OddThinking

Stargazing.net has quite a number of well-explained astronomical calculations implemented in QBasic, including sun position. There’s also a Python library, PyEphem which is fun to play with.

This FAQ recommends Astronomical Algorithms by Jean Meeus.

[Ed: Broken link to PyEphem corrected.]

Couldn’t resist: PyEphem agrees with Julian’s dad.

Alan,

The mathematics matches reality and proves me wrong, but doesn’t satisfy my need for a rough understanding of how this paradox works (i.e. that an object in the North could appear in the South)

I just had a glimmer of understanding while in the shower. Let me see if I can convey it textually.

Imagine you have ordered a freshly terraformed small planet. Have the engineers make it a perfect sphere, covered in flat land.

Pick an arbitrary spot in the far south of the planet, and have the engineers build two roads intersecting at that point.

The first road should start describe a Great Circle around the planet. Its length will be equal to the circumference of the sphere. It should start out due West.

From the original vantage point, it will appear like a straight line, disappearing over the horizon. It doesn’t stick to due West. If you were to follow the straight line, you would notice your compass gradually turns closer to the North, then to the South. You will cross the equator twice.

Have the second road built to stick to the same latitude and head East-West around the planet.

How long is this second road? It is shorter than the first one – its length is proportional to the cosine of the latitude of the point you chose.

It will appear to curve to the left as you look West. The closer you are to the pole, the tighter the curve will be.

Some distance down the second road, have the engineers build a huge tower with a giant bright yellow glowing globe at the top.

Cover the second road in camouflage paint, so you can’t see it easily.

So standing at your arbitrary point, you can now see two landmarks.

One is the first road, that looks straight as a post, and – according to your compass – heads due West.

The other is a giant yellow globe. It appears to the left (South) of the first road, and yet it is exactly due West of you.

Is this the visual solution to the paradox? Does this adequately explain how an object, such as the Sun, can appear further South than you (i.e. left of West) even if it isn’t?

I think you’re kind of on the right track, it is due to the difference between our reality (spherical) and how we perceive it (plane). As my colleagues will confirm, I have spent a reasonable amount of 2006 wandering around the office muttering, “these maps would be a lot easier if the world were flat.”

I had another go at explaining with a ball and a lamp on my blog.

In summer, at the poles, there is no sunset. You can always see the sun. This is true all over the arctic circle if I remember the definition correctly.

So the sun appears South during the “night”, and North during the “day”. Where you live gets a reduced form of this effect.

Your explanation includes the idea that great circles and latitude lines only coincide at the equator, but I find mine easier to think about.

A good explanation to your questions is in this website. Check it out!

http://solar.physics.montana.edu/YPOP/Classroom/Lessons/Sundials/winter.html

The sun actually sets just in west two days a year!

Julian, did you ever come to grips with this? (I know, I am quite late to the comment party here, but your most recent post did link to another post which is “adjacent” to this one.)

I followed most of Alan Green’s ball-and-lamp illustration, but stumbled at the very end:

If you stand behind the ball and sight back to the light across that point, you will see that, from the Earth’s inhabitant’s point of view, the Sun is south of the line of latitude.

(Somehow I doubt buying him a soda would have been sufficient to lure him all the way over to the States with his props to give me the demonstration. I mean, I’d probably at least have to spring for a pint or two.)

But I think I finally got it when I drew myself a few simple pictures, which proved more precise for me than using an actual light and an actual ball. While I really liked your description of the difference between the Great Circle road and the Constant Latitude road, the sun appears to set even farther south than the latter. If I understand correctly, any time the South Pole is closer to the sun, the sun will seem to rise and set south of the observer’s latitude, whether the observer happens to be in the Northern or Southern Hemisphere (except near the poles, where the sun doesn’t even break the horizon). At the equinoxes, the poles are equidistant from the sun, and thus the sun rises and sets exactly due east and west, respectively.

i think it moves from east to west!

Thanks for your contribution, LMN, but I think I covered that answer in the second line.

Sun set changes seasonally. I have tried over and over to explain this to a friend of mine. I have a westward facing window and I can see that in the summer the sun is setting to the north. Today I was fooling around on the web and found this on an astrology website.

“Around 21 March and 23 September, the setting sun is almost due west. Howver, the direction in which the sun sets changes from day to day. If you watch sunsets from the same location for a year, you’ll observe the sun setting a little further towards the south each day between 21 June and 21 December, and a little further towards the north each day between 21 December and 21 June. Around 21 June, the sunsets is furthest to the north, and around 21 December it is furthest towards the south.”

There is a picture on another website that doesn’t click with me, but it may answer your question without a tennis ball…

http://www.scribd.com/doc/12797881/Why-the-sunset-location-and-time-change-throughout-the-year

Thanks Kenyack,

My first suggestion is to use modern astronomy (rather than astrology) web-sites to learn more about your universe.

Your unattributed snippet explains that the sunsets move North-South during the year, but doesn’t explain why the sun, while directly above a more Northerly latitude than you, can appear to set in South of due West.

Your other link explains why the sun moves North-South seasonally from the perspective of an equatorial observer, but again doesn’t address the key question.