Why do the patterns on the moon look crooked when I take pictures of it?
If the phone is held upright, the moon surface pattern may be tilted: first distinguish between "above you" and "north of the celestial sphere".
Sky coordinates and observations
You hold your phone upright and take a picture of the moon once earlier and again later. The orientation of the same pattern appears to have changed. The ground is always at the bottom of the picture, but when the direction on the celestial sphere passes through the sky, it does not always coincide with "up" on the picture.
Guess first
The moon pattern is tilted in the photo. Does that mean the moon suddenly rotates rapidly?
Show answer and explanation
uncertain — The relative direction of local upward and celestial north also changes, making the pattern in the camera appear to rotate.
Then connect experience and science
Give the image an upward direction
The vertical arrow in the figure always points toward the zenith. The blue mark on the schematic disk represents celestial north and is not an actual surface feature of the moon.
Local Up: Toward the zenith
Then mark the direction of the north
The direction from the celestial body to the North Celestial Pole often does not coincide with the direction of the zenith. Their angle is q.
q: The angle between the zenith direction and the north direction
Let the celestial bodies move across the sky
Change the hour angle and watch the marker rotate relative to "above". The equations use atan2 to handle quadrants to avoid losing half a circle using just the arctangent.
q = atan2(sin H, tan φ cos δ − sin δ cos H)
recognize special locations
When the celestial body is exactly at the zenith, the tangential direction to the zenith does not exist and q is not defined. This will be clearly shown here.
H = 0 and δ = φ → q undefined
Expand the calculation
y = cos φ sin H x = sin φ cos δ − cos φ sin δ cos H q = atan2(y,x)
This is a stable writing method adopted by the implementation to avoid directly calculating tan φ. When x and y are zero at the same time, the zenith direction cannot give a unique angle.
give it a try
Compare "on the way up", "passing the highest point" and "lower to the west" in order. The small orange dots mark the same pattern location and are not new spots.
No need to memorize symbols
- q
- Parallax angle, unit: degree; clockwise in the figure indicates positive values
- φ / δ
- Observer latitude/celestial declination
- H
- Local hour angle, positive to the west
Algorithm, accuracy and scope of application
Using the atan2 form of Equation (14.1), the picture shows the direction angle and does not simulate the real lunar surface, camera mirror or optical system rotation. Declination limits distance from the celestial pole. The degradation of the zenith and nadir is represented by null; the geometric angle can still be calculated under the horizon, but the page will prompt that direct observation is not possible. Press AA+ CAAParalllactic::ParalllacticAngle to compare, note that the AA+ hour angle input is hours. 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
Will the outer frame and horizontal indicator line of the mobile phone follow the pattern during the experiment?
Won't — They maintain a local "upward" reference, rotating the celestial sphere patterns relative to their orientation.
Have the shapes of the spots in the left and right pictures changed?
No, just in a different direction — The same fixed pattern is placed according to different reference directions.
Is the parallax angle here caused by the change in distance of the moon?
no — The names are similar, but q in this lesson is the angle between the two directions, not the distance parallax.
"Up" in the camera follows the ground you are standing on, and "north" follows the celestial sphere; if these two directions do not coincide, the pattern may look crooked.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 14 chapter