For the same star, why does the old star catalog add one less optical aberration?
It's not about counting less physics, but it's about avoiding counting twice the E item that's already hidden in the old star catalog.
Sky coordinates and observations
The two catalogs may have used different conventions for "flat positions". The old FK4 used to leave the approximately constant optical aberration E term in the flat position; when calculating the apparent position, if the entire set of corrections is added, it will be included twice.
Guess first
The E item was omitted in the old FK4 visual position processing. Is it because optical aberration no longer exists?
Show answer and explanation
No, to avoid double counting — That part has been left in the flat position convention of the old catalog.
Then connect experience and science
Flat position is not a word without agreement
Let’s first talk about whether the celebrity watch belongs to FK5 or the old FK4. The same group of numbers cannot be arbitrarily labeled with two labels.
Input references must be clear
Calculate optical aberration according to the classical formula
This branch uses the sun's geometric longitude, the earth's orbital eccentricity and the perihelion direction; while retaining the ecliptic 23.2 and equator 23.3 forms.
κ = 20.49552 arc seconds
The old FK4 no longer adds the E item repeatedly
Using Newcomb precession, the terms that depend on e in the classic optical aberration are no longer added, and finally the right ascension zero point correction of the target time is added.
The old table already contains item E → omit item E this time
Distinguish from another route
The original Ron–Vondrák class calculated the aberration of light based on the velocity of the center of mass; this class shows the classical elliptic approximation and the old system processing, without claiming that the two are identical bit by bit.
Classic routes and speedometer routes have different approximations
First confirm whether the input star catalog contains the E item, and then select the classic optical aberration correction. κ is arc seconds, which needs to be divided by 3600 when correcting to right ascension and declination given in degrees; coordinate singularities cannot be ignored near the celestial pole.
give it a try
The FK5 mode uses the original book θ Persei; the FK4 mode uses clear teaching directions. Compare the correction list and do not directly subtract the final coordinates of two different inputs as an error.
No need to memorize symbols
- Item E
- The approximately constant part of optical aberration related to the eccentricity of the Earth's orbit
- Δα / Δδ
- Coordinate correction, output arc seconds
- FK4/FK5
- Agreement on flat positions of different star catalogs
Algorithm, accuracy and scope of application
To realize the classic annual optical aberration between the ecliptic and the equator in Equation 23.2, the true longitude of the sun calls the low-precision route in Chapter 25 (the accuracy required for this correction is sufficient). The FK5 path first precesses, then precesses, and simultaneously calculates the first-order nutation/optical aberration on the daily coordinates and adds them together; the FK4 teaching path is corrected by using Newcomb, deleting the e term, and finally adding 0.0775+0.0850T seconds to the target date. Original book 23.a Independently verified. It is not a complete modern FK4 to ICRS catalog conversion and cannot be consistent bit by bit with the existing Ron–Vondrák result requirements.
my understanding check
Should the eccentricity E term be retained in FK5 classic optical aberration?
should be retained — Complete 23.2/23.3 including item E, suitable for FK5 flat position.
Is the FK4 input in this lesson an actual star catalog?
No, it’s the indicated teaching direction — Fixed 10h, 20°, and self-propelled zero are used to show the processing sequence and do not pretend to be a real star catalog.
Has local atmospheric refraction been covered in this lesson?
Not included — This is still the calculation of the apparent position of the geocentric celestial sphere.
Don't just ask "Which item is missing?" but also ask "Is this item already included in the input?"
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 23 chapter