If there were a primitive civilization on the far side of the moon that never ventured to the earth-facing side would they be able to deduce the existence of the earth by the motion of the sun, stars and planets, or would it require a Copernican/Keplerian level of mathematical ability?
Well, if you look at a diagram of the Earth/Moon’s orbit around the sun and take out Earth, the Moon’s orbit is almost identical with just a mild oscillation. If the Moon was orbiting by itself with a ~28-day “day”, I doubt it’d make any noticeable difference. It would take sufficiently powerful and accurate instruments to detect the ~500,000 mile variance, possibly by noticing that Venus and Mars seem to be slightly changing size for no apparant reason.
I’m guessing they would need their own Copernicus/Kepler/Galileo/Newton to figure it out.
Or a Kepler and a Tycho. Kepler deduced the elliptical nature of orbits from Tycho Brahe’s measurements (which were made without telescopes). That ellipticity is pretty small.
In high school we repeated Kepler’s analysis, using standardized photographs of planetary diameters. I think a Lunarian (Selenite?) cold use accurate measurements of the sun’s diameter and its variation to deduce the true orbit. If he came up with the same kind of pre-Keplerian ideas of epicycles, it wou;ld ironically be correct in his case.
The oscillation is toward/away from the sun, but there is also an oscillation in the speed with which the moon orbits the sun, i.e. it speeds up and slows down once each 28 days. So you wouldn’t just notice Venus/Mars changing size, you’d see their apparent positions change at a time-varying rate. That might be easier to spot.
Does the moon’s axis have a tilt with respect to the sun? If so, they could identify a 365.25-day solar cycle, along with the day that’s about 28 earth-days long.
With no atmosphere, would they be able to make telescopic observations while the sun is shining on them? I would guess yes, since there’s no blue sky blotting out the stars/planets. So they could observe the planets and stars during the day as well as at night; that might help them sort things out faster than we did.
I would guess they could quickly arrive at an accurate model that explains the 28-earth-dayl-long day, the 28-day oscillation in the rate-of-change of position of the planets, and the 365.25 day solar cycle. At some point they would be compelled to make the trek to the earthward side of the moon and see what’s over there, or else launch lunar satellites to make observations for them.
Yes, but at times when it would be speeding up, the sun wouldn’t be visible, if I understand the diagrams right. I suppose the moonlings might note that their day is longer then their night, but it would take quite an advance in math to figure out why.
Heh, just picturing a moonling Columbus cresting a dusty hill and suddenly seeing this giant blue object in the sky. “What on Luna is THAT?!?!”
But Kepler’s theory was merely a mathematical description of the orbits of the known planets as Tycho had observed and measured them. It was in no way capable of predicting the existence of unobserved planets or satellites. (In fact, Kepler thought his theory ruled out the possibility of any more planets, but that part of the theory was simply wrong. The good part of his theory just did not have the conceptual resources to say anything at all about whether or not there might be any more planets or satellites.) You need Newtonian gravitational theory, which actually explains the orbital characteristics that kepler merely described, before you can have any hope of predicting the existence and orbit of any new planet from observations of the motions of ones you already know about. (Neptune was in fact discovered via just such a prediction based on Newtonian theory.)
When they figure out that the 1:4:9 ratio is not naturally occurring, they’ll know something’s up.
I doubt it. Certainly the ancient Greeks, and probably the Babylonians before them, had a pretty good understanding of of where the stars and planets must be in the daytime sky. Even though they could not actually see them during the day, they knew where they were in the sky. It still took about another 2,000 years before anyone managed to figure out the actual motions and mechanics of the solar system (and to invent the telescope, come to that). Furthermore, the fact that the Moon’s motion relative to the Sun is more complex than the Earth’s, is likely to make things distinctly more difficult to figure out.
The Moon’s orbit is about 385,000 km in radius, so its path through the solar system deviates from a Keplarian orbit by about that much. Mars is about 0.6 AU away at opposition, so its position should deviate from Keplarian prediction by about 385,000 km / 0.6 AU = 0.25 degree. Which is pretty big.
I’ve read that Tycho Brahe’s observations were accurate to about 1 arcminute, or 1/60 degree. So a Lunarian Brahe + Kepler might notice this systematic error. It most likely would be noticed and interpreted correctly once Newton’s Laws are discovered.
Could they discover Newton’s laws without a Kepler + Brahe? What else could lead to Newtonian conclusions?
Well, seeing as you’re talking about the dark side of the moon, they wouldn’t even know there was a sun in the first place. Duh!
Far side, not dark side. There is no dark side of the Moon.
John Barnes used this situation in a book - the early scientists on the far side of the planet-sized moon of the Jupiter-sized planet that the moon orbited, were very confused because Eratosthenes type experiments gave one answer for the circumference of the moon (the correct answer) while observations of the change in distance from the Sun as the moon rotated appeared to reveal that the circumference of the moon was much much larger - because what they were actually measuring was the circumference of the moon’s orbit around the big planet (the rotation of the moon and the period of the orbit are identical - so the motion due to the orbit is the same as the motion that would be due to the rotation of a very large planet).
I think you are right that it would be noticed. I believe Brahe’s data was a little better even than you suggest: accurate to about two thirds of an arcminute IIRC. Furthermore, Kepler was an an absolute stickler about fidelity to Brahe’s data. The whole idea of elliptical orbits only arose because the best fit between data and theory that he could get using circles (even together with heliocentrism and a liberal use of the epicycles, eccentric points, and equants inherited from Ptolemaic theory) still had an 8 arcminute discrepancy. Because of this, he threw out years of work, and finally hit on ellipses and his first two laws. Doing mathematical astronomy in terms of ellipses rather than circles was a major conceptual shift, almost comparable to the shift from geocentrism to heliocentrism itself.
So yes, I think a lunar Tycho and Kepler would, between them, have noticed the difference. The trouble is that figuring it all out when your observations are from a lunar vantage point seems sure to be a lot harder than doing it from an Earthly one. The Earth, after all, travels in a nice smooth ellipse around the Sun. Even so, figuring it all out taxed Kepler, the best mathematician of his age, and a man of enormous tenacity, to the very limits of his abilities. Lunar Tycho would maybe have things a touch easier, without atmospheric distortions to reckon with, but lunar Kepler would have it significantly harder.
As a matter of fact, it’s all dark. 
Oh, yeah? Try telling that to Pink Floyd (and The Flaming Lips and Stardeath and White Dwarfs with Henry Rollins and Peaches), man!
(In any case, there is, at least, most certainly, a Dark Side of the Moo.)
Bet it doesn’t make a wooshing sound as it orbits, either. Cuz there’s no atmosphere.
That explains all the lousy restaurants.
Thanks for indulging my little thought experiment. I should have known math would be involved.
The Moon’s orbit is tilted about 5 degrees from the ecliptic (Sun’s “orbit”).