NavList:

Ken, you wrote:

"I feel that the reason many people have trouble REMEMBERING how celestial navigation works after once having learned it (and most people do), is that they have not worked through the abstractness of the concept, which is best accomplished through reflection on what is really happening."

 

Possibly. Figuring out why users forget a skill is a difficult and complex task. There are as many answers as there are students. Some people simply have bad long-term memories. Others have good memories but specifically suited to visual imagery (they love diagrams and probably are more comfortable with the correct geometry over the flagpole/lighthouse analogy). Many others have good memories suited to text and verbal mnemonics. These are the people who remember how to get to a destination (grandma's house) by a list of verbal instructions (turn left at the blue house) while the people with visual memory usually picture some sort of map overview. In navigation, there are many users whose favorite memories while learning the subject are of mnemonic rhymes and word games: "if it's on, it's off" for example. To the topic at hand, I am confident that there are plenty of students who benefit from the flagpole/lighthouse explanation because it suits their particular memory style. And that's good enough for me.

 

And you wrote:

"  As we know, unique positions can only be determined on a curved surface, and never on a flat one (except for space celestial of course)."

 

If you have stars at short distances (lights on top of flagpoles) then you can get circles of position and fixes on an idealized flat surface just like the standard celestial case. This geometry "maps" to the curved case one-to-one. You can think of it this way. There are two extreme cases of possible geometries:

1) stars at infinite distance, surface of finite radius of curvature.

2) stars at finite distance, surface of infinite radius of curvature (a flat plane).

 

Both idealized situations yield many of the same principles -- circles of position, GP is where star is straight up, altitudes increase towards GP, fixes with two possible locations for two circles of position, three circles yield a single-point fix, etc. They differ in mathematical details, especially the relationship between distance from the GP and change in altitude.

 

I DO agree that there are teaching situations where you might get better results by teaching from extreme case 1 and completely ignoring the "lighthouse" analogy, but let's bear in mind that stars at infinite distance and a spherical earth are idealizations, too.