Recently learned that Cassini was able to calculate the distance to Mars quite well using parallax in 1672. I was surprised, since even at opposition of Mars, the parallax (with respect to the Earth's Center) is about 30 sec arc. While I know that a few decades earlier, accuracy of 2 min arc was considered the best in the world. (Later edit: During these "few decades", the telescope emerged and enhanced dramatically the resolution.)
In my research I did find this answer and the refereed document. I am not repeating the question, my question is exactly about the technicalities of the operation. Cassini instead of using Earth's center and several measurements across the day, used two locations at the surface of the Earth 12,000 km apart. That indeed was helpful as it would make the parallax about 45 arc sec (in the referred doc the figure is 20 sec arc - not sure why.). I would say that this would have required a setting (equipment, etc.) that would allow an accuracy of about 10 arc sec or even less to make this parallax calculation legit. So my first question is (*):
What equipment did Cassini use and what was the accuracy?
Now, there is another problem that is addressed in the document, which is basically making the observation at the same time. From my calculation Mars can move (with respect to fixed stars) maybe about 2.5 arc sec in one minute of time (maybe I'm wrong though, please correct me if I am). Hence I would like to the observation at the different locations to be performed within in 3 minutes span at max. I don't think that such accuracy should be too hard to achieve even in 1671 using conventional methods like of specific star at specific azimuth; hence I was surprised again to read in the document some interesting method of time-synchronization:
In addition, the time at which Mars is measured must be precisely synched between Paris and Guiana. This is because the Earth is spinning and the angle is changing throughout the night. While it may not look with your naked eye that the planets are moving, with a strong telescope this motion becomes increasingly rapid. Cassini and Richter used the orbits of Jupiter's moons to sync the clocks in Paris and Guiana.
This leads to my second question:
How can we achieve time synchronization (with resolution of couple of minutes) using Jupiter's moons?
(*) Later edit: thanks to answer I now realized the the figure of 12,000 km I've adapted from the document is not correct. the value is about half. This makes 20 arcsec closer to the truth - and makes it even harder in terms of required resolution. It also raises another question of why this operation was necessary in the first place - as the relative advantage of not using the Earth's center parallax (i.e., measure in the same location but several hours apart) is not that big; maybe the willingness to avoid any calculated (rather than observed) figure. (though in that time the pace of Mars was settled quite well.