Degenerate Conic

Julian Date

Julian date is a count of the number of days since noon on January 1, 4713 BC in the proleptic Julian calendar. This epoch was chosen by Joseph Scaliger in 1583 as the start of the "Julian Period": a 7,980 year period that is the multiple of the 19-year Metonic cycle, the 28-year solar/dominical cycle, and the 15-year indiction cycle. It is a conveniently-located epoch since it precedes all written history. A simple Fortran function for computing Julian date given the Gregorian calendar year, month, day, and time is:

function julian_date(y,m,d,hour,minute,sec)

use, intrinsic :: iso_fortran_env, only: wp => real64

implicit none

real(wp) :: julian_date
integer,intent(in) :: y,m,d ! Gregorian year, month, day
integer,intent(in) :: hour,minute,sec ! Time of day

integer :: julian_day_num

julian_day_num = d-32075+1461*(y+4800+(m-14)/12)/4+367*&
                 (m-2-(m-14)/12*12)/12-3*((y+4900+(m-14)/12)/100)/4

julian_date = real(julian_day_num,wp) + &
              (hour-12.0_wp)/24.0_wp + &
              minute/1440.0_wp + &
              sec/86400.0_wp

end function julian_date

References

1. "Converting Between Julian Dates and Gregorian Calendar Dates", United States Naval Observatory.
2. D. Steel, "Marking Time: The Epic Quest to Invent the Perfect Calendar", John Wiles & Sons, 2000.

Computus

The Computus is the algorithm for the calculation of the date of Easter. The following is a simple Fortran subroutine of the Computus, using the "Meeus/Jones/Butcher" Gregorian Easter algorithm. Note that this subroutine makes use of Fortran integer division.

subroutine easter(year,month,day)
!Compute the date of Gregorian Easter,
! using the "Meeus/Jones/Butcher" algorithm

implicit none

integer,intent(in) :: year
integer,intent(out) :: month,day

integer :: a,b,c,d,e,f,g,h,i,k,l,m

a = mod(year,19)
b = year/100
c = mod(year,100)
d = b/4
e = mod(b,4)
f = (b+8)/25
g = (b-f+1)/3
h = mod((19*a+b-d-g+15),30)
i = c/4
k = mod(c,4)
l = mod((32+2*e+2*i-h-k),7)
m = (a+11*h+22*l)/451
month = (h+l-7*m+114)/31
day = mod(h+l-7*m+114,31)+1

end subroutine easter

The sequence of dates repeat themselves over a cycle of 5,700,000 years. The following histogram shows the percentage occurrence of each date (from March 22nd to April 25th), over the entire cycle:

See also

1. D. Steel, "Marking Time: The Epic Quest to Invent the Perfect Calendar", Wiley, 1999.
2. J. R. Stockton, "The Calculation of Easter Sunday after the Book of Common Prayer of the Church of England".