Here's a scan of the original 1610 publication: https://archive.org/details/Sidereusnuncius00Gali

Jovian diagrams begin here at the bottom of the right-hand page: https://archive.org/stream/Sidereusnuncius00Gali#page/n39/mode/2up

I'm sure there are other translations out there, but this one turned up via a quick Google search:

http://people.reed.edu/~wieting/mathematics537/sideriusnuncius.pdf

If you scroll a little over half way through the document, you will see a number of his sketches. His description of time is a bit vague so I estimated about 6Pm Italy time (e.g. TimeZone -> 1);

JupiterSatellites[DateObject[{1610, 1, 13, 18, 0, 0}, TimeZone -> 1]]

This gives a view almost identical to what he described for Jan 13, 1610. Most of his observations refer to the "first hour of the night" and given its January, I'm assuming 6 PM local time would be a reasonable guess. Keep in mind that Galileo's telescope was very crude so its resolution was poor. If 2 moons were very close, he may not have been able to resolve them so this may appear to result in a discrepancy between what he describes and what the calculation show. But all the test cases I've done seem to be quite close.

The source doesn't specify a range of dates for which the results are valid, at least not in an obvious way. Often, additional references are given for some of the sub-computations. Its possible that if you do enough source spelunking, you might find an originating source that provides that level of analysis.

The first 17 or so variables in the first block of code are defined in chapter 43, while the remaining are in the following chapter 44.

Very nice. I never learned Latin. Can you correlate each of Galileo's drawings with a corresponding calculation or provide a translation?

Thanks!