/pi + 360) % 360
    dec     = Math.atan2(zequat, Math.sqrt(xequat*xequat + yequat*yequat))*180/pi
    body   == "moon" ? par = Math.asin(1/r_b)*180/pi : par = (8.794/3600)/r_b
    gclat   = @lat - 0.1924 * Math.sin(2*@lat.deg)
    rho     = 0.99833 + 0.00167 * Math.cos(2*@lat.deg)
    lst     = @sidtime * 15
    ha      = (lst - ra + 360) % 360
    g       = Math.atan(Math.tan(gclat.deg) / Math.cos(ha.deg))*180/pi
    topRA   = ra  - par * rho * Math.cos(gclat.deg) * Math.sin(ha.deg) / Math.cos(dec.deg)
    topDecl = dec - par * rho * Math.sin(gclat.deg) * Math.sin((g - dec).deg) / Math.sin(g.deg)
    ra      = topRA.round(4)
    dec     = topDecl.round(4)
    r       = Math.sqrt(xequat*xequat + yequat*yequat + zequat*zequat).round(4)
    ri, tr, se = self.rts(ra, dec)
    object  = [ra, dec, r, self.hms_dms(ra, dec), ri, tr, se].flatten
    return object
  end
    
  # START OF INITIALIZE
  @lat   = lat
  @lon   = lon
  @tz    = tz
  y      = date[0..3].to_i
  m      = date[5..6].to_i
  d      = date[8..9].to_i
  @d     = 367*y - 7*(y + (m+9)/12) / 4 + 275*m/9 + d - 730530
  @ecl   = 23.439279444 - 46.8150/3600*(@d/36525) - 0.00059/3600*(@d/36525)**2 + 0.001813/3600*(@d/36525)**3

  self.body_data

  # SUN
  n_s, i_s, w_s, a_s, e_s, m_s = self.get_vars("sun")
  w_s      = (w_s + 360) % 360
  @ms      = m_s % 360
  es       = @ms + (180/pi) * e_s * Math.sin(@ms.deg) * (1 + e_s*Math.cos(@ms.deg))
  x        = Math.cos(es.deg) - e_s
  y        = Math.sin(es.deg) * Math.sqrt(1 - e_s*e_s)
  v        = Math.atan2(y,x)*180/pi
  r        = Math.sqrt(x*x + y*y)
  tlon     = (v + w_s)%360
  @xs      = r * Math.cos(tlon.deg)
  @ys      = r * Math.sin(tlon.deg)
  xe       = @xs
  ye       = @ys * Math.cos(@ecl.deg)
  ze       = @ys * Math.sin(@ecl.deg)
  r        = Math.sqrt(xe*xe + ye*ye + ze*ze)
  ra       = Math.atan2(ye,xe)*180/pi
  ra_s     = ((ra + 360)%360).round(4)
  dec_s    = (Math.atan2(ze,Math.sqrt(xe*xe + ye*ye))*180/pi).round(4)

  @ls      = (w_s + @ms)%360
  gmst0   = (@ls + 180)/15%24
  @sidtime = gmst0 + @lon/15 
  
  @alt_s, @az_s = self.alt_az(ra_s, dec_s, @sidtime)

  @sun     = [ra_s, dec_s, 1.0, self.hms_dms(ra_s, dec_s)].flatten 
  @moon    = self.body_calc("moon")
  @mercury = self.body_calc("mercury")
  @venus   = self.body_calc("venus")
  @mars    = self.body_calc("mars")
  @jupiter = self.body_calc("jupiter")
  @saturn  = self.body_calc("saturn")
  @uranus  = self.body_calc("uranus")
  @neptune = self.body_calc("neptune")

end

Instance Attribute Details

#jupiter ⇒ Object (readonly)

Returns the value of attribute jupiter.



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# File 'lib/ephemeris.rb', line 19

def jupiter
  @jupiter
end

#mars ⇒ Object (readonly)

Returns the value of attribute mars.



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# File 'lib/ephemeris.rb', line 19

def mars
  @mars
end

#mercury ⇒ Object (readonly)

Returns the value of attribute mercury.



