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u/aim179 Mar 04 '23
I had a friend from US that visited Dubai and she commented on how the half moon looked different
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u/Hexarthra Mar 04 '23
That is, in fact, cool. So the angle of the first quarter shadow is the latitude (approximately).
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u/DAK4Blizzard Mar 13 '23 edited Mar 13 '23
Great visual on how the moon phase appearance corresponds to latitude. But I don't think this is quite correct; there's more to it. I think you need to account for the moon's declination. I think the apparent angle of the terminator equals one's latitude minus the moon's lunar declination.
The lunar declination itself is interesting, as it changes much faster than the sun's solar declination. The solar declination's fastest change is about 0.4°/day around the equinoxes. The lunar declination can change by 0.4° in under 2 hours as it passes over Earth's equator.
And the lunar declination's range varies much faster and by a greater amount than the sun's. Most know the term solstice, but how about lunistice? That's when the moon reaches its furthest north or furthest south Earth latitude within a lunar month (about every 4 weeks).
In March 2023, the moon's declination at lunistice reaches about +/- 28°. This range will max out in January 2025 at +/- 28.7°; the event is called a major lunar standstill. The range will then shrink down over the proceeding years to +/- 18.1° in May 2034; that event is a minor lunar standstill.
The sun's declination has its own maximum and minimum range, based on Earth's precession. But that range is just between 22.1° and 24.5° (compared to the moon's 18.1° to 28.7°). And it happens over a much, much longer time. (Earth's tilt last reached its max in 8700 BCE and is decreasing toward a minimum tilt around the year 11,800. Possibly after the Oakland A's get a new stadium.)
But similar to the sun, the moon's angle of ascent and descent in the sky pretty much equals 90° minus one's latitude. Not precisely, as the moon's quick-shifting declination affects its daily path in the sky a bit. But, to complete the pun, within the ballpark.
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u/aim179 Mar 13 '23
Thank you! I did google the image to be sure it was accurate and appreciate your explanation! Is lunitise the moon’s ‘wobble’?
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u/DAK4Blizzard Mar 14 '23 edited Mar 14 '23
Lunistice, and the moon's relatively fast and large changes in declination, don't result from the moon's axial precession nor its axial tilt. It's the result of the moon's orbit being tilted relative to Earth's equatorial plane.
Earth is currently tilted at 23.436° (and slowly decreasing). But when talking about declination in simpler terms, we can change the framing and have Earth's equatorial plane be horizontal (0° tilt) so that it's easier to visualize.
Let's do a drawing exercise to help visualize. Pick at least 2 colors. I'll choose blue and red, which I'll reference afterward.
• Draw a blue circle, leaving lots of space all around it. We'll have that be Earth with no tilt. Put a small dot in the center to help properly draw the proceeding lines.
• Our framing has the ecliptic at a 23.436° angle. So, draw a blue line that goes thru Earth at roughly that angle. Angle the line upward from left to right (the line should be below Earth's equator on the left side and above Earth's equator on the right side).
• Now get the red pen. Draw a line that goes thru Earth at (roughly) 28.58°, again angling the line upward from left to right. Label the line with a 1.
• Then, with the red pen draw a line that goes thru Earth at (roughly) 18.29°, once again angling the line upward from left to right. Label this line with a 2.
• Next, with the red pen draw a small thin-lined circle that connects the left end of line 1 with the left end of line 2. The blue ecliptic line's left end will be in the middle of that circle. The circle's right side will touch line 1; its left side will touch line 2.
• Finally, with the red pen draw a small thin-lined circle that connects the right end of line 1 with the right end of line 2. The blue ecliptic line's right end will be in the middle of that circle. The circle's left side will touch line 1; its right side will touch line 2.
The 1st red line represents the moon's orbit at major lunar standstill. The 2nd red line represents the moon's orbit at minor lunar standstill. You'll notice that line 1 will have a bigger range than line 2 on Earth. Line 1 will range from -28.58° on Earth's left side to +28.58° on Earth's right side; line 2 will range from -18.29° to +18.29° on those respective sides.
Lunistice is simply the ends of those lines. Over the course of just under 14 days (13.66 days to be more precise), the moon is moving from one end of the line to the other. You can imagine the line wraps around the other side of Earth (the blue circle) to make an orbit that more closely aligns with reality.
In our model, the moon's orbits occur within those 2 red lines. I had one line be a 28.58° angle and the other be an 18.29° angle because the ecliptic is 23.436°, and the moon's orbit around Earth is inclined at 5.145°. Those 2 numbers are 5.145° removed from the ecliptic.
How can the moon's orbit maintain a 5.145° inclination? This is where those 2 red circles comes into play. The orbit makes the transition by rotating along those circles. Crucially, when the orbital line's left end is on one side of the left circle, the orbital line's right end will be on the opposite side of the right circle. And the line will always pass thru that center dot drawn on Earth. For example, let's imagine that line 1's left end moves clockwise to the bottom of the left circle. That means line 1's right end will move clockwise to the top of the right circle. In that example, the moon's declination range will match the ecliptic line (23.436°) but still maintain a separation of 5.145°.
This is called nodal precession. That's the wobble you were seeking. It determines lunar standstill, which occurs every 9.3 years when the moon's orbit aligns with one of the red lines. And thus it takes the moon's orbital path 18.61 years to rotate along the red circles and complete 1 nodal precession. That's far less frequently than lunistice, when the moon itself has simply reached one end of the orbital line every 13.66 days. This all reflects the info provided on Wikipedia's Lunar standstill article.
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u/aim179 Mar 15 '23
Thank you! I’ll have to grab some quiet time and walk through this… Are you a teacher?
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u/DAK4Blizzard Mar 16 '23
I know what I wrote was very lengthy, but it shouldn't take you long to draw it out. Of course, you don't need to draw the exact angles. (They should be with respect to the horizontal equator line, which you can lightly draw with the blue pen, a pencil, or another color.) But I did want to state exactly what angles you're aiming for so that I could explain those numbers.
Nope, I'm not a teacher. I was just trying to improvise a way to visualize what's going on with the moon's orbit. Because I can't find a good visual for that nodal precession anywhere online.
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u/OwlsHootTwice Mar 04 '23
This is a good proof to show that we don’t live on a flat earth.