[HN Gopher] Demystifying the Analemma
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Demystifying the Analemma
Author : chemd0ge
Score : 82 points
Date : 2022-03-20 10:29 UTC (1 days ago)
(HTM) web link (mtirado.com)
(TXT) w3m dump (mtirado.com)
| mixedmath wrote:
| These are very beautiful visualizations!
| chemd0ge wrote:
| Why is Earth's Analemma an 8 shaped loop?
| vikingerik wrote:
| It's a combination of up-down (north-south) and east-west
| motions. The up-down component is simple, that comes from the
| axial tilt.
|
| The east-west component arises from this: When the Earth is at
| perihelion (January), the time from solar noon to solar noon is
| slightly longer, because the Earth is moving faster and farther
| in its orbit, so it has to rotate a bit more until the same
| meridian points back at the sun again. At aphelion (July),
| that's reversed, solar noon to solar noon is slightly shorter.
|
| Put another way: A solar day is more than 360deg of rotation
| relative to distant stars. It's very close to 361deg, because
| the angle between the stars and the sun changes as the Earth
| advances in its orbit, by about a degree per day. At perihelion
| in January, it's slightly more yet again, like 361.0002deg, and
| in July, it's 360.9998deg; that difference takes a few seconds
| more or less to rotate. We don't vary our clocks based on that
| variable solar day duration; instead we fix our daily time
| intervals and let the sun's apparent position vary east-west
| slightly relative to that.
|
| The figure-8 shape arises from the relative phase of the two
| cycles. The maximum velocity for the north-south component
| occurs at the equinoxes, while the maximum velocity for the
| east-west component occurs at perihelion/aphelion. On Earth,
| these occur at different times. Interestingly, for Mars the
| converse is true; its equinoxes are near its
| perihelion/aphelion, and so Mars's analemma is almost not a
| figure-8 (it is, but one lobe is very small.)
| mrgriscom wrote:
| It's a misconception that the figure-8 shape is due to the
| eccentricity of the Earth's orbit. Most of the variation in
| the sun's horizontal apparent motion is also due to Earth's
| axial tilt. Orbital eccentricity only contributes the slight
| asymmetry seen in the final analemma. See my reply to the
| sibling comment for more detail.
| tomr_stargazer wrote:
| It would be purely up-and-down (due to the Earth's 23 degree
| orbital tilt) if the Earth was on a perfectly circular orbit.
| But because the orbit is slightly elliptical, and because its
| orbital speed thus varies throughout its orbit[0], the
| alignment of the Sun on the sky at "noon" drifts back and forth
| according to when the Earth's orbit "outpaces" its daily
| rotation or when the daily rotation outpaces the orbital
| motion.
|
| [0]
| https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_mot...
| mrgriscom wrote:
| This is incorrect. The analemma would still be a figure-8
| even with a circular orbit, but it would be symmetric -- the
| orbital eccentricity only adds the asymmetry we see in
| Earth's analemma.
|
| This is because the sun on an axial-tilted plane 'lags
| behind' then 'catches up' to the ideal 0-tilt sun over the
| course of the year. At the equinoxes, the sun's motion has a
| significant vertical component. Therefore, it's horizontal
| speed is slower than an untilted sun (both suns still travel
| through the sky at the same speed of 360/365 degrees per
| day), so it will lose ground and drift back. At the
| solstices, the sun moves horizontally, but at an higher
| latitude (equal to Earth's axial tilt) on the celestial
| sphere, covering more degrees of longitude for the same speed
| than the ideal sun moving along the equator, hence making up
| the lost ground. This variation in horizontal speed
| throughout the year creates the figure-8.
| KineticLensman wrote:
| One interesting consequence of the varying offset between mean
| noon and solar noon is that the when the days get longer /
| shorter around the shortest / longest day, the change in the
| morning isn't always the same as the change in the evening. In
| the southern UK, where I live, sunrise might continue to get
| later for a couple of weeks while sunset gets earlier. It took me
| _ages_ to understand why.
| enriquto wrote:
| Now, can you prove that the shortest night of the year is
| adjacent to the longest day? This is indeed the case for all
| latitudes, but it is wickedly difficult to prove.
|
| Hint: start by setting up an imaginary planet with irregular
| orbit where this is not the case. Then find what property of
| the orbit you needed to force that does not happen with the
| earth.
| notthemessiah wrote:
| I wrote something similar in Pluto.jl (Julia-native reactive
| notebook), but mine focuses more so on the apparent analemma from
| a given point on earth at a given time, rather than explaining
| the fundamentals of how an orbit gives shape to the analemma.
|
| Interactivity requires either running Pluto locally in Julia
| (`using Pluto; Pluto.run()`) or hosted on Binder.
|
| https://notthemessiah.github.io/pluto/analemma.jl.html
| adzm wrote:
| This is awesome work. I had tried to figure this out on my own
| but ran into a lot of trouble, and seeing everything together
| here finally made it click.
| Maursault wrote:
| "Analemma" is a very unfortunate name for something quite
| beautiful.
| OldSchool wrote:
| Reminds me of Lissajous figures on an oscilloscope, visually and
| the principles involved.
| adolph wrote:
| In Neal Stephenson's "Anathem" an analemma observed on an alien
| spacecraft leads the planet's inhabitants to speculate that the
| spacecraft is from ****** (not going to spoil it).
|
| https://en.wikipedia.org/wiki/Anathem
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