NavList:

Commenting about one Bill Ritchie's Suggestion, Frank you indicated here :

QUOTE

You also wrote:
"Of more direct navigation interest, imagine taking Moon meridian passage sights with an accurate theodolite, recording the time of culmination and calculating your latitude and longitude. [...] Perhaps using the Moon for meridian passage sights is not always a good idea. "

Heh. Funny you should mention that! We can fix this. I'm sure if any of our math-y contributors ponder it for a while, we'll see several ways to do it.

UNQUOTE"

Well, here we are.

In the enclosed attachment I am describing an iterative solution. to derive a Non moving Observer's position just from his own Culmination Time and Culmination height.

The final result is within 0.1 Nm of Bill's Solution. Most of this small interval, if not all of it, is explained by slight differences between our respective Ephemeris and in our height correction method, with each of this difference believed to be under 5".

That's the beauty of this iterative method : it is not subject to the Limitations of the "Time interval width around UT culm" applicable to the previous 2nd order, 4th order, 6th order ... "classical" Local Apparent Noon methods. As long as we have accurate determinations for both UT culm and H culm, this method should work in all possible configurations - including with significant time elapsed between N/S Transit and Culmination - so that we can exactly reconstruct the Observer's Position at UT culm.

Nonetheless, the method depicted here is valid for only non moving Observers, as it frees us from computing modified and extra terms containing dLat/dUT since dLat/dUT = 0°/h in this case..

It probably could be improved into taking in account moving Observer's, at the expense of complications which I currently do not have the available time resource to investigate.

Thanks to both of you, Bill and Frank :-) .

Kermit