there must be one day (..well probably two) when they meet and because of this it should be one day with the same amount of daylights hours at 41.45°N and 53.07°N not at the same time but in the same day of the year an equal daylight duration.

Yes, we call this Equinox.

> Yes, we call this Equinox

:D thanks hippo. The name reminds me something indeed :)

But it happens I checked the September 22th dawns, susnset and daylight hours:

41.45°N         06:58    19:05    12:06
53.07°N         07:12    19:21    12:09
[download]

Maybe this is the day when the distance is smallest among daylights hours?

L*

There are no rules, there are no thumbs..
Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.

From the previously linked article:

On the date of the equinox, the [centre] of the Sun spends a roughly equal amount of time above and below the horizon at every location on the Earth, so night and day are about the same length. Sunrise and sunset can be defined in several ways, but a widespread definition is the time that the top limb of the Sun is level with the horizon. With this definition, the day is longer than the night at the equinoxes

---

🦛

While the sun can reach the zenith only in the tropics¹ at noon (your shadow is between your legs) the perceived curve will become always flatter when distancing from the equator.

This curve is always under the horizon at polar night and always above in polar summer. That's because the rotation axis of the earth has an inclination compared to the sun³

Even a flat horizon is practically perceived like the earth's body hiding the sun like a mountain ridge surrounding you in winter. But in summer the horizon "lowers" to a valley and you are subjectively the one standing on a mountain top.

That's a gradual effect from poles to equator.

The combined effect of flattened curve, "moving" horizon and definition of sun rise or sunset effect the calculation. ²

Plus the flatter the curve, the longer does the sun need to fully pass the horizon from one tip to the other.

I found a German website where you can play with coordinates and check all parameters. The graphics are nice at displaying the perceived curve.

https://www.datum-und-uhrzeit.de/?coordinates=true

I compared points near Berlin and Rome with "integer" coordinates

HTH :)

¹) by definition!

²) it's even more complicated because of precession, nutation and uneven shape of the rotating potato ellipsoid we live on

³) more correctly the ecliptic, the plane in which earth is rotating around the sun

FWIW: I found the English version of that website https://www.date-and-time.net/

The graphics are pretty good, if you open the images directly you can play around with the parameters in the URL.

From all effects discussed is earth's axial tilt of 23 degrees the main factor, all the others are marginal.

Try winter solstice for the same latitude and you'll see how the days become shorter the closer you reach the north pole, till you have polar night.

That's the opposite at summer solstice, days become gradually longer till you have polar day.

Try the same location with different dates and you'll see how the curve is seemingly rising and dropping by 2*23° during the year. ( See Sun_path )

Here the images for equinox in Rome,

• day
• night
• earth position
Note how the altitude at noon is exactly 90°- 52.5° (your latitude)

That's why the curve when approaching the pole must become always flatter till it's a line

Together with the variation of altitude of +- 23 ° during the year the curve is rising and falling from the horizon.

Different curves = different sun hours for same latitude.

Cheers Rolf
_{(addicted to the Perl Programming Language :)
see Wikisyntax for the Monastery}

Update

I don't think the graphs are correct for the southern hemisphere. Sun should wander in the north.

It's complicated and related to seasons and the shape of the Earth (Earth is not round in case you didn't know), the Earth's orbit and precession all come into it. It may help to to remember that at the poles during mid winter there is constant darkness and constant daylight during mid summer. At the equator there is little seasonal change in day length. So at points between the equator and the poles the seasonal change in day length becomes more dramatic as you get toward the poles.

As already pointed out there are two times a year when the day length is nominally equal everywhere. The reason for all this strangeness is that the Earth's polar axis (the knitting needle the Earth turns around) is tilted over about 23.5 degrees. As the Earth moves around its orbit the poles alternate in pointing toward the Sun (summer for that pole) and away from the Sun (winter). This gives the seasons and the seasonal change in day length.

Equinox happens when the poles are "side on" to the Sun and is a point in time (an epoch). That means that strictly speaking there can only be one line of longitude where there is an equal day and night time around an equinox.

