(20S, 21S): Precession

[Eddie W. Shore]

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)

Code:

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

Blog entry: http://edspi31415.blogspot.com/2018/09/h...ssion.html