For the "facts" about the Moon in-period, and so the practical difficulties involved in-period, the box text on p.17 of Art & Academe covers them all fairly comprehensively. It doesn't particularly seem like anything that needs any new Breakthroughs (as opposed to mere clever application of Hermetic magic) unless the limit of the Lunar Sphere applies before you get there (A&A establishes magi are not quite sure where the limit would stop magic).
In terms of modern knowledge, that the Moon was a sphere, that it reflected the light of the Sun, and a decent approximation of its distance from Earth (close in units of Earth radii, but as poorly as the Earth's radius in usual units) were all known in period, at least to some scholars. The existence of vacuum would be unknown, or the fact that the Moon has its own gravity that would hold people to it.
In either case, you need something that will let you travel the unquestionably vast distance involved and keep you alive through the hostile environment, or magic that can teleport you directly. (With an AC, direct teleportation is Leap of Homecoming. Without an AC, well you can see it, and each order of magnitude in Rego Corpus seems to translate to a seven-to-ten-fold increase in range, so, 30,000 leagues [Bacon] to 70,000 leagues [modern] would be, what, +4 or +5 Magnitude over the level 30 ReCo guideline, by raw extraploation, for a guideline of level 50 or 55.) If you're using Aristotelian physics instead of the Newton or Einstein varieties, you're also going to need a trick to let you stay there, since otherwise you'll fall right back to the Earth.