Then she infered (why dont you have to desume in English?)

thanks etj,

probably yes, but as I choice always English words with Latin origins (...well: roots ;) I already known the existence of to deduce but in Eatalian we have both: to deduce and to desume with the second with a bit of personal sense, not irrational but somenthing bound to your own perception. The two verbs are generally used as synonyms but the semantic is, at least for me, a bit different.

desumere: derivation from Latin desumĕre (de-sumĕre) to take for yourself
dedurre: derivation from Latin deducĕre (de-ducĕre) to take from smth

L*

There are no rules, there are no thumbs..
Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.

Wiktionary: desume

But yeah, no one ever uses that (anymore?).

Well, they say the devil is in the details.

It is certainly true that in summer days are longer at higher latitude and in winter they are shorter. If the continuum hypothesis held, there would definitely be a day (around but not on the equinox) when both were the same. But the continuum hypothesis does not hold, because day length between summer and winter is not a continuous function but a discrete one, so you can't guarantee a day when they are exactly the same, only a day when they are "pretty close."

TL;DR

There are three things that make the magic day different than the equinox:

1. As previously mentioned, the equinox occurs when the ecliptic longitude of the center of the Sun is at 0 or 180 degrees, but sunrise and sunset are the moments when the upper limb of the Sun is on the horizon. Since the apparent diameter of the Sun's disk is 0.5 degrees, this represents a difference of 0.25 degrees in position.
2. Atmospheric refraction causes distant objects to appear higher in the sky than they actually are. Obviously the magnitude of this effect depends on precise atmospheric conditions, but the accepted "typical" value is about 0.5 degrees near the horizon. This effect applies to Sunrise, but not the time of equinox.
3. Unless you are on the Equator, the Sun does not rise "straight up," but at an angle from the vertical equal to your latitude. This affects the amount of time it takes for the Sun to (apparently) travel the 0.75 degrees of arc from apparent Sunrise (when we see the upper limb of the Sun) and what I guess you would call geometric Sunrise (when the center of the Sun's disk is on the plane of the horizon).

I have not thought particularly about why the day changes length at different rates at Sunrise and Sunset, but I think it has to do with the fact that usually (meaning, not at equinox) the ecliptic (i.e. the path the Sun appears to take across the sky) intersects the horizon at a different angle at Sunrise than at Sunset (see point 3 above).

Disclaimer: I am strictly an amateur in the realm of computational astronomy. I believe the above to be basically correct, but I may have garbled the details. I am also the author of (among other things) Astro::Coord::ECI::Sun and friends, which (if you want to roll up your sleeves and get your hands dirty) can be used to investigate the above phenomena quantitatively. The POD says where the computations come from if you want to dig deeper.

Thanks Tom for your detailed reply!

I want to thanks also other monks for their replies and yes: it was dumb from my part to forget the very basic definition of equinox.. but as always asking here is a pure pleasure because you have chances to get not only the correct answer but, more important, a lot panorama behind and sweeties to feed your brain.

L*

*PS* incidentally I discovered Win32API::File::Time where Tom thanks dada and that the company they seem to work for produced the black and white film used in Eatalian neorealism movies as well all Totò's and Fellini's ones. Not all chemistry comes to hurt :)

There are no rules, there are no thumbs..
Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.

And don't forget, the length of a solar day changes over time, mostly due to redistribution of mass: liquid core, tectonic plate movement, tides (thanks, moon!), weather moving huge quantities of water, filling the Three Gorges Dam, and other stuff. That's why we have occasional leap seconds.

Oh, and the place where you are is also moving around, thanks again to tectonic plate movement. Some places on earth only move millimeters/century. Others, like locations near the San Adreas fault can move at a nippy 5-7 centimeters per year (and presumably much faster when the next big earthquake hits, but in that case equinoxes might be the least of your problems).

So if you need a very precise forecast, you may be out of luck. (If you need the to measure the day cycle to nano-second precission, you should also include air density, local gravity and your own speed to account for most relativistic effects).

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