Why are there two "north directions" for the same sky photo?
The equatorial grid and the ecliptic grid use different north poles. Choose a coordinate system before marking the direction.
Sky coordinates and observations
When drawing a grid for a photo, some people follow the direction of the celestial equator and some follow the direction of the ecliptic. Both sets of grids may be correct, but their north arrows at the same point may not coincide.
Guess first
Is "north" necessarily the same arrow in equatorial coordinates and ecliptic coordinates?
Show answer and explanation
uncertain — The North Pole of the two sets of coordinates is different, and the tangential arrows in the same celestial direction will also be different.
Then connect experience and science
Compare two kinds of "north" in the direction of celestial bodies
North on the equatorial coordinates points to the North Celestial Pole, and north on the ecliptic coordinates points to the North Ecliptic Pole. Their local orientations are usually not the same.
Project the two north pole directions to the point tangent plane
Rotate the ecliptic position and the angle also changes
The two arrows in the picture both start from the same direction point and do not represent two different stars.
tan q=cosλ tanε/(sinβ sinλ tanε−cosβ)
Relying on the tangent value alone is not enough to determine the quadrant
Angles with the same tangent may differ by 180°. This lesson uses the actual tangent vector facing north to determine the directed angle, and then gives the small angle between the two lines.
q determines the orientation using vector dot product/cross product
Degeneration occurs at the celestial pole
If a celestial body is exactly at the North Pole for a set of coordinates, there is no unique value for the tangential direction of "continue north" for that set. You cannot force zero filling.
zero tangent vector → direction undefined
First, project the ecliptic north pole and the equatorial north pole onto the tangent plane of the target point, and then use dot product/cross product to determine the angle and direction. tan q only gives a ratio and cannot alone distinguish directions that are 180° apart; degradation must be reported when the projection is zero.
give it a try
First look at 0° and 90° on the ecliptic, and then try the degraded position of the North Celestial Pole. The arrows here only compare the coordinate direction, not the observer's horizon.
No need to memorize symbols
- λ / β
- Zodiac latitude and longitude
- q
- The directed angle measured from the north direction of the celestial sphere to the east of the celestial sphere
- line angle
- Two lines whose directions differ by 180° still coincide with each other
Algorithm, accuracy and scope of application
Original book printed page 100 general formula and tan q₀=−cosλ tanε when β=0. Here, the north celestial pole and north ecliptic pole vectors are projected onto the tangent plane of the celestial body, and atan2 is used to obtain the directional angle of the actual northward arrow; the tangent original formula or AA+ single branch may differ by 180°. In the figure, the celestial sphere points north upward and east toward the left, and the arrows and data adopt the same convention. If the output direction is not unique, it will be null, and pseudo 0° will not be output.
my understanding check
The two arrows start from the same point, what do they mean?
Orientation of two reference systems — What is compared here is the coordinate datum.
If the tangent values are the same, does it mean they must be the same directed angle?
Not necessarily, it’s the same if it’s 180° different — Must be combined with quadrant or true vector direction.
When it is exactly at the North Celestial Pole, what is the tangential direction continuing toward that North Pole?
undefined — The directional projection is zero, requiring explicit handling of degradation.
When drawing direction arrows, you also need to indicate the coordinate system; "North" with the same symbol may point to different celestial poles.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 14 chapter