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# File 'lib/ephemeris.rb', line 19

def mercury
  @mercury
end

#moon ⇒ Object (readonly)

Returns the value of attribute moon.



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# File 'lib/ephemeris.rb', line 19

def moon
  @moon
end

#neptune ⇒ Object (readonly)

Returns the value of attribute neptune.



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# File 'lib/ephemeris.rb', line 19

def neptune
  @neptune
end

#saturn ⇒ Object (readonly)

Returns the value of attribute saturn.



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# File 'lib/ephemeris.rb', line 19

def saturn
  @saturn
end

#sun ⇒ Object (readonly)

Returns the value of attribute sun.



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# File 'lib/ephemeris.rb', line 19

def sun
  @sun
end

#uranus ⇒ Object (readonly)

Returns the value of attribute uranus.



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# File 'lib/ephemeris.rb', line 19

def uranus
  @uranus
end

#venus ⇒ Object (readonly)

Returns the value of attribute venus.



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# File 'lib/ephemeris.rb', line 19

def venus
  @venus
end

Instance Method Details

#alt_az(ra, dec, time) ⇒ Object 



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# File 'lib/ephemeris.rb', line 96

def alt_az(ra, dec, time)
  pi      = Math::PI
  ra_h = ra/15
  #ha   = (@sidtime - ra_h)*15
  ha   = (time - ra_h)*15
  x    = Math.cos(ha.deg) * Math.cos(dec.deg)
  y    = Math.sin(ha.deg) * Math.cos(dec.deg)
  z    = Math.sin(dec.deg)
  xhor = x * Math.sin(@lat.deg) - z * Math.cos(@lat.deg)
  yhor = y
  zhor = x * Math.cos(@lat.deg) + z * Math.sin(@lat.deg)
  az   = Math.atan2(yhor, xhor)*180/pi + 180
  alt  = Math.asin(zhor)*180/pi
  return alt, az
end

#body_alt_az(body, time) ⇒ Object 



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# File 'lib/ephemeris.rb', line 112

def body_alt_az(body, time)
  self.alt_az(self.body_calc(body)[0], self.body_calc(body)[1], time)
end

#body_calc(body) ⇒ Object

CALCULATE FOR THE BODY



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# File 'lib/ephemeris.rb', line 173

