Module: Lunation::Calculation::Timekeeping

Included in:
Lunation::Calculation
Defined in:
lib/lunation/calculation/timekeeping.rb

Constant Summary collapse

SECONDS_PER_DAY = 
86_400
EPOCH_J2000_JDE =

expressed in terms of Julian Ephemeris Day

2_451_545
JULIAN_CENTURY_IN_DAYS = 
36_525.0
DELTA_T_500BC_500AD =

rubocop:disable Layout/LineLength

[10_583.6, -1_014.41, 33.78311, -5.952053, -0.1798452, 0.022174192, 0.0090316521].freeze
DELTA_T_500AD_1600AD = 
[1_574.2, -556.01, 71.23472, 0.319781, -0.8503463, -0.005050998, 0.0083572073].freeze
DELTA_T_1600AD_1700AD = 
[120, -0.9808, -0.01532, 1.fdiv(7_129)].freeze
DELTA_T_1700AD_1800AD = 
[8.83, 0.1603, -0.0059285, 0.00013336, -1.fdiv(1_174_000)].freeze
DELTA_T_1800AD_1860AD = 
[13.72, -0.332447, 0.0068612, 0.0041116, -0.00037436, 0.0000121272, -0.0000001699, 0.000000000875].freeze
DELTA_T_1860AD_1900AD = 
[7.62, 0.5737, -0.251754, 0.01680668, -0.0004473624, 1.fdiv(233_174)].freeze
DELTA_T_1900AD_1920AD = 
[-2.79, 1.494119, -0.0598939, 0.0061966, -0.000197].freeze
DELTA_T_1920AD_1941AD = 
[21.20, 0.84493, -0.076100, 0.0020936].freeze
DELTA_T_1941AD_1961AD = 
[29.07, 0.407, -1.fdiv(233), 1.fdiv(2_547)].freeze
DELTA_T_1961AD_1986AD = 
[45.45, 1.067, -1.fdiv(260), -1.fdiv(718)].freeze
DELTA_T_1986AD_2005AD = 
[63.86, 0.3345, -0.060374, 0.0017275, 0.000651814, 0.00002373599].freeze
DELTA_T_2005AD_2050AD = 
[62.92, 0.32217, 0.005589].freeze

Instance Method Summary collapse

Instance Method Details

#delta_t ⇒ Object

ΔT Difference between Dynamical Time (TD) and Universal Time (UT, more commonly

known as Greenwhich Time).

The formula for ΔT was taken from a later paper written by Espenak and Meeus

(https://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html). ΔT is described less
precisely in the book (A.A. p. 78-79, formulae 10.0 and 10.2).

UNIT: seconds



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# File 'lib/lunation/calculation/timekeeping.rb', line 35

def delta_t
  @delta_t ||= begin
    result = case datetime.year
    when -1_999...-500
      elapsed_years = (@decimal_year - 1_820).fdiv(100)
      -20 + 32 * elapsed_years**2
    when -500...500
      Horner.compute(@decimal_year.fdiv(100), DELTA_T_500BC_500AD)
    when 500...1_600
      Horner.compute((@decimal_year - 1_000.0).fdiv(100), DELTA_T_500AD_1600AD)
    when 1_600...1_700
      Horner.compute(@decimal_year - 1_600.0, DELTA_T_1600AD_1700AD)
    when 1_700...1_800
      Horner.compute(@decimal_year - 1_700.0, DELTA_T_1700AD_1800AD)
    when 1_800...1_860
      Horner.compute(@decimal_year - 1_800, DELTA_T_1800AD_1860AD)
    when 1_860...1_900
      Horner.compute(@decimal_year - 1_860, DELTA_T_1860AD_1900AD)
    when 1_900...1_920
      Horner.compute(@decimal_year - 1_900, DELTA_T_1900AD_1920AD)
    when 1_920...1_941
      Horner.compute(@decimal_year - 1_920, DELTA_T_1920AD_1941AD)
    when 1_941...1_961
      Horner.compute(@decimal_year - 1_950, DELTA_T_1941AD_1961AD)
    when 1_961...1_986
      Horner.compute(@decimal_year - 1_975, DELTA_T_1961AD_1986AD)
    when 1_986...2_005
      Horner.compute(@decimal_year - 2_000, DELTA_T_1986AD_2005AD)
    when 2_005...2_050
      Horner.compute(@decimal_year - 2_000, DELTA_T_2005AD_2050AD)
    when 2_050...2_150
      -20 + 32 * ((@decimal_year - 1_820) / 100)**2 - 0.5628 *
        (2_150 - @decimal_year)
    when 2_150..3_000
      -20 + 32 * @decimal_year**2
    end
    result.round(1)
  end
end

#dynamical_time ⇒ Object

(TD) Dynamical time (A.A. p. 77) UNIT: ISO 8601 Date and time with offset



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# File 'lib/lunation/calculation/timekeeping.rb', line 77

def dynamical_time
  @dynamical_time ||= datetime + delta_t.round.fdiv(SECONDS_PER_DAY)
end

#julian_ephemeris_day ⇒ Object

(JDE) Julian ephemeris day (A.A. p. 59) UNIT: days, expressed as a floating point number



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# File 'lib/lunation/calculation/timekeeping.rb', line 83

def julian_ephemeris_day
  @julian_ephemeris_day ||= dynamical_time.ajd.to_f.round(5)
end

#time ⇒ Object

(T) time, measured in Julian centuries from the Epoch J2000.0 (22.1, A.A. p. 143) UNIT: centuries from the Epoch J2000.0



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# File 'lib/lunation/calculation/timekeeping.rb', line 24

def time
  @time ||=
    (julian_ephemeris_day - EPOCH_J2000_JDE).fdiv(JULIAN_CENTURY_IN_DAYS).round(12)
end

#time_millennia ⇒ Object

(t) time, measured in Julian millennia from the epoch J2000.0 (32.1, A.A. p. 218) UNIT: millennia from the Epoch J2000.0



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# File 'lib/lunation/calculation/timekeeping.rb', line 89

def time_millennia
  @time_millennia ||= time.fdiv(10).round(12)
end

#time_myriads ⇒ Object

(U) Time measured in units of 10_000 Julian years from J2000.0 (A.A. p. 147) UNIT: 10_000 years (myriads) from the Epoch J2000.0



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# File 'lib/lunation/calculation/timekeeping.rb', line 95

def time_myriads
  @time_myriads ||= time.fdiv(100)
end