NavList:

Ahhh. Thank you very much.  This is precisely the answer to my question, which I am not sure I stated very clearly.  I had an inkling that the formula for altitude vs. time might involve a solution for a spherical triangle, but I wasn't even close to figuring it out. I won't have time to get to this immediately, but it will be a most enjoyable exercise for winter days.   

As you say, this can be approched using a spreadsheet, which is how I'll start, as it's quite "hands on".  Another method is to use an application that allows you to specify a mathematical model, and its free parameters, for which you have to input an inital estimate. The algorithm then varies the value of the free pararameters until the sum of squares is minimized.

One of these software packages is Kaleidagraph, which is not freeware but not too pricy. Once one figures out the somewhat quirky syntax it requires to enter an equation, it is not hard to use. The two best known programs are Matlab and Octave, which have a built-in function called "lsqcurvefit" to accomplish this. Octave is freeware, and is a Matlab clone without some of its powerful features, which are not requireed for this problem. Matlab is now extremely expensive, unless one's workplace has an institutional license. Unfortunately, both have a somewhat steep learning curve.

I'll definitely look into the book(s) by Hewitt Schlereth, whose welcome is much appreciated.

Kind regards, Rafael