Walking towards the sun

Assume that you’re at point X in the northern hemisphere.

When the sun rises, you start walking towards the sun. You continue walking towards the sun all day, maintaining a steady pace (assume the surface of the globe is flat and free of bodies of water, so you don’t have to worry about running into anything). You start by walking east, then trend south, then head west, always walking directly toward the sun.

At the end of the day, you are … where. Due south of your starting point?

And if you do it the next day and the next and the next … you’ll eventually end up at the equator? [Each day with less southward drift?] And once you’re at the equator, you’ll just go east and west along the equator all day and not move off it?

And if you started somewhere in the southern hemisphere, it would be the same, only you’d go north till you got to the equator?

Or would something completely different happen?

An obvious complication in the scenario is that the sun will appear at different angles depending on the time of year. At the equinox, the sun is above the equator, but at the June solstice, there are points in the northern hemisphere (between the equator and the tropic of cancer) at which walking towards the sun is walking north. This variation means that your stable point – where you end up just moving back and forth – isn’t on the equator, but at the sub-solar latitude, which varies sinusoidally throughout the year – 23°S in December, 0° in March, 23°N in June, etc.

I’m trying to work out whether there will be a net curve in your trajectory that pulls you away from due south as a result of the spreading meridians, longitudinal movement that changes the position time of your local noon during the walk, and decreasing latitude that results in more steeply angled (away from south) trajectory at the end of the day than the start. My first guess is that the effects cancel each other out; in any case they will be small if you’re actually walking, and not traveling an appreciable fraction of the Earth’s circumference in a single day.

If we assume that the seasonal change is negligible over the course of a single day, and that the distance you can cover in a single day is negligible compared to the size of the Earth, then at the end of the day you’ll be due south of where you were at the beginning of the day. For any infinitesimal period of time in the morning when you’re walking at some angle relative to due east, for the corresponding period of time in the afternoon, you’re walking at the same angle relative to due west, so the east-west components cancel out.

In the limit of extremely high “walking” speeds, you’ll end up trending westward, following the Sun around the Earth. Suppose, for instance, that you can walk fast enough to just go straight to the sub-solar point and follow that point as the Earth rotates: You’d end up walking due west, and never stopping (because the day would never end for you).

I would imagine you’d trend westward and southward, but with the errors made by an average walker plus the influence of terrain you may not be able to see the effect on a map over anything less than a long span of time.

At starting points north of the tropics there’d also be some north in your walking. At that time of year, the sun rises north of due east and sets north of due west, and the effect is of course more pronounced at higher latitudes. Near the arctic circle the sun rises just east of due north, and sets just west of it.

I think this is true only at the equinox (when sun is over the equator). At other times, there’s some north and south in the sun’s path over the earth.

Right, when I said that I was only relaxing the “slow walking” approximation, not the “slow seasons” approximation. But the north-south motion is maximized at the equinoces, not zero: For zero north-south motion, you’d want the solstices (the word itself means “sun still”, referring precisely to the fact that the north-south motion is zero at those times).

Doesn’t the equation of time imply that there is some asymmetry in the amount of time between sunrise and local solar noon and local solar noon and sunset? It would be only a fraction of a minute, and would vary between shorter morning and shorter afternoon over the course of a year, but still…

So, ignoring all other effects, you would tend to end up just east or west of due north or south from your starting point each day. When you factor in that moving westward of your starting point allows you to lengthen the day slightly, the westerly effects probably dominate over the course of a whole year.

No, you will be west of your starting point.

Let’s assume that the sun rises at exactly 06:00 and sets at 18:00, so the sun is due south at 12:00. You start walking east. By the time “noon” rolls around, your several miles east of your starting point. At this new location, the sun is due south before 12:00 (Let’s say 11:58). So your walk eastward is four minutes less than your walk westward.

Here’s a typical sun path diagram.
(They vary by latitude)

Depending on the time of the year you’ll leave your destination heading somewhere between NE and SE and continually vere to the right as you walk. Your path will look like a clockwise spiral and your destination will again vary by latitude and time of year.

No southward trending at all?

Sorry. I did not mean to imply that there was no southward trending. You will be south of your origin, but not due south. More like south-southwest.

If you did it from Philadelphia today, your path would look like this: D

If you walk at 2mph, you’d end up about 5 1/2 miles south and 1/2 mile west of where you started.

With north to the left of the “D,” I’m guessing. My starting point would be where the straight line meets the bottom of the curve?

North up, south down. Starting point would be would be where the curve and straight line meet at the TOP. Ending point would be where they meet at the bottom. Walking path would be the curve. Straight line isn’t really part of the path. And the curved line would actually extend a bit further west.

^ Yeah, that.

The straight line isn’t part of your path - just a straight line drawn from your starting point to your end point.

:smack:

Thanks.

Every time I see this thread I’m imagining a gag in the original Monkey Island, where in one area the sun was a selectable object. If you chose “Walk to” the sun, Guybrush would just look at you and say “Right. Walk to the sun.”