Saturday, February 23, 2019

HP Prime: Determining the Date For a Phase of Earth's Moon

HP Prime:  Determining the Date For a Phase of Earth's Moon

Introduction

The program MOONDATE determines when a desired phase of Earth's moon given month and year.  The four phases of the moon available are:

New Moon  (0.00)
1st Quarter (0.25)
Full Moon (0.50)
3rd Quarter (0.75)

The following equations are used:

Let  y = year, m = month, t = type (see the above)

y' = y + (m -1)/12
k = integer( (y - 2000) * 12.3685) + t/4
t = k/1236.85

J = 2451550.09765 + 29.530588853 * k + (1.337 * 10^-4) * t^2 - (1.5 * 10^-7) *t^3 + (7.3 * 10^-10) * t^4

J is the Julian Date and will need to be converted to the Gregorian Date.  With the DATE+ function, the HP Prime makes this easy.  Look to Dieter's post on this thread for details, link:  http://www.hpmuseum.org/forum/thread-12184.html?highlight=julian+date

Caution:  This program is designed to work with all dates after January 1, 2000.  If you choose any dates before, you may have to adjust the month

HP Prime Program MOONDATE

EXPORT MOONDATE()
BEGIN
// EWS 2019-02-19
LOCAL P,Y,K,M,T,l,c,s;
LOCAL J,D,N,R;
l:={"New","First Qtr","Full",
"Third Qtr"};
INPUT(
{Y,
{M,{1,2,3,4,5,6,7,8,9,10,11,12}}
,{c,l}},
"Moon Phase Date",
{"Year: ","Month:","Stage:"});
s:=(c-1)/4;
N:=M;

REPEAT 
R:=Y+(N-1)/12;
K:=IP((R-2000)*12.3685)+s;
T:=K/1236.85;
J:=2451550.09765+29.530588853*K
+1.337ᴇ−4*T^2-1.5ᴇ−7*T^3
+7.3ᴇ−10*T^4;
J:=IP(J)-2451545;
D:=DATEADD(2000.0101,J);
N:=N+1;
UNTIL D≥(Y+M/100);

RETURN D;
END;

Note:  You can use an alternate of 1/1/2000 (date code 2000.0101) with corresponding Julian Date 2451545.

Example:

January 2019:
New:  2019.0105 (1/5/2019)
1st Qtr: 2019.0113 (1/13/2019)
Full: 2019.0120 (1/20/2019)
3rd Qtr: 2019.0127 (1/27/2019)

Source:
Meeus, Jean.  "Astronomical Algorithms"  Willmann-Bell, Inc.:  Richmond, VA  1991  ISBN 0-943396-35-2

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.


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