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Question

In my alternate reality, Earth is not a planet. It is a moon and orbits a gas giant (however it has all of Earth's characteristics, it is also full of humans and life as we know it). This is the only moon the gas giant has.
This alternate Earth is tidally locked. This means that the people who live on the "outer" side of the moon have never seen the planet they orbit. And here comes the question:
Assuming Astronomy develops as it did on our Earth. When will they be able to discover they donÃ‚Â´t rotate around the sun alone?

When I say "when" I am asking which stage of astronomical development. Could Galileo and Copernicus have noticed that? Ptolomeo, perhaps? Or maybe the Greek astronomer Aristarco de Samos (310-230 BC) could have noticed that with his observations of the sky? (No, these are not multiple questions. I am just explaining the type of answer I am looking for).

Of course, as I said before, I am assuming all these inhabitants of the continent on the "outer" side of the Earthly moon have never navigated to the other side of their moon, so they have never seen the big gas giant in the sky.

Does your gas giant have other moons? That will make a big difference. — 2 hours ago
You are right Mike. I have edited the question. It is the only moon the gas giant has. — 2 hours ago
It's pretty likely they will circumnavigate their moon, and have a really big HOLY COW moment, before they will figure out the planetary law of motion. In addition, if there are people who live on the other side, their legends / primitive science / etc will probably be passed mouth-to-mouth over their trade routes before anyone circumnavigates. — 2 hours ago
Does anyone know if, at a distance from the sun that's in the habitable zone, the planet would cast enough light on the tidally locked side to effect either weather on the moon OR to have effects in the night sky on the opposite side, by diffusion of that light across the terminator? — 32 mins ago
@tbrookside - Exactly so. The gas giant theory would spread to become common knowledge long before any detailed scientific observation takes place. — 17 mins ago

Alexander 15.9k42663 · Answer 1 · 2018-09-20 18:10:53Z

I think astronomy should advance to the level of Johannes Kepler (early XVII century) to correctly theorize the presence of a host planet.

To the eyes of early astronomers (like Ptolemy), the world would be still Earth-centric. The only odd thing would be a minor parallax caused by orbital movement. Without any scientifically sound theory of planetary movement, this parallax would be likely explained as a feature of celestial movement.

Copernicus would have every reason to put the sun to the center of the universe and even propose a correct explanation that the parallax is caused by Earth's own movements - but he would have no mechanism to explain these movements. He may theorize the host planet, but this theory would have no way of being proved.

It would take a telescope and accurate observation of another planets to suggest that the most plausible explanation of planet's own movement is the presence of a massive host planet.

I agree with this answer - but Magellan comes before Kepler, so sea navigation will reveal the secret before astronomy does. — 2 hours ago
@tbrookside - I agree here. They may not even need Magellan, Columbus may be sufficient. — 2 hours ago
This is not right. The parallax change is not minor. Do the calculation. And what about the luminosity change? — 1 hour ago
@kingledion - Ok, if the "Earth-moon" orbit is wide enough, I can take back the "minor" parallax. Still, its observable effects are hard to properly explain. What people should see it that planets, over the course of the night, will move slightly faster than the background stars. I.e. their Ptolemaic model may postulate that "Earth-moon" is not stationary, but that would be it. — 1 hour ago

score 5 · Answer 2 · 2018-09-20 19:21:22Z

I think @Alexander 's answer is good but not entirely correct.

Consider the gas giant's axial tilt. Gas giants tend to rotate rapidly due to conservation of axial momentum and the collapse of an enormous volume into a planet. Jupiter has a 3 degree Axial Tilt but Saturn has 25 and Uranus, 98 - basically flipped on it's side.

Due to the gas giant's rotation and equatorial bulge, it's likely that the planet-moon would orbit around the gas giant's equator. That means that the Axial tilt of the gas giant would effect the movement of the moon above and below the gas giant's ecliptic. For the stars, this wouldn't make much difference, but the other planets and Sun would observably move in a sign wave up and down. Against the fixed stars, this would be noticeable against the fixed stars (hmm, Mars was in a different place relative to that star last time around), but probably explained by additional epicycles early-on, similar to the Ptolemaic models that were the standard for over 1,500 years.

