What kind of Original Research goals should a magus go through to enable the singular purpose of going to the Moon?
In theme this would be a Hermetic Breakthrough cause it breaks the Lesser Limit of the Lunar Sphere, not that such a thing should stop any played magus.
I would say that this is a very difficult question since I am not sure the best ways to manipulate already existing Hermetic magic to allow such a thing. I think alternate and manipulated Ignem, Aurum, and Terram effects to allow those Arts to provide magi with the ability to live, inhabit, and travel on the moon. Heck, Terram is where the portal type magic exists so I could see trying to create gates to the distant location. I think Vim would help with manipulating magic at such a distant place.
The big thing is figuring out what would allow magi to break the Lunar Limit and what does that place actually represent. Is it actually a material, mundnae location in space (as we would assume in real life) or is it a part of the Magic realm or maybe home of Faerie, or a bit of the Divine.
The answer to this question is honestly saga dependent, so I am not sure the best way to answer it. Maybe if you provided more information on what you are thinking about and trying to achieve that other ideas could be presented.
The players are joining a covenant with two elder magi who want to do uninterrupted work without having to bother with covenant maintenance. One of them wants to go to the Moon, and needs to begin research on it.
I'm wanting to cleave as close to known scientific awareness before swiping in Mythical stuff; so the RL size & distance, its proximity causing the tides, & it's light being a reflection of sunlight are knowable and true.
I... don't think this was the scientific knowledge of the era. It is connected, on the other hand, to other things, through the science of astrology. This is your saga, of course, but are you sure you want to start with such a modern, scientific view of the moon?
At any rate - if one knows it's real size and distance and that its light is reflected, then one pretty much also knows it's a sphere. There isn't any way to explain the phases of the moon otherwise. Making it a kind of terrestrial-like sphere.
From such a real-world basis, I'd suggest attempting to research spells that teleport to the moon. Since flying there is too wide a power (you could fly elsewhere!), and it's definitely a place one could reach by simply traversing space. I would hence develop very long-range teleportation spells, including attempting to teleport into areas that are warded or inaccessible in some way (Aegis, regio). I would then draw Insight from some Arcadian Travel practitioners, that are able to travel into Faerie; from the ancient magic of Orpheus, that allowed him to travel to Tartarus (Magic); from Infernal magic allowing one access to Hell (Infernal); from the Tower of Babel that would have allowed them access to Heaven (Divine); and finally from the Thessalonikian Witches that can "call down the moon". Combining Insight from all these sources, and having acquired a special Stone/Artifact that is somehow from the Moon, and using a powerful Ritual ReCo teleportation spell, one could teleport to the moon.
That's my suggestion. 
Have fun now.
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.
If understanding and breaking the Limit of the Lunar Sphere is needed, I would suggest studying and Armillary Sphere, its mechanism and its enchantment. Amongst other, it has "Know the Heavens" and "Track the Heavens", both InVi which are able to sense the astrological time and the influence of the planets. To me, it sounds as close as you can get from probing the Lunar Sphere (The Mysteries, Revised ed, p 53).
Studying and exploring area with strong astrological connection, like Stonehenge could also give insights. Maybe also some observatory in Levant Tribunal, in Persia. Possibly even getting some documents from the Mythic Cathay (and of course being able to decipher them).
Finally, getting to the Purple Islands could also lead to some significant Insight, after all, if they are the reference point for the Geographyca from Ptolemée, there must be some strong connection with the star and the Axis Mundi.
Note that the Earth radius was known pretty accurately: Eratosthenes had computed it with 99% accuracy (although in part because some of his measurement errors had cancelled out - let's say he "deserved" a 90% accuracy).
Eratosthenes had also computed the Moon-Earth distance, coming up with a number that was between a half and a third of what we know today (keep also in mind that the Moon-Earth distance varies over time by some 15-20%). Aristarchus got a better estimate, that was slightly more than 70% the actual distance.
