The old star catalog says B1950, can it be used directly as J2000?
Check the units of the coordinate ruler and the self-propelled axis first, and then decide how to convert.
Sky coordinates and observations
If you take an old star catalog and look for stars, the numbers will look like right ascension and declination, but the old FK4 and the new FK5 are not just different in years. The ecliptic address, equatorial address and proper motion component also each have their own coordinate datum. We separate these routes that are easy to mix.
Guess first
If I change the label of the old star catalog from B1950 to J2000, will the numbers remain unchanged?
Show answer and explanation
No, the reference definition is also different. — Corresponding transformations need to be used depending on the coordinate type and reference system.
Then connect experience and science
First look at the reference label of the star catalog
B and J are not just two eras. The old processing of FK4 and FK5 also involves the difference between the E item and the right ascension zero point, so you cannot just change the year.
Reference systems, equinoxes, and epochs are recorded separately
The direction of the ecliptic is also affected by precession
Equations 21.5–21.7 change the same ecliptic direction to another equinox; this does not mean that the celestial body is actually moved.
Rotate the ecliptic coordinates using η, Π, p
You need to change the portions yourself, not just the name.
If the same moving direction is projected into different coordinate networks, the components will be different. First multiply the right ascension time seconds by 15 variable angle seconds.
μα: time second → arc second, then coordinate transformation
The old system had its own processing route
Use Newcomb precession to process FK4; calculate the optical position to remove the E term, and finally add the equinox correction of the target date. A complete modern FK4→FK5 directory conversion is not an alias for these three steps.
Δα zero point = (0.0775 + 0.0850T) seconds
First distinguish the reference system, equinoxes and epochs, and then choose the ecliptic rotation or FK4/FK5 branch. The time seconds of the right ascension proper motion must be multiplied by 15 variable angle seconds; T in the zero point correction must use the base century of the corresponding branch.
give it a try
"Ecliptic address" demonstrates equinox changes in the same direction; "proper motion component" replaces Sirius's equatorial motion with ecliptic components; "Old FK4" demonstrates Newcomb's pure precession with the other listed equinox corrections.
No need to memorize symbols
- λ / β
- yellow longitude / yellow latitude
- μα / μδ
- Equatorial proper motion component, interfaces are in arcseconds/year
- FK4 / FK5
- Different star catalog reference systems
- T
- Final equinox correction uses target time in the Julian century from J2000
Algorithm, accuracy and scope of application
Completed the ecliptic precession of 21.5–21.7, printed pages 138 of equatorial motion to ecliptic motion, and pages 139–140 of Newcomb’s old precession and right ascension equinox corrections. The ecliptic direction uses atan2 to process the near pole; the ecliptic proper has no unique longitude component when cosβ≈0, and returns null. The old precession and the zero point correction are output separately; the corrected T is the century from J2000 to the target date according to the book, and the local AA+ FK4 package mixes another T, so the zero point item added to it is first removed when comparing. A complete 6×6 FK4/FK5 catalog conversion is not implemented which only references external sources in the book.
my understanding check
The right ascension proper motion of 0.1 time seconds/year is equivalent to how many arc seconds/year?
1.5 — Multiply time seconds by 15 to convert to arc seconds.
Does changing the proper motion into the ecliptic component make the star change its path?
No, just change the description component — The same movement is cast to another set of substrates.
In this lesson, Newcomb combined with route E is a complete modern 6×6 catalog conversion?
no — What is given in the book is the route for processing the old star catalog's visual position. It cannot be renamed to pretend to be another complete catalog conversion.
Read the coordinate labels first, and then convert the values; "change the reference system", "change the equinox" and "the star's own motion" cannot be mixed into one step.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 21 chapter