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I have a habitable moon orbiting a gas giant. The moon is not tidally locked with the gas giant. The orbital plane of the moon around the gas giant is the same as the orbital plane of the gas giant around the sun.

What I want is a combination of moon's rotation speed around itself and orbital speed around the gas giant that will result in the gas giant eclipsing the sun every day, as seen from the surface of the moon.

Edit: My original question above is not correctly defined. What I actually want is not an eclipse once per objective day somewhere on the moon, but rather this: I want every inhabitant of the moon to experience an eclipse approximately once per their subjective day, no matter where they are on the surface of the moon.

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The gas giant can only eclipse the sun when the moon is on the far side of the gas giant from the sun. The eclipse is then seen from everywhere on the day side of the moon. I'm using the natural definition of "day", relative to the sun, rather than the gas giant.

Now, that doesn't happen exactly once per orbit of the moon around the gas giant. During the time the moon takes to orbit the gas giant, the gas giant moves a bit in its orbit, so the moon has to make slightly more than one orbit of the gas giant to reach the next eclipse.

So if P is the orbital period of the gas giant around the sun, and p is the orbital period of the moon around the (edit) gas giant, the correct rotation period for the moon to have an eclipse exactly every day is $p * (1+(p/P))$. The eclipse happens at the same time each day, and only one side of the moon ever sees the eclipse.

I've assumed that the planetary system works in what we think of as the normal way, like our own solar system, with all the orbits and rotations in the same direction.

For any plausible setup, with P much larger than p, the moon is rotating a little slower than tide-locked, and that raises the question of how it got to be that way. As best we know, moons would start off rotating rapidly and gradually spin down under tidal forces until they tide-lock. Some external force would be required to slow the spin further, such as a collision.

Addendum: If the moon is orbiting in the opposite direction to all the other circular paths, then its rotation period needs to be a little less than its orbital period to have an eclipse happen every day: $p * (1-(p/P))$.

Addendum 2: To have an eclipse clearly visible from everywhere on the moon every moon-day, you need to have the moon rotating much slower than tide-locked, so that it completes several orbits per day. You probably want at least three orbits per day, to ensure that the sun is definitely above the horizon for at least one of them. This means that some places will see at least part of more than one eclipse per day, but this is unavoidable.

If it were me, I'd be tempted to have $pi$ orbits per day, which would tempt the inhabitants of the moon towards mystical numerology as a part of their early development of astronomy and astrology.

If you were trying to have realistic astrophysics, and a day length that isn't vastly longer than that of Earth, I'd be worried that the moon would have to orbit too close to the gas giant, and would be at risk of being inside the Roche Limit and falling apart. However, for an explicitly fantasy world, don't worry about this.

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  • $\begingroup$ This is a fantasy universe, so I am open to more crazily looking planetary systems. What if the moon rotates around the gas giant in the opposite direction of the moons rotation round itself, i.e. the gas giant and the sun move in opposite directions in the sky? $\endgroup$ – Xylem Sep 25 '16 at 14:02
  • $\begingroup$ Doesn't make a huge difference: I've added to the answer. If you could be more precise about what effect you're trying to achieve, you might get more answers. Is it that you want an eclipse every day? Is the moon/gas giant configuration just a means to that end, or do you want it for other reasons? $\endgroup$ – John Dallman Sep 25 '16 at 14:40
  • $\begingroup$ So if P is the orbital period of the gas giant around the sun, and p is the orbital period of the moon around the sun - I think you have a typo here. Small p is orbital period of the moon around gas giant, I suppose? $\endgroup$ – Xylem Sep 25 '16 at 14:42
  • $\begingroup$ Another question: correct me if I'm wrong, but it seems like your scenario is not very different from a scenario where the moon is tidal locked? It seems that if it was locked, the hemisphere facing the gas giant would still get an eclipse per day, regardless of the direction of rotation around the gas giant. $\endgroup$ – Xylem Sep 25 '16 at 14:51
  • $\begingroup$ Indeed, it is not very different. The main difference from a tidelocked scenario is that the place on the moon where the eclipse is centred is constant. If the moon is tidelocked, that place moves around the moon, circling it once in the gas giant's year. $\endgroup$ – John Dallman Sep 25 '16 at 15:05
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Since it is fantasy...

Use a Lissajous orbit around the gas giants L2 Lagrangian point.

Then have fun describing the predictions the diviners make from reading the movements of the burning eye of the God.

Such orbits are used by spacecraft (example) since they are fairly easy to maintain and your planet should be less sensitive to random fluctuations and have less stringent orbital requirements as well.

This set up is AFAIK extremely unlikely to arise naturally, but if you can assume active creation (or fudging) with divine power, it should be stable long enough for a civilization to think it is permanent. With active divine upkeep it would be permanent I think.

Until the Gods die, of course.

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  • $\begingroup$ This is a very cool idea, actually, although Dallman's is closer to what I had in mind. $\endgroup$ – Xylem Sep 25 '16 at 16:40
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    $\begingroup$ There is no "thermal shock" and nothing breaks if anything passes through an eclipse zone. Images from really advanced space telescopes get slightly blurry for a few weeks because of minuscule deformations due to thermal expansion. $\endgroup$ – Karl Sep 25 '16 at 16:56
  • $\begingroup$ @Karl "Gaia can not afford to enter eclipse during its mission because it would cause a significant thermal shock to the system that would render the observatory useless." <-- from the example linked above. True I should have been less colloquial. $\endgroup$ – Ville Niemi Sep 26 '16 at 16:30
  • $\begingroup$ I know, this bullshit even made it to wikipedia and into the press. Some NASA PR idiot was told that temperature changes during a passage through earths penumbra would create problems, and made "thermal shock" out of that info. "Thermal shock" means destruction of surface layers of material due to sudden, extreme temperature changes, like dropping red-glowing material into water etc. The problem with Gaia would be a week or two of less-than-ideal imaging conditions, and an annoying recalibration of all systems afterwards, $\endgroup$ – Karl Sep 26 '16 at 19:39
  • $\begingroup$ @Karl You sure? I always thought "thermal shock" simply means deformation from rapid temperature change with whether anything "breaks" depending on how sensitive the object is to that and being simply a possible consequence. And while "broken" is too loose language on Gaia, that would shorten both possible lifetime and the amount of usable observations during that lifetime, so it isn't really that wrong word to use. Just realized the comment (already in parentheses, no less) is actually useless regardless of correctness, so I'll just edit it out. $\endgroup$ – Ville Niemi Sep 27 '16 at 13:37

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