# UTC.txt, 29 May 11

!title UTC

!fuzz 0.000001

!msgpostfix \n

86400.0      | Seconds in a solar day (actual)
86400.0002   | Seconds in a solar day (estimated)
86164.09053  | Seconds in a sidereal day
23.93447     | Hours in a sidereal day
0.99726957   | SI days in a siderial day
86164.09890  | Seconds in a stellar day

1.002737923  | Relative speed of sidereal and solar time

354.37       | Days in mean year in lunar calendars
365.24219    | Days in mean tropical year near the year 2000
365.2424     | Days in vernal equinox year
365.2425     | Days in mean year in the Gregorian calendar
365.25       | Days in mean year in the Julian calendar
365.2564     | Days a sidereal year
365.242198781 | Days in tropical year B1900

27.3217      | Days in sidereal month
29.53059     | Days in mean synodic month
30.436875    | Days in mean length of a Gregorian calendar month

# Astronomical Algorithms by J. Meeus is a source for claim that
# adding 0.0001 mitigates against rounding error
30.6001      | Average days in month ignoring Jan/Feb (adding 0.0001 to avoid rounding error)

36525.0      | Days per Julian century

2305813.5    | Julian date for 1601-01-01 00:00:00
2415021.0    | Julian date of 1 Jan 1900
2440587.5    | Julian date for 1970-01-01 00:00:00
2451544.5    | Julian date for 2000-01-01 00:00:00

2400000.5    | Julian Date of Modified Julian Date zero
51544.5      | Reference epoch (J2000.0), Modified Julian Date

2415020.313   | Julian date of 1 Jan 1900 Besselian Epoch (1992 Supplement to the Astronomical Almanac)
2433282.423   | Julian date of 1 Jan 1950 Besselian Epoch (1992 Supplement to the Astronomical Almanac)
# 2415019.81352 | Besselian date of 1 Jan 1900 (2009 IAU SOFA Review board)

1900.000858   | Julian epoch for B1900.0
1949.999790   | Julian epoch for B1950.0
1999.998723   | Julian epoch for B2000.0

1899.999142   | Besselian epoch for J1900.0
2000.001278   | Besselian epoch for J2000.0

7.2921159e-5 | Angular rotation of the Earth in radians per second


!msgpostfix  Julian date on which a leap second was added\n

2437300.5  | 1961 Jan  1
2437512.5  | 1961 Aug  1
2437665.5  | 1962 Jan  1
2438334.5  | 1963 Nov  1
2438395.5  | 1964 Jan  1
2438486.5  | 1964 Apr  1
2438639.5  | 1964 Sep  1
2438761.5  | 1965 Jan  1
2438820.5  | 1965 Mar  1
2438942.5  | 1965 Jul  1
2439004.5  | 1965 Sep  1
2439126.5  | 1966 Jan  1
2439887.5  | 1968 Feb  1
2441317.5  | 1972 Jan  1,  10.0
2441499.5  | 1972 Jul  1,  11.0
2441683.5  | 1973 Jan  1,  12.0
2442048.5  | 1974 Jan  1,  13.0
2442413.5  | 1975 Jan  1,  14.0
2442778.5  | 1976 Jan  1,  15.0
2443144.5  | 1977 Jan  1,  16.0
2443509.5  | 1978 Jan  1,  17.0
2443874.5  | 1979 Jan  1,  18.0
2444239.5  | 1980 Jan  1,  19.0
2444786.5  | 1981 Jul  1,  20.0
2445151.5  | 1982 Jul  1,  21.0
2445516.5  | 1983 Jul  1,  22.0
2446247.5  | 1985 Jul  1,  23.0
2447161.5  | 1988 Jan  1,  24.0
2447892.5  | 1990 Jan  1,  25.0
2448257.5  | 1991 Jan  1,  26.0
2448804.5  | 1992 Jul  1,  27.0
2449169.5  | 1993 Jul  1,  28.0
2449534.5  | 1994 Jul  1,  29.0
2450083.5  | 1996 Jan  1,  30.0
2450630.5  | 1997 Jul  1,  31.0
2451179.5  | 1999 Jan  1,  32.0
2453736.5  | 2006 Jan  1,  33.0
2454832.5  | 2009 Jan  1,  34.0


!msgpostfix  Modified Julian date on which a leap second was added\n

37300.0  | 1961 Jan  1
37512.0  | 1961 Aug  1
37665.0  | 1962 Jan  1
38334.0  | 1963 Nov  1
38395.0  | 1964 Jan  1
38486.0  | 1964 Apr  1
38639.0  | 1964 Sep  1
38761.0  | 1965 Jan  1
38820.0  | 1965 Mar  1
38942.0  | 1965 Jul  1
39004.0  | 1965 Sep  1
39126.0  | 1966 Jan  1
39887.0  | 1968 Feb  1
41317.0  | 1972 Jan  1,  10.0
41499.0  | 1972 Jul  1,  11.0
41683.0  | 1973 Jan  1,  12.0
42048.0  | 1974 Jan  1,  13.0
42413.0  | 1975 Jan  1,  14.0
42778.0  | 1976 Jan  1,  15.0
43144.0  | 1977 Jan  1,  16.0
43509.0  | 1978 Jan  1,  17.0
43874.0  | 1979 Jan  1,  18.0
44239.0  | 1980 Jan  1,  19.0
44786.0  | 1981 Jul  1,  20.0
45151.0  | 1982 Jul  1,  21.0
45516.0  | 1983 Jul  1,  22.0
46247.0  | 1985 Jul  1,  23.0
47161.0  | 1988 Jan  1,  24.0
47892.0  | 1990 Jan  1,  25.0
48257.0  | 1991 Jan  1,  26.0
48804.0  | 1992 Jul  1,  27.0
49169.0  | 1993 Jul  1,  28.0
49534.0  | 1994 Jul  1,  29.0
50083.0  | 1996 Jan  1,  30.0
50630.0  | 1997 Jul  1,  31.0
51179.0  | 1999 Jan  1,  32.0
53736.0  | 2006 Jan  1,  33.0
54832.0  | 2009 Jan  1,  34.0

