(20S, 21S): Precession
09-16-2018, 11:19 PM (This post was last modified: 10-09-2018 10:32 PM by Gene.)
Post: #1
 Eddie W. Shore Senior Member Posts: 979 Joined: Dec 2013
(20S, 21S): Precession
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
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