The star catalog records only one position, so why does the telescope need to make small corrections?
Treat "the star is moving by itself", "the observer is moving" and "the coordinate ruler is changing" separately.
Sky coordinates and observations
To give the telescope a star catalog address, you must also indicate which year the star catalog is from and which set of coordinate axes it uses. Looking at the moving Earth today, there are slight changes in the direction of the light and the coordinate datum. This lesson follows θ Persei in the book and completes these corrections step by step.
Guess first
Can the changes in coordinate numbers explain that the stars are moving on their own?
Show answer and explanation
No, it depends on the observer and the coordinate datum. — Proper motion, aberration of light, precession and nutation come from different reasons and cannot be explained together.
Then connect experience and science
First get the star catalog address with reference system
This lesson uses the book example θ Persei's FK5 J2000.0 right ascension, declination and proper motion. The proper motion represents the motion of the star itself, first advanced to the observation date in the J2000 coordinate axis.
Star catalog J2000 → Add proper motion to the coaxial system
The earth is moving and light reaches different directions
The propagation speed of light is limited, and the movement of the earth will change the direction of the observed light. This is called optical aberration. This lesson uses the 36 earth center of mass velocities in Table 23.A, which are still revised in the J2000 framework.
Ron–Vondrák aberration precedes precession
Change the scale to the observation date
Precession changes the coordinate axis from the J2000 mean axis to the mean axis of the day; the numerical change at this time mainly includes the scale change effect and cannot be regarded as the displacement of the star itself.
Proper motion → aberration of light → precession
Add the small swing of the day to get the apparent position of this model
Finally, add nutation and change it to the true equator and true vernal equinox of the day. The apparent position here is still the geocentric model, excluding parallax, gravitational deflection and atmospheric refraction that are not included in this site.
Add nutation → Today’s true equatorial apparent position
It transforms step by step according to the motion → speedometer annual optical deviation → precession → nutation, and the output of each level becomes the input of the next level. The velocity components in the table must match the coordinate axes, and these steps cannot be changed into an unconditional angle addition.
give it a try
Select "Calculation Examples in the Book" to gradually switch calculation stages. Mark the reference system on each card. Don't draw the numbers on different coordinate axes directly as the path the stars have traveled.
No need to memorize symbols
- FK5 / J2000.0
- Fixed star catalog reference system and epoch in this lesson
- μα / μδ
- Right ascension angle proper motion and declination proper motion; here μα is not μα cosδ
- X′ Y′ Z′
- J2000 Earth’s center of mass velocity on the equatorial axis
- α / δ
- Right ascension and declination; right ascension output hours, calculated internally in degrees
Algorithm, accuracy and scope of application
Realize the Ron–Vondrák path in Chapter 23: Fixed FK5 J2000.0 star catalog parameters, linear motion → Table 23.A All 36 earth center of mass velocities and Equation 23.4 optical aberration → Equation 21.3/21.4 precession → Table 22.A nutation and Equatorial first-order correction of Equation 23.1. θ The Persei star catalog and proper motions are taken from Example 21.b: α=2h44m11.986s, δ=49°13′42.48″, μα=0.03425 time seconds/Julian year (converted (replaced as 0.51375 arc seconds/year), μδ=−0.0895 arc seconds/year. The control range is 1900–2100, 1–28 days in the month, and the example star is fixed far away from the celestial pole. Check Example 23.b. 2028-11-13.19 TT, and compared with the same local AA+ model. This package does not implement another classic 23.2/23.3 optical aberration route, complete space proper motion, annual parallax or relativistic gravitational deflection; these omissions cannot be called a full-precision observation system.
my understanding check
Which set of axes does the Ron–Vondrák speedometer use?
J2000.0 fixed equatorial axis — Therefore, the optical aberration must be processed before the precession reaches the same day.
Which one primarily represents the star's own motion?
self-propelled — Precession and nutation mainly change the reference direction, not the space motion of the star itself.
Can the final apparent position of this lesson be directly used as all observation corrections of the local telescope?
cannot — This is the geocentric direction, and factors such as location, parallax, diurnal effect, and atmospheric refraction have not yet been added.
First ask, "Are the stars moving, the people moving, or the ruler moving?" and then correct the coordinates according to the correct reference system and order.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 23 chapter