!msgpostfix \n

134774.0      | Days between January 1, 1601 and January 1, 1970\n
11644473600.0 | Seconds between January 1, 1601 and January 1, 1970\n

2145859200.0  | Maximum Unix time 12/31/2037

!msgpostfix Calculate Besselian date from Julian date
# 1900.0 + (Julian date - 2415020.31352) / 365.242198781

!need all
    1900.0
-2415020.31352
     365.242198781


!msgpostfix Compute Year/Month/Day from Julian day number\n

!need all
#0.5
-1867216.25
   36524.25
#1524
-122.1
 365.25
  30.6001 
#-4716
#-4715


# JD = D + (153 * M - 457) \ 5 + 365 * Y + [Y / 4] - [Y / 100] + [Y / 400] + 1721118.5
!msgpostfix Convert a Gregorian date to a Julian date\n

!need all
    153.0
-   457.0
    365.0
1721118.5

# Astronomical Algorithms,1991, page 61, Jean Meeus gives the algorithm (essentially) as
# JD=FIX(365.25(Y+4716))+FIX(30.6001(m+1))+D+2-FIX(Y/100)+FIX(FIX(Y/100)/4)-1524.5
!msgpostfix Convert a Gregorian date after 1524 to a Julian date (Astronomical Algorithms, J. Meeus)\n

!need all
  365.25
 4716.0
   30.6001
-1524.5

# For dates in the Gregorian calendar at noon,
# The Explanatory Supplement to the Astronomical Almanac,1992, page 604
# the value for the Julian Day Number for a Gregorian Date after November 23, -4713
# JD=(1461*(Y+4800+(M-14)\12))\4+(367*(M-2-12*((M-14)\12)))\12-(3*((Y+4900+(M-14)\12)\100))\4+D-32075
!msgpostfix Convert a Gregorian date after -4713 to a Julian date\n

!need all
  1461.0
  4800.0
   367.0
  4900.0
-32075.0

# A model comparison for daylength as a function of latitude and day of the year.
# Forsythe, William C., Edward J. Rykiel Jr., Randal S. Stahl, Hsin-i Wu and Robert M. Schoolfield.
# Ecological Modeling 80:87-95, 1995.
# The following numbers calculate a value that plugs into another expression
# whose values may not be expressed as floating-point literals, so play safe
# and don't require them to be present.

!msgpostfix Calculate day length at a given latitude\n
!need all
0.39795
0.2163108
0.9671396
0.00860
# 186


# 1960,  1,  1.4178180
# 1961,  1,  1.4228180
# 1961,  8,  1.3728180
# 1962,  1,  1.8458580
# 1963, 11,  1.9458580
# 1964,  1,  3.2401300
# 1964,  4,  3.3401300
# 1964,  9,  3.4401300
# 1965,  1,  3.5401300
# 1965,  3,  3.6401300
# 1965,  7,  3.7401300
# 1965,  9,  3.8401300
# 1966,  1,  4.3131700
# 1968,  2,  4.2131700
!msgpostfix List of Dynamic time delta-T before leap seconds introduced\n

!need all
1.4178180
1.4228180
1.3728180
1.8458580
1.9458580
3.2401300
3.3401300
3.4401300
3.5401300
3.6401300
3.7401300
3.8401300
4.3131700
4.2131700


!msgpostfix Difference between dynamical time and Universal time, since 1955 in 5 year interval\n
!need all

#1955.0
31.1
#1960.0
33.2
#1965.0
35.7
#1970.0
40.2
#1975.0
45.5
#1980.0
50.5
#1985.0
54.3
#1990.0
56.9
#1995.0
60.8
#2000.0
63.8
#2005.0
64.7

!msgpostfix Difference between dynamical time and Universal time, since 1974 in 1 year interval\n
!need all
# 1974
44.4841
# 1975
45.4761
# 1976
46.4567
# 1977
47.5214
# 1978
48.5344
# 1979
49.5861
# 1980
50.5387
# 1981
51.3808
# 1982
52.1668
# 1983
52.9565
# 1984
53.7882
# 1985
54.3427
# 1986
54.8712
# 1987
55.3222
# 1988
55.8197
# 1989
56.3000
# 1990
56.8553
# 1991
57.5653
# 1992
58.3092
# 1993
59.1218
# 1994
59.9845
# 1995
60.7853
# 1996
61.6287
# 1997
62.2950
# 1998
62.9659
# 1999
63.4673
# 2000
63.8285
# 2001
64.0908
# 2002
64.2998
# 2003
64.4734
# 2004
64.5736
# 2005
64.6876
# 2006
64.8452
# 2007
65.1464
# 2008
65.4574
# 2009
65.7768
# 2010
66.0699