def body_calc(body) # CALCULATE FOR THE BODY
  pi      = Math::PI
  n_b, i_b, w_b, a_b, e_b, m_b = self.get_vars(body)
  w_b     = (w_b + 360) % 360
  m_b     = m_b % 360
  e1      = m_b + (180/pi) * e_b * Math.sin(m_b.deg) * (1 + e_b*Math.cos(m_b.deg))
  e0      = 0
  while (e1 - e0).abs > 0.0005
    e0    = e1
    e1    = e0 - (e0 - (180/pi) * e_b * Math.sin(e0.deg) - m_b) / (1 - e_b * Math.cos(e0.deg))
  end
  e       = e1
  x       = a_b * (Math.cos(e.deg) - e_b)
  y       = a_b * Math.sqrt(1 - e_b*e_b) * Math.sin(e.deg)
  r       = Math.sqrt(x*x + y*y)
  v       = (Math.atan2(y, x)*180/pi + 360) % 360
  xeclip  = r * (Math.cos(n_b.deg) * Math.cos((v+w_b).deg) - Math.sin(n_b.deg) * Math.sin((v+w_b).deg) * Math.cos(i_b.deg))
  yeclip  = r * (Math.sin(n_b.deg) * Math.cos((v+w_b).deg) + Math.cos(n_b.deg) * Math.sin((v+w_b).deg) * Math.cos(i_b.deg))
  zeclip  = r * Math.sin((v+w_b).deg) * Math.sin(i_b.deg)
  lon     =  (Math.atan2(yeclip, xeclip)*180/pi + 360) % 360
  lat     =  Math.atan2(zeclip, Math.sqrt(xeclip*xeclip + yeclip*yeclip))*180/pi
  r_b     =  Math.sqrt(xeclip*xeclip + yeclip*yeclip + zeclip*zeclip)
  m_J     = @body["jupiter"]["M"] 
  m_S     = @body["saturn"]["M"] 
  m_U     = @body["uranus"]["M"] 
  plon    = 0
  plat    = 0
  pdist   = 0
  case body
  when "moon"
    lb     = (n_b + w_b + m_b) % 360
    db     = (lb - @ls + 360) % 360
    fb     = (lb - n_b + 360) % 360
    plon  += -1.274 * Math.sin((m_b - 2*db).deg)
    plon  +=  0.658 * Math.sin((2*db).deg)
    plon  += -0.186 * Math.sin(@ms.deg)
    plon  += -0.059 * Math.sin((2*m_b - 2*db).deg)
    plon  += -0.057 * Math.sin((m_b - 2*db + @ms).deg)
    plon  +=  0.053 * Math.sin((m_b + 2*db).deg)
    plon  +=  0.046 * Math.sin((2*db - @ms).deg)
    plon  +=  0.041 * Math.sin((m_b - @ms).deg)
    plon  += -0.035 * Math.sin(db.deg)
    plon  += -0.031 * Math.sin((m_b + @ms).deg)
    plon  += -0.015 * Math.sin((2*fb - 2*db).deg)
    plon  +=  0.011 * Math.sin((m_b - 4*db).deg)
    plat  += -0.173 * Math.sin((fb - 2*db).deg)
    plat  += -0.055 * Math.sin((m_b - fb - 2*db).deg)
    plat  += -0.046 * Math.sin((m_b + fb - 2*db).deg)
    plat  +=  0.033 * Math.sin((fb + 2*db).deg)
    plat  +=  0.017 * Math.sin((2*m_b + fb).deg)
    pdist += -0.58  * Math.cos((m_b - 2*db).deg)
    pdist += -0.46  * Math.cos(2*db.deg)
  when "jupiter"
    plon  += -0.332 * Math.sin((2*m_J - 5*m_S - 67.6).deg)
    plon  += -0.056 * Math.sin((2*m_J - 2*m_S + 21).deg)
    plon  +=  0.042 * Math.sin((3*m_J - 5*m_S + 21).deg)
    plon  += -0.036 * Math.sin((m_J - 2*m_S).deg)
    plon  +=  0.022 * Math.cos((m_J - m_S).deg)
    plon  +=  0.023 * Math.sin((2*m_J - 3*m_S + 52).deg)
    plon  += -0.016 * Math.sin((m_J - 5*m_S - 69).deg)
  when "saturn"
    plon  +=  0.812 * Math.sin((2*m_J - 5*m_S - 67.6).deg)
    plon  += -0.229 * Math.cos((2*m_J - 4*m_S - 2).deg)
    plon  +=  0.119 * Math.sin((m_J - 2*m_S - 3).deg)
    plon  +=  0.046 * Math.sin((2*m_J - 6*m_S - 69).deg)
    plon  +=  0.014 * Math.sin((m_J - 3*m_S + 32).deg)
    plat  += -0.020 * Math.cos((2*m_J - 4*m_S - 2).deg)
    plat  +=  0.018 * Math.sin((2*m_J - 6*m_S - 49).deg)
  when "uranus"
    plon  +=  0.040 * Math.sin((m_S - 2*m_U + 6).deg)
    plon  +=  0.035 * Math.sin((m_S - 3*m_U + 33).deg)
    plon  += -0.015 * Math.sin((m_J - m_U + 20).deg)
  end
  lon   += plon
  lat   += plat
  r_b   += pdist
  if body == "moon"
    xeclip  = Math.cos(lon.deg) * Math.cos(lat.deg)
    yeclip  = Math.sin(lon.deg) * Math.cos(lat.deg)
    zeclip  = Math.sin(lat.deg)
  else
    xeclip += @xs
    yeclip += @ys
  end
  xequat  = xeclip
  yequat  = yeclip * Math.cos(@ecl.deg) - zeclip * Math.sin(@ecl.deg)
  zequat  = yeclip * Math.sin(@ecl.deg) + zeclip * Math.cos(@ecl.deg)
  ra      = (Math.atan2(yequat, xequat)*180/pi + 360) % 360
  dec     = Math.atan2(zequat, Math.sqrt(xequat*xequat + yequat*yequat))*180/pi
  body   == "moon" ? par = Math.asin(1/r_b)*180/pi : par = (8.794/3600)/r_b
  gclat   = @lat - 0.1924 * Math.sin(2*@lat.deg)
  rho     = 0.99833 + 0.00167 * Math.cos(2*@lat.deg)
  lst     = @sidtime * 15
  ha      = (lst - ra + 360) % 360
  g       = Math.atan(Math.tan(gclat.deg) / Math.cos(ha.deg))*180/pi
  topRA   = ra  - par * rho * Math.cos(gclat.deg) * Math.sin(ha.deg) / Math.cos(dec.deg)
  topDecl = dec - par * rho * Math.sin(gclat.deg) * Math.sin((g - dec).deg) / Math.sin(g.deg)
  ra      = topRA.round(4)
  dec     = topDecl.round(4)
  r       = Math.sqrt(xequat*xequat + yequat*yequat + zequat*zequat).round(4)
  ri, tr, se = self.rts(ra, dec)
  object  = [ra, dec, r, self.hms_dms(ra, dec), ri, tr, se].flatten
  return object
end

