## 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

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