**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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content copyright, © 2011-2018. Edward
Shore. Unauthorized use and/or
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