#body_data ⇒ Object 



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# File 'lib/ephemeris.rb', line 21

def body_data
@body = {
"sun" => {
  "N" => 0.0,
  "i" => 0.0,
  "w" => 282.9404 + 4.70935e-5 * @d,
  "a" => 1.000000,
  "e" => 0.016709 - 1.151e-9 * @d,
  "M" => 356.0470 + 0.9856002585 * @d},
"moon" => {
  "N" => 125.1228 - 0.0529538083 * @d,
  "i" => 5.1454,
  "w" => 318.0634 + 0.1643573223 * @d,
  "a" => 60.2666, 
  "e" => 0.054900,
  "M" => 115.3654 + 13.0649929509 * @d},
"mercury" => {
  "N" => 48.3313 + 3.24587e-5 * @d,
  "i" => 7.0047 + 5.00e-8 * @d,
  "w" => 29.1241 + 1.01444e-5 * @d,
  "a" => 0.387098,  
  "e" => 0.205635 + 5.59e-10 * @d,
  "M" => 168.6562 + 4.0923344368 * @d},
"venus" => {
  "N" => 76.6799 + 2.46590e-5 * @d,
  "i" => 3.3946 + 2.75e-8 * @d,
  "w" => 54.8910 + 1.38374e-5 * @d,
  "a" => 0.723330,
  "e" => 0.006773 - 1.302e-9 * @d,
  "M" => 48.0052 + 1.6021302244 * @d},
"mars" => {
  "N" => 49.5574 + 2.11081e-5 * @d,
  "i" => 1.8497 - 1.78e-8 * @d,
  "w" => 286.5016 + 2.92961e-5 * @d,
  "a" => 1.523688,
  "e" => 0.093405 + 2.516e-9 * @d,
  "M" => 18.6021 + 0.5240207766 * @d},
"jupiter" => {
  "N" => 100.4542 + 2.76854e-5 * @d,
  "i" => 1.3030 - 1.557e-7 * @d,
  "w" => 273.8777 + 1.64505e-5 * @d,
  "a" => 5.20256,
  "e" => 0.048498 + 4.469e-9 * @d,
  "M" => 19.8950 + 0.0830853001 * @d},
"saturn" => {
  "N" => 113.6634 + 2.38980e-5 * @d,
  "i" => 2.4886 - 1.081e-7 * @d,
  "w" => 339.3939 + 2.97661e-5 * @d,
  "a" => 9.55475,
  "e" => 0.055546 - 9.499e-9 * @d,
  "M" => 316.9670 + 0.0334442282 * @d},
"uranus" => {
  "N" => 74.0005 + 1.3978e-5 * @d,
  "i" => 0.7733 + 1.9e-8 * @d,
  "w" => 96.6612 + 3.0565e-5 * @d,
  "a" => 19.18171 - 1.55e-8 * @d,
  "e" => 0.047318 + 7.45e-9 * @d,
  "M" => 142.5905 + 0.011725806 * @d},
"neptune" => {
  "N" => 131.7806 + 3.0173e-5 * @d,
  "i" => 1.7700 - 2.55e-7 * @d,
  "w" => 272.8461 - 6.027e-6 * @d,
  "a" => 30.05826 + 3.313e-8 * @d,
  "e" => 0.008606 + 2.15e-9 * @d,
  "M" => 260.2471 + 0.005995147 * @d}}
end

