I found it on the star map, but I couldn’t find it when I looked up: where should I look?
Turn around first, then look up. Turn the address of the star catalog into an action you can follow.
Sky coordinates and observations
A friend sends you a star coordinate. You take the star map and walk outside, but you still don’t know where to look. We break this thing into two actions: first use the compass to turn to its direction, and then look up from the horizon.
Guess first
To tell a friend where a star is, is it enough to just say "look up 30°"?
Show answer and explanation
Also tell me in which direction? — The head angle only gives the height, and also requires a horizontal orientation.
Then connect experience and science
First let the date be a consecutive number of days
Convert the UT1 date to JD; then find the Greenwich mean sidereal time to get the orientation of the prime meridian relative to the celestial sphere.
Date + UT1 → JD → θG
Put the longitude in
The longitude here is due east. As you move eastward, local sidereal time increases; compass north is always pointing up in the diagram.
Local sidereal time θL = θG + λ
Compare with star's right ascension
Right ascension is expressed in hours on the interface. First multiply by 15 to convert to degrees. After subtraction, the local hour angle is obtained, and then converted into horizon coordinates.
H = θL − 15α
Read out bearing and altitude
A compass only indicates direction, not altitude. A dotted line is used below the horizon; at the zenith or nadir, there is no unique azimuth angle.
North 0° · East 90° · South 180° · West 270°
Expand the calculation
θ地方 = (θ格林尼治 + λeast longitude) mod 360° H = θ地方 − 15αHour e = −cos δ sin H n = cos φ sin δ − sin φ cos δ cos H A = atan2(e,n) mod 360° h = asin(sin φ sin δ + cos φ cos δ cos H)
The directions in this lesson are measured from north to east: north 0°, east 90°. e and n are the eastward and northward direction components respectively; when both are zero at the same time, the orientation is undefined.
give it a try
Click "Facing South" and "Turn West" to compare the compass and the angle of the head; "Occluded by the Earth" means that it cannot be seen directly now. Locations and star catalog addresses can be modified in more conditions.
No need to memorize symbols
- λ
- Geographical longitude, this lesson uses east plus west minus
- α / δ
- Stellar right ascension (hours) and declination (degrees)
- H
- Local hour angle, positive to the west
- A / h
- Azimuth (from north to east) and geometric altitude
Algorithm, accuracy and scope of application
Follow Chapters 7, 12, and 13 in series. This lesson uses the azimuth convention of starting from the north and heading east, while the book and AA+ Equatorial2Horizontal use the convention of starting from the south and heading west; when comparing, add 180° and then normalize. The inputs are imaginary flat equatorial coordinates that are compatible with the mean sidereal time used and do not directly represent the unprecessed J2000 catalog. Nutation, aberration, refraction, parallax, and topography are omitted; return "undefined" at zenith/nadir. 24h means 0h the next day. The scenario view only replaces the same result with a fixed pattern or ground observation action, and the scientific model and numerical range remain unchanged.
my understanding check
On the compass in this lesson, where does 90° point?
East — Measure angles from north to east, 90° is due east.
Time has passed and the location and star catalog address remain unchanged. Does the telescope need to be adjusted?
need — The Earth's rotation changes the position and height of the local sky.
When the target is directly overhead, do we have to turn to true north first?
No, there is no unique value for horizontal orientation — Any horizontal direction raised directly above points to the same zenith.
Finding stars requires "which way to turn" and "how high to raise your head." Both actions are determined by location, time, and star catalog address.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 13 chapter