NavList:

Kermit, thank you so much (and Frank_R, Paul_H, Lars_B, Chuck_V) for helping me understand the issues involved in the topic.

I have bookmarked in a new Folder on my desktop computer, your answers - as a learning resource for me.

I had assumed that I was *safe* to use the JPL ephemeris, because it would take into account all the subtleties of the various components of celestial coordinates. It was very "eagle-eyed" of you to spot the problem Kermit, where the semi-diameters of the Sun and Moon were the *same* between the airless and refraction models.

So my own conclusions from the topic are:

 - Flat Pythagoras code can be used to determine the contact times in an eclipse using the JPL ephemeris coordinates (but to use their refraction model for best results).

 - DeltaT variations probably explain the reason that online eclipse calculators - all give different answers.

 - To be mindful of the subtleties of refraction as explained here and here.

 - That for some people, knowing exact Eclipse times are important for studies like "Baily's Beads" 

To help elevate my own level of mathematics from the simple 'flat' Pythagoras to Spherical Trigonometry, I have started (and very much enjoying) the Kindle book "Heavenly Mathematics" .

Regards, Geoff Hitchcox, Christchurch, New Zealand.