Where does the sun set?

Question

It's commonly said that the sun sets in the west.

However from my balcony I can clearly see that it sets significantly farther in the south during winter, and much farther north in the summer.

Why is this? Where does it set?

Answer 1

Where it sets depends on 1) your latitude and 2) the Sun's declination, which varies throughout the year between -23° (December) and +23° (June). Consider the following pictures, taken from A Quick Guide to the Celestial Sphere by Jim Kaler.

Objects that are on the celestial equator (like the Sun on approximately March 20th and September 23rd), rise in exactly East and set in exactly West:

However, if during the year the Sun travels more to the southern celestial pole (denoted SCP) in the winter on the northern hemisphere, or the northern one (denoted NCP) in the summer, that circle moves, and you see the point where it crosses the horizon (corresponding to sunset and sunrise) moves to the South resp. to the North as well:

Answer 2

The expression "the sun sets in the west" means that it is generally in the west compared to North, South, or East. It is not meant to say that it sets due west.

The position on the horizon where the Sun rises or sets can be calculated from the declination (dec) of the Sun (or any object) and latitude (lat) of the observer using $$cos(\theta_R)=-sin(dec)/cos(lat)$$ where $\theta_R$ is measured from due south (for us living in the northern hemisphere).

The Sun's maximum declination is +23.5 around June 21. If at 40 N latitude, the sun rises 121 degrees from due south (placing it at 180-121=58 degrees azimuth which is between NE and NNE). The sunset occurs between the WNW and NW (at 180+121=301 degrees azimuth).

The Sun's minimum declination is -23.5 around December 21. Sun rise and set are at 121 degrees (between SSE and SE) and 239 degrees azimuth (between SW and SSW), respectively.

(All values are approximate in my calculations.)

Answer 3

I tried working this out myself years ago. Back in the days of dialup to a Compuserve local node, before they had an internet interface. But it was also the other side of a visit from the burglars, who thought the rack of "gold" CDs must be worth stealing too, and that was my backup.

It's a common "problem" in celestial mechanics, and I recall the solution involving the square of the cosine of the observatory's latitude, as well as, obviously, the date. But I'd have to re-create 30 .... 26 year old notes from a college course to go any more detail. That course, and the college that did "Navigation by Sextant" as a compulsory course for sailors wanting to get their "Master" certificate are long since bulldozed. Along with the observatory.