It's worth noting that Aristarchus and his early heliocentric model was based on observing Earth's shadow on the Moon and that would no longer be an option, so a version of the Ptolemaic model is highly likely for your scenario.

So, it matters how much your planet-moon moves above and below the ecliptic because that would be observable relative to the other planets and the position of the Sun at Sunrise and Sunset - even if the movement was less than 1 degree, that's measurable with equipment and buildings like the Mayans had.

If the gas giant's axial tilt is zero, the planet-moon simply moves closer and further from the Sun as it orbits the gas giant. That would visually cause the observed other planet's motions to not move at Keplerian predicted velocity but wouldn't move them up and down.

Up and Down movement would be probably be tied to epicycles up and down from the ecliptic, but it might not be too long before somebody says, "wait instead of all these circles, if the Earth moves, that would explain everything", and then they get persecuted by the church and all that good stuff.

If the gas giant has close to zero eccentricity everything becomes much harder. Kepler was only able to do what he did using both very careful observations over many years, and the best astrological observation equipment ever made because the Earth returns to the same spot relative to the Sun every year. Having a fixed observation point makes triangulation possible and Kepler relied on triangulation to work out his formulas.

If you have the planet-moon moving around a gas giant in a tidally locked orbit, you lose that "fixed" position at the same date every year unless the Planet-Moon's orbit around the gas giant and the gas giant's orbit around the Sun are neatly divisible, which is unlikely. Now if the planet is very close to the Moon, it's movement becomes smaller and maybe this problem goes away. If it's a significant variation in distance, that makes Kepler's work more difficult.

If you lose the fixed position you can't perform triangulation, or, you need to wait several years for a relatively equal position and you'd need to know how many years to wait. That makes Kepler's calculations much harder and I'm not sure he pulls it off.

And without Kepler, Newton might still work out Calculus, but it's unclear if he works out orbits, which wouldn't make sense based on observation.

Worst case, most difficult scenario, I would guess that they'd need advanced telescopes to begin to observe objects passing into the shadow of the gas giant (that's funny, I was tracking that object and it vanished), and circumnavigation would almost certainly precede that. It might take a mathematician of the skill of Laplace to work out the specifics from observations of the night sky because your scenario could be quite a bit more complicated. (IMHO).

kingledion 66.2k22217379 · Answer 3 · 2018-09-20 18:43:10Z

How far is your Earth-moon from the planet?

Let us assume that the Earth-moon is the same distance from the planet that Callisto is from Jupiter. Callisto's semi-major axis is 1.9 million km relative to Jupiter. Assuming that the Sun is still the same, and the Earth-moon is in the same habitable zone, then the distance to the sun is 150 million km.

The diameter of the Earth-moon's orbit around the gas giant is twice the semi-major axis. This forms an isosceles triangle with a vertex angle of 0.025 radians; or 1.4 degrees. Detecting this angle is well within the capabilities of ancient astronomers (as in Babylonian/Chinese/Indian).

Furthermore, in this case, there is a 2.5% variation in distance from the sun with various orbital positions around the gas giant. This corresponds to a 4.9% drop in luminosity of the sun from nearest to farthest point. This too would be readily observable to the ancients...as far back as the Paleolithic, I would think.

If you don't want the Earth-moon so far from the gas giant, then these numbers are reduced. At the distance of Ganymede, this becomes 0.014 radians and 2.8% luminosity, both still noticeable. At the distance of Io, this becomes 0.005 (only 20 minutes of arc) and 1.1 % luminosity. I'd have to do more research on ancient instruments to see how noticeable this is; but it is at least plausible that both would be noticed. Once first detected, many would devise experiments to calculate more carefully, so I think both differences would be detected, even if the Earth-moon were very close to the gas giant.

Observation of these distances

So the ancients would know from observation that neither "Earth-moon orbits the Sun" or "Sun orbits the Earth-moon" is a true statement.

