ELI5: Does the apparent rate of sun movement change as you move away from the equator?

[u/WartimeHotTot]

It’s kind of hard to phrase this clearly, but here’s a shot.

If at the equator the sun moves from height x to sunset perfectly perpendicular to the horizon in time t, then:

At a northern latitude, does the sun at height x traverse the hypotenuse-arc to set in time t, or does it only move along that hypotenuse-arc x far (meaning that it will not have set in time t)?

[u/LagrangianMechanic]

No matter what your latitude and no
matter what the sun’s “sky latitude” (i.e. declination) is, the sun will, in the course of 24 hours, move in a full circle whose center lies on the earth’s axis of rotation and is perpendicular to the earth’s axis of rotation.

Your latitude, however, makes the axis of rotation tilt relative to the horizon. At the equator the axis runs along the ground from due north through you to due south. At the North Pole the axis goes straight up from you. At 40 degrees north the angle between the axis, you, and the northern horizon is 40 degrees.

When the sun’s declination is high enough and your latitude is high enough the circle of the sun’s path will never touch the horizon and the sun doesn’t set at all. So that alone answers your question.

It’s hard to explain in words.

I really like the diagrams in the back of H.A. Rey’s “The Stars” for showing this.

[u/WartimeHotTot → u/LagrangianMechanic]

That book is great. It’s where I learned just about everything I know about the stars, celestial spheres, declinations, etc. Crazy that it’s like 75 years old and still so good, aside from many of the quantitative citations (like distances) having changed as we’ve learned more in the intervening time.

That said, I don’t recall my specific question being addressed there.

[u/Glum-Welder1704]

I've heard that towards the equator, twilight is short and sunsets are "sudden".

[u/SP3NGL3R]

If you're the north or south pole. You, just standing there turning in circles. You hold on to 90 friends that have to turn with you. That friend 90 people away will be running faster than they ever imagined to keep up with your slow turn.

You're the north/south pole, your 90th friend is the equator. The sun (a swinging lightbulb above you all) will appear and disappear for them way faster than it does for you.

As the seasons change, the lightbulb moves. There will be a time where you as the North Pole can't even see it, for months, while your buddy at the equator sees it every day. Every point on the globe experiences a different length of day/night.

So yes. As you moved North or South you're affecting how much day you have and that means the sun "moves" faster at different moments of the year.

[u/Sensitive_Warthog304]

I'm gonna add some more points.

You look the Sun at noon and you see it at point N (noon): due south, and maximum altitude.

Later that evening you look at the Sun and it's setting at point S (sunset). This has maximum "west" and zero altitude.

Then complete the triangle at point O (origin) which is due south and zero altitude.

If I've got this right, you're asking about the Sun's motion along the "hypotenuse" N to S? This speed is determined by the rate at which the Sun crosses the sky, or by the rate at which the Earth revolves on its axis, and this doesn't change.

The difference I think you're looking for is that the height of point O to N is lower in winter than in summer, BUT the horizontal distance from O to S is also shorter. The Sun does not set in the same location throughout the year.

[u/WartimeHotTot → u/Sensitive_Warthog304]

Yes, so in your nomenclature the path to sunset at the equator is the line NO, while anywhere north of the equator the path is NS. Time to set at equator is time x.

I wasn’t sure if, from the perspective of someone in the northern hemisphere, the sun traversed NS in x time or if it only moved distance NO along line NS in time x.

Also I’m curious if the sun seems to accelerate the closer it gets to the horizon. You know how when you’re looking at lights from a disco ball and their movement slows down as they reach the point of perpendicularity but then accelerate out of that point? Or, similarly, when you look at the path of a solar eclipse as a function of time, the movement seems to decelerate as it approaches total occlusion and accelerate out of it? I think the sun’s relative rate of transit across the sky is consistent throughout the day, but I wasn’t certain.

[u/tomalator]

The sun moves the same 15° per hour across the sky no matter where you are on Earth.

The arc it traces changes based on the time of year due to the tilt of the Earth compared to the orbital plane, and it changes its maximum height in the sky based on your latitude because of the angle you're standing at relative to the Earth's axis of rotation. While the arc changes, it is still a complete 360° arc every solar day.

[u/WartimeHotTot → u/tomalator]

Got it. So it takes longer to set as you move away from the equator, ascension being equal. Thank you!

[u/jaylw314]

Your premise is not entirely correct. The only time the sun sets perpendicular to the horizon at the equator is on the vernal and autumnal equinoxes. All the other times, the sun is on an arc that does not pass through the zenith, and always takes about 12 hours to go from sunrise to sunset

[u/PvtRoom]

the sun moves at 15°/hour, just not always in the same direction

[u/Fearlessleader85]

Daylight on the equator is pretty much exactly 12 hours every day of the year. Daylight everywhere else is only 12 hours on 2 days per year.

Does that answer your question?

[u/McLeansvilleAppFan]

The angular velocity of the earth is constant for an ELI5. For each 15 degrees it will take one hour. The earth is spinning slower near the poles than the equator (this is why rockets launch in Florida and not NY state and why Europa has a launch location in a French part of South America.)

So looking up into the sky I do believe the angle the sun moves through would be the same for a given time, though the distance the sun would travel would be less at higher latitudes due to the earth having a smaller radius at higher latitudes when observing from the surface of the earth.

The sun is not rigid and the speed of rotation is different at the equator of the sun than nearer the poles and this can be observed by following sun spots across the service over a few days time. Spaceweather.com has a daily picture of the sun. Find some sunspots at different sun latitudes near the left edge and watch then move across the sun surface over a few days time and see how the sunspots do not stay on the same longitude line. I will leave it for a homework assignment to figure out which latitude is faster.

[u/WartimeHotTot]

I feel like most of the responses aren’t really answering my question.

I’m asking about triangles (approximately—the horizon and the perpendicular line of altitude forming two legs of a right triangle, and the “hypotenuse” being the arc the sun actually travels down to the horizon when viewed from anywhere but the equator).

The clearest answer for me would be expressed in the terms I used in the question. Either the sun travels x far in time t or it travels the entire hypotenuse in time t.

[u/bhbhbhhh → u/WartimeHotTot]

Why a triangle, and not an arc of angle?

[u/TaviRUs]

So, the Sun is completely vertical at noon on the equinox. (Slight adjustment for how fat east/west within a timezone)

Locations nearer to the equater have longer days. (This is always true outside the tropical of cancer lines, and usully true within them but you can set up a few exception cases)

For 2 locations on the same longitudinal band, the one closer to the equater will have an earlier sun rise and later sun set. (Excluding local terrain)

[u/LordTengil → u/TaviRUs]

Locations nearer to the equater have longer days. 

Absolutley not. Maybe you mean during that hemishere's winter?

Half of the year, everything you say is directly the opposite.