## Sunday, January 13, 2019

### HP Prime, TI-84 Plus, and Casio fx-CG 50: Julian Date/Gregorian Calendar Conversions

HP Prime, TI-84 Plus, and Casio fx-CG 50:  Julian Date/Gregorian Calendar Conversions

Introduction

One conversion that is common in astronomy is to convert dates from our Gregorian calendar (the most commonly used day-to-day calendar) to a Julian Date Number, and visa versa.

JD:  Convert Gregorian Date to Julian Date Number

GREG:  Convert Julian Date Number to Gregorian Date

The Julian date number of 2451545 corresponds to January 1, 2000.

Gregorian Date to Julian Date Number

HP Prime Program JD:  Gregorian Date to Julian Date Number
Arguments:  four digit year, month, day
JD(y,m,d)

EXPORT JD(y,m,d)
BEGIN
// Gregorian to Julian
// year, month, day
// 2019-01-12 EWS
//  Wikipedia
LOCAL x0:=IP((m-14)/12);
LOCAL x1:=IP(((1461*(y+4800+x0))/4));
LOCAL x3:=IP(367*(m-2-12*x0)/12);
LOCAL x5:=IP((y+4900+x0)/100);
LOCAL x6:=IP(3*x5/4);
LOCAL j:=x1+x3-x6+d-32075;
RETURN j;
END;

TI-84 Plus Program JD:  Gregorian Date to Julian Date Number

"GREGORIAN TO JULIAN"
"2019-01-13 EWS"
Input "YEAR: ",Y
Input "MONTH: ",M
Input "DAY: ",D
iPart((M-14)/12)→X
iPart(((1461*(Y+4800+X))/4))→A
iPart(367*(M-2-12*X)/12)→B
iPart((Y+4900+X)/100)→C
iPart(3*C/4)→C
A+B-C+D-32075→J
Disp "JD: ",J

Casio fx-CG50 Program JD:  Gregorian Date to Julian Date Number
This version can be typed in directly in the calculator (not a text file)

"GREGORIAN TO JULIAN"
"2019-01-19 EWS"
"YEAR?"→Y
"MONTH"?→M
"DAY"?→D
Int ((M-14)÷12)→X
Int (((1461×(Y+4800+X))÷4)) →A
Int (367×(M-2-12×X)÷12) →B
Int ((Y+4900+X) ÷ 100) →C
Int (3×C÷4)→C
A+B-C+D-32075→J
ClrText
Locate 1,1,"JD"
Locate 1,2,J

Julian Date Number to Gregorian Date

HP Prime Program GREG:  Julian Date Number to Gregorian Date
Argument:  Julian Date Number
GREG(j)

EXPORT GREG(j)
BEGIN
// Julian to Gregorian
// Wikipedia
// 2019-01-12 EWS
LOCAL x1:=IP((4*j+274277)/146097);
LOCAL x2:=IP(x1*3/4);
LOCAL f:=j+1401+x2-38;
LOCAL E:=4*f+3;
LOCAL G:=IP((E MOD 1461)/4);
LOCAL H:=5*G+2;
LOCAL D:=IP((H MOD 153)/5)+1;
LOCAL M:=((IP(H/153)+2) MOD 12)+1;
LOCAL Y:=IP(E/1461)-4716+IP((12+2-M)/12);
RETURN {Y,M,D};
END;

TI-84 Plus Program GREG:  Julian Date Number to Gregorian Date

"JULIAN TO GREGORIAN"
"2019-01-13 EWS"
Input "JD: ",J
iPart((4*J+274277)/146097)→X
iPart(X*3/4)→X
4*(J+1401+X-38)+3→E
5*iPart(remainder(E,1461)/4)+2→H
iPart(remainder(H,153)/5)+1→D
remainder(iPart(H/153)+2,12)+1→M
iPart(E/1461)-4716+iPart((12+2-M)/12)→Y
Disp "YEAR, MONTH, DAY:",Y,M,D

Casio fx-CG50 Program GREG: Julian Date Number to Gregorian Date
This version can be typed in directly in the calculator (not a text file)

"JULIAN TO GREGORIAN"
"2019-01-13 EWS"
"JD"?→J
Int ((4 ×J+274277) ÷146097) →X
Int (X ×3 ÷4) →X
4 ×(J+1401+X-38)+3 → E
5 × Int( MOD(E,1461) ÷ 4)+2 → H
MOD(Int  (H ÷153)+2,12)+1 →M
Int (E ÷1461) -4716+Int ((12+2-M) ÷12) → Y
ClrText
Locate 1,1,"YEAR, MONTH, DAY"
Locate 1,2,Y
Locate 1,3,M
Locate 1,4,D

Examples

Gregorian Date:  1988, October 31
JD:  2447466

Gregorian Date:  1999, January 11
JD:  2451190

Gregorian Date:  2017, March 21
JD:  2457834

Source:

"Julian Day"  Wikipedia.  Edited (when retrieved) November 19, 2018.  Retrieved January 11, 2019.  https://en.wikipedia.org/wiki/Julian_day

Eddie

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