How high should you raise your head when you see a star?
Turn the abstract "elevation angle" into the action of raising your head while standing on the ground.
Sky coordinates and observations
Look straight at the distant horizon, then slowly look up until you can see the top of your head. The "height" of a star is the angle at which it looks up, not how far it is from the earth. Change the location or wait for a while, and the position of the same star will also change.
Guess first
When astronomy says a star has an "altitude of 30°," does it mean that it is 30 kilometers above the ground?
Show answer and explanation
It's the angle of looking up — It represents 30° upward from the horizon and does not represent the actual distance.
Then connect experience and science
Stand firm first: Find the horizon
The horizontal line is the altitude angle 0°. Above is positive and below is negative; negative height indicates that the geometric position is below the horizon.
h = 0°: horizon
Give the stars a celestial address
Declination is the angle relative to the celestial equator, and latitude determines your zenith orientation.
φ: your latitude; δ: declination of the star
Let the earth spin
Drag hour angle H: 0° means ascending the Midheaven, a positive value means heading west across the meridian.
H = local sidereal time − right ascension
Project the celestial sphere into your sky
Project the star direction to the zenith direction and take the inverse sine to get the height. The picture below is a curve of height versus time angle.
sin h = sin φ sin δ + cos φ cos δ cos H
Expand the calculation
H = θ地方 − α u = sin φ sin δ + cos φ cos δ cos H h = asin(u)
If α is given in hours, first multiply by 15 to convert to degrees. u is the unit component toward the zenith; the arcsine reduces it to an altitude angle.
give it a try
Change the latitude to 70° and the declination to 60°, and make a full circle. Will this star ever fall again?
No need to memorize symbols
- φ
- Geographical latitude, north plus south minus
- δ
- Declination, north of the celestial equator is positive
- H
- Local hour angle, positive to the west, unit is degrees
- h
- Geometric altitude angle, positive on the horizon
Algorithm, accuracy and scope of application
This lesson only demonstrates the height component from the equatorial coordinate to the horizon coordinate, equation (13.6), and does not calculate the azimuth angle. Excludes atmospheric refraction, terrain occlusion and geocentric parallax. The hour angle parameter of AA+ Equatorial2Horizontal is in hours, which needs to be divided by 15 for comparison.
my understanding check
When the stars are overhead, how high are you looking up relative to the horizon?
90° — From the horizon to the top of your head is one quarter of a turn, or 90°.
The star is below the horizon. Can you see it if you look underground?
No, the earth is blocking it — Below the horizon means that the direction is blocked by the earth, and the dotted line does not mean that there are real stars underground.
Could the same star appear higher or lower at different latitudes?
possible — The location changes, and so does the direction of your horizon and zenith.
The altitude angle is "how high you want to raise your head." It talks about direction, not distance.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 13 chapter