Why does the sun rise and set north of E and W?

In Montreal, the day length on the equinox is about 12:05 and I understand the reasons for that. (A combination of refraction and definition of sunrise and sunset). But according to the World Clock, the sun rises at 89 deg and sets at 271 deg. It is the previous day (March 19) that it rises at 90 and sets at 270. The equinox here is in late afternoon (5:58 PM, EDT). Explanation?

Montreal’s latitude and earth’s seasonal tilt?

Slight error in the site?

Try NOAA’s website, though you’ll need the lat/long for Montreal:

https://www.esrl.noaa.gov/gmd/grad/solcalc/sunrise.html

ETA: Updated site is probably better: https://www.esrl.noaa.gov/gmd/grad/solcalc/

For any latitude other than the equator, the sun rises and sets due E/W only at the equinoxes.
In Montreal, at the summer solstice the sun rises/sets 35° north of E/W (i.e. almost NE and NW); at the winter solstice the sun rises/sets 35° south of E/W (i.e. almost SE and SW).

Take a look at the 3rd image down on this page, the one with the stick man on a green circle at the center.

https://physics.weber.edu/schroeder/ua/sunandseasons.html

Imagine a vertical plane extending E/W and up/down from where you are standing. Due to your northern latitude and the curvature of the earth, the path of the sun through the sky is tilted. At midday, it is always south of this plane, in the southern part of the sky; at midnight, it is always north of this plane - if the earth were transparent, you would see the sun at midnight to the north of directly underfoot. This part is a function only of latitude and the curvature of the earth - it has nothing to do with the tilt of the Earth’s axis of rotation.

The tilt of the Earth’s axis of rotation shifts this tilted plane of the sun’s path in parallel higher or lower in the sky during the year, as shown in the diagram. In winter, the sun is visible for less than half of the rotation, all in the half when it is south of the E/W plane described above. So it rises toward the SE, remains in the southern part of the sky all day, and sets in the SW. In summer, the sun is visible for more than half the rotation, including the entire half when it’s south of the plane and a part early and late in the day when it’s north of the plane. So it rises toward the NE, passes into the southern half of the sky an hour or two after rising, is high in the southern sky at midday, passes back into the northern half of the sky an hour or two before sunset, and sets toward the NW.

This website gives the path of the sun for any location.

https://www.sunearthtools.com/dp/tools/pos_sun.php

Search the location, and page down to the circular diagram, it shows the range for different times of year.

It’s the same reason that the day is a little bit longer than 12 hours. From the unrefracted center of the Sun being on the horizon at sunrise to the unrefracted center being on the horizon at sunset is exactly 12 hours, and the places where those two events happen are at 90º and at 270º. When the top edge of the Sun first makes its refracted appearance over the horizon is a little bit earlier than that, so it’s still a little further north, and likewise at the setting end.

D’oh, I should have read the OP more carefully. Based on the title of the thread, I assumed that you were asking another question that comes up a lot in navigation, and copied in an answer I wrote for somebody else.

I think Chronos has the answer.

I’m not sure it is an error. On March 20th in Montreal, at both sunrise and sunset the apparent declination of the sun is a bit north, enough so that the azimuths of 89.x and 270.y round off to 89 and 271, respectively.

ETA ninjaed by Chronos

:smack: Why didn’t I realize that? Thanks Chronos.

Let me add to his post the comment that, leaving refraction aside, the sunrise is defined as the instant of the first appearance of the sun on the horizon. Sunset is the time of the last appearance. A more logical definition (but almost impossible to observe accurately without fancy instruments) would be the time that the horizon bisects the sun. But then refraction would rear its head anyway.

And in fact, atmospheric refraction is about 0.6 degrees at the horizon, while the Sun’s apparent radius is about 0.25 degrees, so refraction is the larger of these effects.

Extreme-ish example:

If you are somewhat south of the Arctic Circle on the summer equinox you would see the Sun rise just to the right of true north, circle around and then set just to the left of true north. (Further north on the summer equinox it wouldn’t set at all.)

The further south you are on that day, the farther away from true north the sunrise/set would be. Nearing the Antarctic Circle, the rise and set would be very close to true north.

There is no summer equinox. Equinox is what we’re talking about here, but June/December 22 is solstice.

Here’s a really useful site I frequently use to determine sun angles.

The calendar at the top selects the day of the year; the slider at the bottom of the page adjusts the time.

This handy web page will output data for any solar-system body. There is also a service which generates nautical almanac pages (useful for the Sun, Moon, planets, bright stars).

Sorry. Solstice it is.

But the point is, the OP isn’t asking about solstice. Of course the Sun will be far north at the June solstice. It’ll be north by a lot more than the 1º discrepancy he’s noticing. But at the equinoxes, one would expect it to be exactly due east and west, and it isn’t, quite.

Thank you for the link; that’s a great site.

Does it? I’ve got no intuition on spherical geometry, and I haven’t looked at the numbers. Does the fact that the sun appears to rise earlier than expected explain it’s northing bias?

I was expecting an explanation that although the sun is directly overhead at 12:00 noon pm the equinox at the center of the correct time zone, the curvature of the earth biases the sunrise - sunset locations.

The relevance of the curvature of the Earth depends on how high your vantage point is above the surface. But a person’s height is negligible compared to the radius of the Earth, so the effect due to curvature is likewise negligible.

It will be proportional to the square root of your eyes’ height and not entirely negligible: easily a couple of minutes of arc. Also, varying temperature and pressure may produce refractive effects of similar or even greater magnitude, all of which could affect the observed time of sunrise and sunset.