Monday, September 3, 2018

HP Prime and TI-84 Plus CE: Precession


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.

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