HP Prime and TI-84 Plus CE: Precession
Introduction
The program PRECESS estimate the new position (right ascension
(RA), declination (δ)) of a celestial object given their position in Epoch 2000
with the object’s proper notion.
Estimation formulas:
Change in RA and δ before accounting for proper notion
ΔRA = m + n * sin RA * tan δ (in seconds)
Δδ = (15 * n) * cos RA
(in arcseconds)
With m = 3.07496 seconds and n = 1.33621 seconds (for epoch
2000)
For other epochs (in seconds, updated 9/12/2018):
1900: m = 3.0731, n =
1.33678
2100: m = 3.07682, n
= 1.33564
Then:
RA_new = (RA_old + Y * (ΔRA + RA_proper) / 3600 ) / 15 (hours)
δ_new = (δ_old + Y * (Δδ + δ_proper) / 3600 (degrees)
Y = years from 2000
(or the appropriate epoch)
HP Prime Program
PRECESS
EXPORT PRECESS()
BEGIN
// 2018-09-01 EWS
LOCAL A,D,T,C,F,B,E;
HAngle:=1; // degree
INPUT({A,D,T,C,F},"Precession",
{"RA: ","δ:
","YRS: ",
"Prop-RA ","Prop-δ
"},
{"Epoch 2000",
"Epoch 2000",
"Years from 2000",
"Proper Notion",
"Proper Notion"});
A:=15*A;
B:=3.07496+1.33621*SIN(A)*TAN(D);
E:=20.0431*COS(A);
A:=(A+T*(B+C)/3600)/15;
D:=D+T*(E+F)/3600;
PRINT();
PRINT("Precssion
Results");
PRINT("RA: "+→HMS(A));
PRINT("DEC: "+→HMS(D));
END;
Note:
Enter in degrees, minutes, and
seconds/arcseconds using the template from the [ Shift ] + [ 9 ] menu.
Enter in RA using the degrees,
minutes, seconds template. Example: to
type 15h24m30s, type 15° 24’ 30”.
TI-84 Plus CE Program PRECESS
"EWS
2018-09-01"
Degree
Disp "EPOCH
2000"
Input "RA:
",A
15*A→A
Input "DEC:
",D
Input "YRS FROM
2000: ",T
Disp "ANNUAL
PROPER NOTION"
Input "RA:
",C
Input "DEC:
",F
3.07496+1.33621*sin(A)*tan(D)→B
20.0431*cos(A)→E
(A+T*(B+C)/3600)/15→A
D+T*(E+F)/3600→D
Disp "RA:
",A>DMS
Disp "DEC:
",D>DMS
Note:
Enter degrees by pressing [ 2nd
], (angle), 1.
Enter minutes by pressing [ 2nd
], (angle), 2.
Enter seconds by pressing [ alpha
], ( “ )
Enter in RA using the degrees,
minutes, seconds template. Example: to
type 15h24m30s, type 15° 24’ 30”.
Examples
Estimate the RA and δ of Regulus (Alpha Leonis) and
Sadalmelik (Alpha Aquarii) for 2020 (Y = 20).
(data from Wikipedia)
Regulus (A) – Leo the
Lion
Epoch 2000: RA = 10h 8m 22.311s, δ = +11° 58’ 0.195”
Proper Notion:
RA_prop = -0.016582 arcsec/yr, δ_prop = 0.00556 arcsec/yr
(arcsec = “)
Results:
RA_2020 ≈ 10h 8m 26.56557s
(shown as 10°08’26.56557”)
‘δ_2020 ≈ +11° 52’ 6.06118”
Sadalmelik – Aquarius
the Water Bearer
Epoch 2000: RA = 22h
5m 47.03593s, δ = -0° 19’ 11.4568”
Proper Notion:
RA_prop = 1.216667 * 10^-3 arcsec/yr, δ_prop = -0.00939 arcsec/yr
Result:
RA_2020 ≈ 22h 5m 51.14225s
δ ≈ -0° 13’ 19.5407”
Convert mas/yr to arcsec/yr:
For RA: (x/15) /1000
For δ: x/1000
Sources:
Jones, Aubrey. Mathematical
Astronomy with a Pocket Calculator
John Wiley & Sons: New York.
Printed in Great Britain. 1978.
ISBN 0 470 26552 3
Meeus, Jean. Astronomical
Algorithms William-Bell, Inc. Richmond, VA 1991. ISBN
0-943396-35-2
Eddie
All original
content copyright, © 2011-2018. 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. Please contact the author if you have questions.
