The stars haven't moved, so why do the address numbers change when I change the star map?
In the same direction, the celestial equator, ecliptic or galactic plane can be used as the starting point for measuring angles.
Sky coordinates and observations
The same house can be located using the street number and the longitude and latitude on the map. Star maps also have different coordinate grids: if you change the grid, the numbers will change, but the stars will not move.
Guess first
Just changing the star map coordinate grid, will the stars themselves move?
Show answer and explanation
Won't — What changes are the numbers describing the same direction.
Then connect experience and science
First determine the same line of sight
The golden dots represent the original right ascension and declination directions. Earth observers use directional coordinates, not the true distance of the stars.
Unit direction vector u=(cosδcosα,cosδsinα,sinδ)
Remeasure angles using the ecliptic plane
The ecliptic is tilted from the celestial equator, so the new latitude and longitude are usually different. This transformation is an axis rotation.
(x,y,z)黄 = Rx(−ε)·u
Then change it to the address of the Milky Way plane.
The galactic system has another set of poles and zero directions. This is defined according to B1950 in the book, and the J2000 coordinates are not directly inserted into the old constants.
North Galactic Pole α=192.25°, δ=27.4° (B1950)
If you can turn it around, you should be able to turn it back.
Use the inverse transformation to return to the original equatorial coordinates, and you should find the same direction. The longitude at the pole is not unique, but the direction is still determined.
Inverse transformation using the transpose of an orthogonal matrix
Expand the calculation
x = cos δ cos α；y = cos δ sin α；z = sin δ x黄 = x y黄 = y cos ε + z sin ε z黄 = −y sin ε + z cos ε λ = atan2(y黄,x黄)；β = atan2(z黄,√(x黄²+y黄²))
The above expands the equator → ecliptic branch. The inverse transformation changes ε to −ε; the galactic branch uses the B1950 datum specified in the course and cannot be directly mixed with this set of axes.
give it a try
First keep the original direction unchanged and only switch the ecliptic/galactic grid. The gold dot on the left will not move, but the address on the right will change. More parameters allow selection of another imaginary line of sight.
No need to memorize symbols
- α/δ
- Right ascension/declination; enter the unified cost in this lesson
- λ/β
- Zodiac Longitude/Latitude
- l/b
- Galactic Longitude/Latitude
- ε
- B1950 yellow-red intersection angle 23.4457889°
Algorithm, accuracy and scope of application
Complements Chapter 13 13.1–13.4 ecliptic/equator forward and reverse conversion, as well as 13.7–13.8 and subsequent inverse B1950 galactic transformation. Use unit vectors and orthogonal bases to avoid tan latitudes diverging at the poles. The program also provides the inverse horizontalInverse of the equatorial direction from north to east, and checks it against the existing forward transformation grid. The location/sidereal time operation of horizon coordinates is in another lesson in this chapter, "From Time to Azimuth". Not the J2000 modern galactic matrix.
my understanding check
Can ecliptic latitude and declination be regarded as the same number?
cannot — The starting plane is different.
Can the galactic formula here directly refer to the right ascension and declination of J2000?
No, you need to match the reference system first — The constants in the book are defined according to B1950.
Is the longitude still unique to the North Pole of a certain set of grids?
Not unique — All meridians meet there, with direction determined but longitude degraded.
Changing coordinates means changing the grid describing the direction; it is not moving the stars to another place.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 13 chapter