HP 20S and HP 21S: 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)
= 3.07496 + 1.33621 * sin RA * tan δ (for epoch 2000)
Δδ = (15 * n) * cos RA (in arcseconds)
= 20.0431 cos RA (epoch 2000)
With m = 3.07496 seconds and n = 1.33621 seconds (for epoch 2000)
For other epochs:
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)
For the HP Prime and TI-84 Plus CE versions, click here: http://edspi31415.blogspot.com/2018/09/hp-prime-and-ti-84-plus-ce-precession.html
HP 20S and HP 21S Program: Precession
The key codes for both calculators are the same.
STEP KEY KEY CODES
01 LBL D 61, 41, d
02 DEG 61, 23
03 RCL 0 22, 0
04 →HR 51, 54
05 × 55
06 1 1
07 5 5
08 = 74
09 STO 0 21, 0
10 RCL 1 22, 1
11 →HR 51, 54
12 STO 1 21, 1
13 3 3
14 . 73
15 0 0
16 7 7
17 4 4
18 9 9
19 6 6
20 + 75
21 1 1
22 . 73
23 3 3
24 3 3
25 6 6
26 2 2
27 1 1
28 × 55
29 RCL 0 22, 0
30 SIN 23
31 × 55
32 RCL 1 22, 1
33 TAN 25
34 = 74
35 STO 5 21, 5
36 2 2
37 0 0
38 . 73
39 0 0
40 4 4
41 3 3
42 1 1
43 × 55
44 RCL 0 22, 0
45 COS 24
46 = 74
47 STO 6 21, 6
48 RCL 0 22, 0
49 + 75
50 RCL 4 22, 4
51 × 55
52 ( 33
53 RCL 5 22, 5
54 + 75
55 RCL 3 22, 3
56 ) 34
57 ÷ 45
58 3 3
59 6 6
60 0 0
61 0 0
62 = 74
63 ÷ 45
64 1 1
65 5 5
66 = 74
67 →HMS 61, 54
68 STO 7 21, 7
69 R/S 26
70 RCL 1 22, 1
71 + 75
72 RCL 4 22, 4
73 × 55
74 ( 33
75 RCL 6 22, 6
76 + 75
77 RCL 3 22, 3
78 ) 34
79 ÷ 45
80 3 3
81 6 6
82 0 0
83 0 0
84 = 74
85 →HMS 61, 54
86 STO 8 21, 8
87 RTN 61, 26
Instructions
Store the following values in the registers:
R0: Initial RA in HH.MMSSSS format
R1: Initial δ in DD.MMSSSS format
R2: RA proper notion
R3: δ proper notion
R4: number of years from 2000. For 2022, store 22. For 1978, store -22.
Result:
R7: New RA in HH.MMSSSS format, press [ R/S ] to get
R8: New δ in DD.MMSSSS format
Examples
Estimate the RA and δ of Regulus (Alpha Leonis) and Sadalmelik (Alpha Aquarii) for 2020 (Y = 20). (data from Wikipedia)
Regulus (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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