Thanks for the many responses to my questions. I think am starting to get a grip on the situation. In the first place, the time between the discovery of America and the measurement of the exact longitude using a total lunar eclipse was not all that long - 85 years in an age when a single voyage could take years. The alternative of using the position of the moon relative to the stars would have been just too complicated for the knowledge of the time. Of course, chronometers and telescopes (to observe Jovian eclipses) did not exist. And it's not like the Europeans had a lot of time on their hands to measure the longitude of Asia either. Vasco da Gama did not reach India until 6 years after the discovery of America.
What I still don't understand is this: Even without an exact measurement of the longitude, how could Cabrillo still think it was only a hop, skip, and a jump from Mexico to Asia 20 years after Magellan had taken 4 months to cross the Pacific? Magellan was sailing for Spain, so the knowledge of the rough size of the Pacific must have been available to Cabrillo (as if you could keep such a story secret anyway). --Art Carlson