Tim Fergeson's "Alpine Apocrypha," posted to his blog, contains material originally written for the Greater Alps Tribunal but which was cut from that book. Included there is the Covenant of the Shadow of the Moon, which is a research covenant supported by the Order with the explicit goal of reaching the Moon. You will find it interesting.
You will want to decide, for your story, if the Limit of the Lunar Sphere includes the moon itself. That is, does the prohibition against working magic extend to the actual physical surface of the moon. If it does, then your story is about a Breakthrough. If it does not, your story is more about logistics.
Even if the moon is immune to Hermetic magic, it is theoretically possible to move something with a burst of sudden initial magical force powerful enough that, even though it no longer has magic working on it, it would reach the moon. This is the goal of a Verditius at the covenant I mentioned, who has made a magical crossbow that can shoot the moon. This is for a specific purpose: to determine if it is safe to reach the moon. In that document, it has been determined that the moon is on the border of the sphere of fire, and that anything which tried to reach it would be exposed to supernatural flame.
Another magus, from House Merinita, has another idea. There are many faerie stories about going to the moon. Why not use one of those to accomplish the task? (In my saga, this Merinita hitched a ride on the Cat Who Jumped Over The Moon and, at the proper time, simply jumped off). This book was written before the 5e Faeries book, however. I expect now, if a Merinita tried to reach the moon through Arcadia, she would instead end up on a faerie version of the moon rather than the real thing.
Good luck.
A dream magic initiate could perhaps do it.
- Enter dream
- Dream up cat or other lunar vehicle. (not hermetic magic)
- Use dream magic to make it real and bring it from dream to reality
- Go to moon (no hermetic magic)
{
5) Discover moon is made of cheese
6) Discover that pock marks on moon are due to moon mice eating cheese
7) Cat runs off to catch mice
8) Hermetic magic cannot be used to catch cat or return to earth
9) Learn to love cheese (ritual CrAq might work, since the created water is not at the lunar sphere before it exists)
}
Unfortunately, the ancients (like Eratosthenes) gave their accurate estimates in "stades", and in-period, the length of a stade was uncertain. Which is why Roger Bacon got the distance to the Moon underestimated by a factor of 3, despite having Ptolemy's distance of 59 Earth radii to work with.
I'm thinking of having the basics of the Limit of the Lunar Sphere including being able to affect anything from the Lunar Sphere and beyond as a way to explain the shadow inherent in basic invisibility spells. I could say that early in the Order, they incorporated ways to circumvent the Lesser Limit by either targetting objects' species emission or going at it indirectly (artificially created objects still cast shadows, for example). This would extrapolate to being unable to target non-terrestrial objects/terrain with magic.
You could also try it conventionally by creating a series of tough, floating disks (1 month duration), grab (temporary) arcane connections to them all, and then use a Teleportation spell to throw them towards the moon. Then use your AC to teleport to Leap of Homecoming to that disk, and throw the next one as far as possible - thereby building a series of teleportable platforms you can stand on. This would take longer than conventionally creating the lvl 55 spell, but you could do it with a non-ritual effect.
Alternately, you could try a number of these, and have them fail, but the partial results have given Insights. For example, this suggestion one might fail because it stops at the edge of the Lunar Sphere. However, that tells you how close you can get with conventional magic, and can be created within a few seasons using known magics.
Summon Scorpio
CrHe(Te) 25
R: Touch; D: Diam; T: Ind
Create an exceptionally high quality Scorpio.
Construction: Base 2 + 1 Touch + 1 Diam + 1 Terram requisite + 4 Complexity
Moonshot
A single bolt designed for use in the scorpio, it magnifies the initial momentum when shot so its range is sufficient reach the Moon.
Construction ReHe 40: Base 4 + 1 Touch + 7 Distance
Test the Boundary
InIm(Cr/Co) 25
R: Arcane; D: Ring; T: Ind
You summon the image of an idealized human within a circle. Their body reacts as if standing at the location of the Arcane Connection. If the Arcane Connection is that of a person, then the image and condition of the image will match that of the person rather, additionally providing information of their personal health in addition to the nature of the environment itself.
Base 2 + 4 ArC + 2 Ring + 1 Requisite