NavList:

Roger,

Thanks for your insights.

You asked:

A theodolite on a stable tripod or pier would certainly be much better than any marine sextant for measuring altitudes, but I don't have one of those either.  Regardless, wouldn't altitudes of celestial bodies measured that way be subject to the Earth's local (and poorly known) gravitational anomalies?

Indeed and uncertainties in the atmospheric refraction model will also play a role. This question is only loosely related to the one on eclipses and really about the accuracy that can be achieved of a theodolite versus a sextant. I know that there are some Navlisters who have sprung for a theodolite and may have studied the question,

Regards,
Robin