Julian Date

There are several methods for finding the Julian date. The following one, developed by Fliegel and Van Flandern in 1968, is well adapted for computer programs. Let y be the year (with all four digits), m the month and d the day. The Julian date J at noon is then

- (3{[y + (m - 9)/7]/100 +1})/4 + 275m/9 + d +1721029 .

The division here means an integer division, the decimal part being truncated: e. g. 7/3 = 2 and -7/3 = -2.

Example. Find the Julian date on January 1, 1990. Now y = 1990, m = 1 and d = 1.

- 3 x {[1990 + (1 - 9)/7]/100 +1}/4 + 275 x 1/9 +1 +1,721,029

= 730,330 - 3482 - 15 + 30 +1 +1,721,029 = 2,447,893 .

Astronomical tables usually give the Julian date at 0 UT. In this case that would be 2,447,892.5.

The inverse procedure is a little more complicated. In the following J is the Julian date at noon (so that it will be an integer):

a = J + 68,569 , b = (4a)/146,097 , c = a - (146,097b + 3)/4 , d = [4000(c +1)]/1,461,001, e = c - (1461d)/4 + 31, f = (80e)/2447, day = e - (2447f)/80 , g = f/11, month = f + 2 - 12g , year = 100(b - 49) + d + g .

Example. In the previous example we got J = 2,447,893. Let's check this by calculating the corresponding calendar date:

a = 2,447,893 + 68,569 = 2,516,462 , b = (4 x 2,516,462)/146,097 = 68 , c = 2,516,462 - (146,097 x 68 + 3)/4 = 32,813 , d = [4000(32,813 +1)]/1,461,001 = 89 , e = 32,813 - (1461 x 89)/4 + 31 = 337 , f = (80 x 337)/2447 = 11, day = 337 - (2447 x 11)/80 = 1, g = 11/11 = 1, month = 11 + 2 - 12 x 1 = 1, year = 100(68 - 49) + 89 +1 = 1990 .

Thus we arrived back to the original date.

Since the days of the week repeat in seven day cycles, the remainder of the division J/7 unambiguously determines the day of the week. If J is the Julian date at noon, the remainder of J/7 tells the day of the week in the following way:

Example. The Julian date corresponding to January 1, 1990 was 2,447,893. Since 2,447,893 = 7 x 349,699, the remainder is zero, and the day was Monday.

Telescopes Mastery

Telescopes Mastery

Through this ebook, you are going to learn what you will need to know all about the telescopes that can provide a fun and rewarding hobby for you and your family!

Get My Free Ebook


Post a comment