The odd rotation of the Earth-moon around the sun is what the Greeks called an epicycle. The Hellenistic era Greeks explained the apparent retrograde motion of the planets in the sky by a system of epicycles. If they were able to apply this concept to something that does not exist in reality, then we could assume that by 300 BC, Greek astronomy would know that the motion of the Earth-moon was in orbit around something, and that something was in turn orbiting the sun.

As far as travel to the far side of the planet to see the gas giant first hand, that is more a matter of exploring. But one whisper of such and explanation would quickly establish itself, as the most reasonable explanation for why the Earth-moon is apparently orbiting a random point in space.

Conclusion

The ancient astronomers would know that neither the Earth-moon orbits the sun, nor the sun orbits the Earth-moon because of discrepancies in rotation rate and changes in luminosity of the sun.

By the time of the ancient Greeks, this apparent observations could be (accurately) explained by the existing theory of epicycles.

By the time the first explorer got to the opposite side of the world and saw the gas giant, looming enormous in the sky, the cause of the epicycles would be fully explained.

How long this exploration would take is up to you and the orientation of planets. If Eart's Old World lay in the away-facing hemisphere; Irish or Japanese fishermen in the Atlantic or Pacific would have seen the gas giant in antiquity.

A consideration - the farthest point from the sun will correspond to the night on the "Earth-moon". The closest point will be high noon. Analyzing distance effect on luminosity will be quite tricky. — 1 hour ago
@Alexander Ok, acknowledged that that is an issue. But the parallax from orbit will be apparent against the stars in addition to the sun, so that is more measurable. — 1 hour ago

Fabby 742311 · Answer 4 · 2018-09-20 19:56:06Z

Unless all the land mass on the tidally locked planet is on the side not facing the gas giant, the humans will discover they're orbiting a gas giant during the stone age:

Human migration

If the land mass is on the far side of the moon, they will discover it a bit later, maybe as early as prehistory but certainly no later than the invention of the lateen sail...

Source for map

o.m. 54.7k677182 · Answer 5 · 2018-09-20 18:32:52Z

Consider two different scenarios:

The moon is the center of the universe. The planet orbits around the moon. The sun orbits around the planet. Lots of other moons orbit around the planet. Lots of other planets orbit around the sun, with their own moons.

The sun is the center of the universe. The planet orbits around the sun, just like other planets and some junk. The moon orbits around planet, just like other moons.

One could go quite far with the first option, building an ever more complicated model of the celestial spheres.

What makes the second option "more scientific" is that it needs fewer special cases, and that it groups like with like. All planets orbit around the sun, and so on.

Note that both models are equally wrong, but one can go quite far with the helicentric model.

Alexander 15.9k42663 · Answer 6 · 2018-09-20 18:10:53Z

I think astronomy should advance to the level of Johannes Kepler (early XVII century) to correctly theorize the presence of a host planet.

To the eyes of early astronomers (like Ptolemy), the world would be still Earth-centric. The only odd thing would be a minor parallax caused by orbital movement. Without any scientifically sound theory of planetary movement, this parallax would be likely explained as a feature of celestial movement.

Copernicus would have every reason to put the sun to the center of the universe and even propose a correct explanation that the parallax is caused by Earth's own movements - but he would have no mechanism to explain these movements. He may theorize the host planet, but this theory would have no way of being proved.

It would take a telescope and accurate observation of another planets to suggest that the most plausible explanation of planet's own movement is the presence of a massive host planet.

I agree with this answer - but Magellan comes before Kepler, so sea navigation will reveal the secret before astronomy does. — 2 hours ago
@tbrookside - I agree here. They may not even need Magellan, Columbus may be sufficient. — 2 hours ago
This is not right. The parallax change is not minor. Do the calculation. And what about the luminosity change? — 1 hour ago
@kingledion - Ok, if the "Earth-moon" orbit is wide enough, I can take back the "minor" parallax. Still, its observable effects are hard to properly explain. What people should see it that planets, over the course of the night, will move slightly faster than the background stars. I.e. their Ptolemaic model may postulate that "Earth-moon" is not stationary, but that would be it. — 1 hour ago

score 5 · Answer 7 · 2018-09-20 19:21:22Z