#distf(d) ⇒ Object 



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# File 'lib/ephemeris.rb', line 139

def distf(d)
  int = d.to_i.to_s.rjust(2)
  f   = d % 1
  frc = "%.4f" % f
  return int + frc[1..5]
end

#get_vars(body) ⇒ Object

GET VARIABLES FOR THE BODY



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# File 'lib/ephemeris.rb', line 168

def get_vars(body) # GET VARIABLES FOR THE BODY
  b = @body[body]
  return b["N"], b["i"], b["w"], b["a"], b["e"], b["M"]
end

#hms_dms(ra, dec) ⇒ Object

Show HMS & DMS



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# File 'lib/ephemeris.rb', line 88

def hms_dms(ra, dec) # Show HMS & DMS
  h, m, s = (ra/15).hms
  ra_hms  = "#{h.to_s.rjust(2)}h #{m.to_s.rjust(2)}m #{s.to_s.rjust(2)}s"
  d, m, s = dec.hms
  dec_dms = "#{d.to_s.rjust(3)}° #{m.to_s.rjust(2)}´ #{s.to_s.rjust(2)}˝"
  return ra_hms, dec_dms
end

#print ⇒ Object 



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# File 'lib/ephemeris.rb', line 137

def print

  def distf(d)
    int = d.to_i.to_s.rjust(2)
    f   = d % 1
    frc = "%.4f" % f
    return int + frc[1..5]
  end

  out   = "Planet  │ RA          │ Dec          │ Dist. │ Rise  │ Trans │ Set   \n"
  out  += "────────┼─────────────┼──────────────┼───────┼───────┼───────┼────── \n"

  #["sun", "moon", "mercury", "venus", "mars", "jupiter", "saturn", "uranus", "neptune"].each do |p|
  ["mercury", "venus", "mars", "jupiter", "saturn", "uranus", "neptune"].each do |p|
    o     = self.body_calc(p)
    n_o   = (p[0].upcase + p[1..]).ljust(7)
    ra_o  = o[3].ljust(11)
    dec_o = o[4].ljust(12)
    d_o   = distf(o[2])[0..-3]
    ris_o = o[5][0..-4].rjust(5)
    tra_o = o[6][0..-4].rjust(5)
    set_o = o[7][0..-4].rjust(5)

    out  += "#{n_o } │ #{ra_o    } │ #{dec_o    } │ #{d_o } │ #{ris_o} │ #{tra_o} │ #{set_o} \n"
  end
  return out
end

#rts(ra, dec) ⇒ Object 



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# File 'lib/ephemeris.rb', line 116

def rts(ra, dec)
  pi      = Math::PI
  transit = (ra - @ls - @lon)/15 + 12 + @tz
  transit = (transit + 24) % 24
  cos_lha = (-Math.sin(@lat.deg) * Math.sin(dec.deg)) / (Math.cos(@lat.deg) * Math.cos(dec.deg))
  if cos_lha < -1
    rise  = "always"
    set   = "never"
  elsif cos_lha > 1
    rise  = "never"
    set   = "always"
  else
    lha   = Math.acos(cos_lha) * 180/pi
    lha_h = lha/15
    rise  = ((transit - lha_h + 24) % 24).to_hms
    set   = ((transit + lha_h + 24) % 24).to_hms
  end
  trans = transit.to_hms
  return rise, trans, set
end