Julian to Calendar Date Conversion
Date: 02/24/2001 at 14:53:12 From: Steven Attwell Subject: Julian Date Conversion I need to find an algorithm to convert Julian date values to calendar date values. (e.g. Julian date 2451964 = 02/24/2001.)
Date: 02/25/2001 at 16:10:51 From: Doctor Fenton Subject: Re: Julian Date Conversion Hi Steven, Thanks for writing to Dr. Math. I generally use one of two algorithms, either that of Jean Meeus in "Astronomical Formulae for Calculators" (an outstanding book), or the Fliegel-Van Flandern algorithm given in the Astronomical Almanac. Here is Meeus's version: it works for any positive Julian date. 1. Add .5 to the JD and let Z = integer part of (JD+.5) and F the fractional part F = (JD+.5)-Z 2. If Z < 2299161, take A = Z If Z >= 2299161, calculate alpha = INT((Z-1867216.25)/36524.25) and A = Z + 1 + alpha - INT(alpha/4). 3. Then calculate: B = A + 1524 C = INT( (B-122.1)/365.25) D = INT( 365.25*C ) E = INT( (B-D)/30.6001 ) The day of the month dd (with decimals) is: dd = B - D - INT(30.6001*E) + F The month number mm is: mm = E - 1, if E < 13.5 or mm = E - 13, if E > 13.5 The year yyyy is: yyyy = C - 4716 if m > 2.5 or yyyy = C - 4715 if m < 2.5 An example from Meeus' book is for JD = 2436116.31 JD + 0.5 = 2436116.81, so Z = 2436116 F = 0.81 alpha = INT((2436116 - 1867216.25)/36524.25 ) = 15 A = 2436116 + 1 + 15 - INT(15/4) = 2436129 Then B = 2437653 C = 6673 D = 2437313 E = 11 So, dd = 4.81, mm = E-1 = 10, and yyyy = C-4716 = 1957, so the date is: Oct 4.81, 1957 If you have further questions, please write again. If you want the Fliegel-Van Flandern algorithm, which uses only integer arithmetic, write back, or if you can find the Explanatory Supplement for the current Astronomical Almanac, I'm sure it has it. - Doctor Fenton, The Math Forum http://mathforum.org/dr.math/
Date: 05/29/2003 at 05:12:20 From: Roberto Fioravanti Subject: Fliegel-Van Flandern algorithm Can I have the Fliegel-Van Flandern algorithm to convert Julian date values to calendar date values? (e.g. Julian date 2451964 = 02/24/2001.)
Date: 05/29/2003 at 08:39:20 From: Doctor Fenton Subject: Re: Fliegel-Van Flandern algorithm Hi Roberto, Thanks for writing to Dr. Math. The algorithm for converting from a Julian date to a Gregorian date is the following. Let J be the Julian day number (since this algorithm uses integer arithmetic, this will be the Julian day number which begins at noon on the calendar day), and let Y, M, and D denote the corresponding calendar date. Then compute the following quantities, using integer arithmetic: p = J + 68569 q = 4*p/146097 r = p - (146097*q + 3)/4 s = 4000*(r+1)/1461001 t = r - 1461*s/4 + 31 u = 80*t/2447 v = u/11 . Then Y = 100*(q-49)+s+v M = u + 2 - 12*v D = t - 2447*u/80 . For example, using the data you supplied, J = 2451964 p = 2520533 q = 69 r = 359 s = 0 t = 390 u = 12 v = 1 D = 23 M = 2 Y = 2001 . It appears that you gave the integer part of the Julian date of midnight for Feb. 24, 2001, which would be 2451964.5. This algorithm gives the calendar date on which the Julian date 2451964 begins, which is at noon on Feb. 23, 2001. Just for completeness, although you didn't ask for it, here is the Fliegel-Van Flandern algorithm to convert from a Gregorian calendar date to the Julian date: Given Y,M,D, the year, month, and date, define (using integer arithmetic) M1 = (M-14)/12 Y1 = Y + 4800 . Then the Julian date J is J = 1461*(Y1+M1)/4 + 367*(M-2-12*M1)/12 - (3*((Y1+M1+100)/100))/4 + D - 32075 . For example, for Y = 2001, M = 2, and D = 24, M1 = -1 Y1 = 6801 , and J = 2483700 + 367 - 51 + 24 -32075 = 2451965 . These algorithms are available in the Explanatory Supplement to the Astronomical Almanac, 2nd edition, P. Seidelmann (ed.), or in Fliegel and Van Flandern's original paper, Fliegel, H. F., and Van Flandern, T. C., "A Machine Algorithm for Processing Calendar Dates," Communications of the Association of Computing Machines, vol. 11 (1968), p. 657. If you have any questions, please write back and I will try to explain further. - Doctor Fenton, The Math Forum http://mathforum.org/dr.math/
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