2. Julian Day Number

2. Julian Day Number

For the calculation of calendars such as the Myanmar calendar, it is convenient to calculate based on number of days. When counting the number of days, it is necessary to define a starting date called epoch. A popular day counting system used by astronomers is Julian Day Number (JDN). Julian Day Number is the day count starting from noon November 24, 4714 BC in the Gregorian calendar. A method to calculate Julian Day Number from a Gregorian date [UTSA, 2011] is shown below. The operation called floor takes the integer part of a number and discards its decimal part. For example, the result of floor(3.2)=⌊3.2⌋ is 3.

a = ⌊(14 − month / 12)⌋
y= year + 4800 − a
m = month + (12 * a) − 3
jdn = day + ⌊(153 * m  + 2) / 5⌋ + (365 * y) + ⌊(y / 4)⌋ −⌊(y / 100)⌋ + ⌊(y / 400)⌋ − 32045

where jdn = Julian Day Number.

A method which can be used to convert a Julian Day Number to the corresponding Gregorian date [Myers, 2011] is also shown below.

j = j − 1721119
y = ⌊( 4 * j − 1) / 146097⌋
j = 4 * j − 1 − 146097 * y
d = ⌊j / 4⌋
j = ⌊(4 * d + 3) / 1461⌋
d = 4 * d + 3 − 1461 * j
d = ⌊d + 4 / 4⌋
m = ⌊(5 * d − 3) / 153⌋
d = 5 * d − 3 − 153 * m
d = ⌊(d + 5) /5⌋
y = (100 * y )+ j
if m < 10 then
m = m + 3
else
m = m − 9
y = y + 1
end if

where y = year; m = month; d= day; j = Julian Day Number.

Example: Find the Julian Day Number for 2000 CE January 1.year = 2000 Solution:

year = 2000
month = 1
day = 1
a = floor((14-month)/12) = 1
y = year+4800-a = 2000+4800-1 = 6799
m = month+12a-3 = 1+12-3 = 10
jdn = 1+306+365*6799+1699-67+16-32045
= 2451545

The Julian Day Number (JDN) is obtained as 2451545.