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I have a habitable Earth-like moon that orbits a gas giant.

This moon is inhabited by a pre-medieval civilisation that has spread out across just one continent.

The inhabitants of this civilisation are unaware that the moon they are on is orbiting a gas giant.

I am guessing this is possible because the moon's rotation is in sync with its orbit around the gas giant, so the inhabitants always have the moon (or ground) between them and the gas giant. Similar to being on the dark side of our moon and not being able to see the planet Earth.

My 2 questions are:

  • Without actually going around to the other side of the moon and seeing the gas giant for themselves, how could the civilization figure out that they were orbiting a gas giant, and what level of technology/understanding would be required to prove this?

  • I am guessing that seasons on such a moon would be extreme to say the least. Are there any alterations I can make to this situation to have less extreme seasons, whilst still keeping the gas giant hidden from the civilization?

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The unseen giant

In the second century BCE Eratosthenes calculated the circumference of the Earth based on the distance between two wells on the day of the summer Solstice and the shadow cast in one but not the other. Your world's equivalent of Eratosthenes, upon attempting the same calculation, would find his circumference for the "moon" is actually the circumference of its orbit around the gas giant.

A little over a thousand years later Abu Rayhan al-Biruni calculated the radius of the Earth by measuring the distance from a point on the horizon to the top and base of a mountain. Your world's al-Biruni would realize these two numbers can only make sense if the planet is a smaller sphere moving in a circle around an unseen point (the gas giant).

So this discovery is possible by mid-medieval times at the latest, without any technology more advanced than sun dials and some basic math. The exact nature of the gas giant would be conjecture at this point, but don't forget that even ancient Greeks believed the Earth orbited the sun: your world's Eratosthenes or his contemporaries would be open to the idea of their world orbiting another body, and both orbiting the sun.

Seasons

Reducing orbital inclination of the moon-giant system to zero would mean that, as a tidally locked body, your moon wouldn't have any seasonal variation through the year. (Assuming, also, that the orbit has low eccentricity.) There are hard limits as to how fast your moon can orbit, due to the mechanics and distances involved, but this would guarantee that if any part of the moon's surface is habitable it would remain so year-round.

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  • $\begingroup$ would find his diameter for the "moon" is actually the diameter of its orbit around the gas giant. - statement looks wrong, can you elaborate it. $\endgroup$ – MolbOrg Sep 21 '16 at 20:07
  • $\begingroup$ @MolbOrg For some reason I wrote "diameter" three times instead of "circumference". $\endgroup$ – rek Sep 21 '16 at 20:52
  • $\begingroup$ As I understand Eratosthenes' experiment, the measurements were simultaneous - so whether or not you're orbiting something else should be irrelevant. Am I missing something? $\endgroup$ – Reese Sep 22 '16 at 2:38
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    $\begingroup$ Reese is right. The well at noon thing measures the curvature of the line of longitude you're on, not the movement of the ground over time. $\endgroup$ – JDługosz Sep 22 '16 at 5:33
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To answer the first question - figuring out you're orbiting a gas giant would be hard. While they're still in the Aristotelian model of the cosmos (that is, the cosmos is fixed and rotates around Earth/whatever planet you're on) they simply wouldn't notice. They might observe that the paths of stars are very complex - from the perspective of such a moon, the positions of other planets in the solar system would change wildly over the course of a day - but on Earth we just dealt with that by introducing epicycles (little miniature crystal spheres that allowed particular stars to travel out of sync with the rest of the sky). It wouldn't be until their version of Copernicus or Galileo came along that they'd spot it. But for that, all they would need would be an imaginative mathematician with an eye to the sky and possibly a telescope. By observing other planets in the solar system at different times of the day, this mathematician would notice that the only reasonable explanation is that his vantage point is rotating, with a certain very large radius, which he could then compute; to do this, he'd need to be able to see at least two other planets, so that he could solve for his distance from each and the radius of his own rotation. Now, as rek pointed out in a previous answer, there are several low-tech ways to determine the radius of the moon - by the time our Copernicus came along, the radius would be well-known. He would notice that it is much smaller than his calculated radius - and with a burst of inspiration, would realize that this must mean that the "planet" is orbiting some central point, which itself is orbiting the sun.

Now, our Copernicus might, out of concern for elegance, posit that the point we're orbiting is actually another body; most likely he'd suggest a second Sun. I suspect that with or without this suggestion, the absence of a concrete explanation would make his theory less appealing to the public; heliocentrism would take considerably longer to catch on than on Earth. To prove that there's something there, you need someone like Newton - someone who can come up with a theory of gravity. With a theory of gravity and its effect on the cosmos, you can justify the existence of something this moon orbits, and thereby deduce that there's something there. You would not be able to determine whether it was a gas giant, a star, a black hole, whatever; for that, you'd have to look.

As for the seasons: As rek pointed out, if you don't tilt the system there won't be any seasons. But there will be a killer day/night cycle - at dusk, the moon will be significantly further from the Sun than at noon. I'd think of this like having a miniature winter hit every morning and evening. It wouldn't help, either, that the other side of the moon isn't getting much sunlight, so would be in perpetual winter and would no doubt cool the rest of the moon. To fix this, I have a couple of suggestions: have the gas giant radiate heat (easy enough, if it's large enough to nearly be a brown dwarf star) or just cover the moon with lots and lots of water. Water has extremely high specific heat, so it resists drastic temperature changes - the heat of noon would stick around well into the night. I think the moon would still be a bit colder than we're used to, or intolerably hot in the day if you put it too close to the Sun, but it would be livable.

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