For the same star, why are there not enough addresses on the old star map?
Only by separating the movement of the stars from the rotation of the coordinate grid can the year of the star catalog be read.
Sky coordinates and observations
If you check the right ascension and declination of a star, you will also see marks such as "J2000.0". This is not irrelevant small print: the coordinate grid of the sky will also slowly change, directly mixing addresses from different eras together, just like finding a way with two maps facing different directions.
Guess first
If the old and new right ascensions of the same star in the star catalog are different, does it necessarily mean that it really crosses the same large angle in the sky?
Show answer and explanation
Not necessarily, the coordinate grid is also changing — Precession changes the reference grid; it is necessary to separate the true proper motion from the coordinate changes.
Then connect experience and science
Why do star catalogs still have years?
Right ascension and declination are addresses relative to a set of sky coordinate grids. The Earth's axis and reference plane change slowly, and the grid changes over time, so the address needs to be accompanied by an epoch.
Year J corresponds to JDE = 2451545 + (year −2000)×365.25
First separate the proper motion and precession
When a star moves by itself, it changes its direction, which is called its proper motion; precession changes the coordinate frame that describes the direction. The proper motion is first included in the old frame, and then the grid is converted.
First α←α+μαt, δ←δ+μδt
Let the new mesh cover the same sky
The golden mark in the picture is the original direction, the gray dotted line is the angle scale of the fixed window, and the blue line is the new grid. When proper motion is turned off, the star's direction does not change, but its new coordinate numbers change.
Rotate the coordinate datum using ζ, θ, z in sequence
Don’t call all changes precession
Near stars can also use distance and radial velocity to calculate space motion; this lesson only provides this branch for Sirius for which these data are given. The result is the flat position, not the apparent position including nutation and optical aberration.
Use atan2(C,√(A²+B²)) to maintain stability near the celestial pole
First use its own motion to advance the star to the target epoch, and then rotate the reference direction by ζ, θ, and z. The J year is not the same unit as the Julian century; it is a slow change in the coordinate datum, rather than treating all stars as moving together.
give it a try
First turn off the automatic movement, change the year, and see that the original direction of the gold does not move but the new blue grid rotates. Then turn on the proper motion and compare the small direction changes of the star itself. The case of Polaris is particularly suitable for observing that "the right ascension difference is not equal to the angular distance".
No need to memorize symbols
- α / δ
- Right ascension (interface cost and hours)/Declination
- J2000.0
- Starting flat equatorial coordinate frame and epoch
- ζ,θ,z
- Original book precession rotation angle
- μα / μδ
- The proper motion of right ascension is measured in time seconds/year, and the proper motion of declination is measured in arcseconds/year.
- JDE
- Julian Day in Dynamic Time
Algorithm, accuracy and scope of application
Chapter 21 of the original book, equations (21.2)–(21.4), Example 21.b, and Polaris exercises; for spatial motion, use printed pages 141–142 and Example 21.d. Realize precessional rotation, uniform proper motion and linear space motion with distance/radial velocity suitable for the FK5 flat position in the book; use the precession coefficient in the book and do not pretend to be a modern IAU2006/ICRS precision ephemeris. The interactive target is limited to J1900–J2100. Only Sirius has distance and radial velocity in space motion. The other stars still explicitly use uniform proper motion when selecting this option. The image is fixed to the local tangent plane in the J2000 direction; the new grid is mapped back to the same view by the transpose of the precessional rotation matrix, so pure precession does not move the stars. The original direction and the direction behind the motion may be so close that it is difficult to distinguish with the naked eye. The numbers show the real difference and do not exaggerate the motion. Verification covers compiling AA+ forecast values, book examples, matrix distance-preserving and inverse transformations. The full set of FK4/FK5 including the interaction of E-term conversion, ecliptic precession and equatorial self-rotation to ecliptic self-propelled motion has not yet been implemented; it cannot be extrapolated across tens of thousands of years or used as the observed apparent position.
my understanding check
In the order of this lesson, what should we deal with first?
Includes self-property within the starting frame — The proper motion first acts on the direction of the star, and then converts the direction to the target flat equatorial coordinate frame.
The large change in right ascension figures near Polaris does it necessarily mean that the actual angular displacement is also large?
Not necessarily — The right ascension and longitude lines converge near the celestial pole, so the right ascension difference cannot be directly regarded as the true angular distance.
Is the output of this lesson already the precise visual position directly seen by the telescope?
no — Also missing are nutation, optical aberration and other apparent position corrections, as well as local observation transformations.
The stars will move and the coordinate grid will change; the star catalog must specify the epoch and reference frame, and the two changes must be calculated separately.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 21 chapter