Writing: Input Wanted How would an Earth-like Planet fair with a Uranus like moon system?

[DiamondTiara]

Earth has one large natural satellite in reality. This is only talking about the context of a habitable, planet that has the conditions as Earth, with similar axial tilt.

It would have a moon system similar to that of Uranus. Let's say it has 6 moons, similar in size to Puck, Miranda, Ariel, Umbriel, Titania, and Oberon. These 6 moons would orbit in safe, stable orbits around the Earth-like planet. What would their apparent size, and realistic distance be from the Earth-like planet? What would be stable orbital distances, appearances, and likely effects on their parent planet's tides be? Would it be possible for such a moon system around an Earth mass planet to form under these conditions?

 

[.Scott]

The moon system of Uranus is not that stable. According to the wiki article, the inner moons perturb each other and collisions are likely within any 10-million year period.

It is most likely possible for an Earth-size planet to have 6 small moons with a distribution, size, inclinations, and distances similar to what Uranus has. Since Earth is a much smaller mass than Uranus, the orbital periods of these moons would be much longer than what they are around Uranus.

The arrangement of moons is often explained from how the planet was formed, how its star system was formed, and how much other stuff has been in the vicinity of its orbit during its history.

Tides are another issue. If any of these moons is large enough and close enough to created appreciable tides, they would tend to have a face to the Earth (as our moon does) and they would tend to interfere severely with the orbits of the other moons.

It might be an interesting story line if visitors to star system could demonstrate that one of the planet/moon systems that could not have happened by chance.

 

[Bandersnatch]

What would their apparent size

For this you can use the small angle approximation, which makes it a simple proportionality - if you start with the size, distance and apparent size of the Moon, then anything e.g. twice the distance looks half as small while anything twice the size looks twice as large. In terms of angular diameter.

and realistic distance be from the Earth-like planet?

The orbits must lie above the Roche limit and below the radius of the Hill sphere. The former is somewhat dependent on satellite composition, but it's already close enough - approx 10k km measured centre to centre - that you probably wouldn't want to put anything that nearby. The latter is approx 1.5 million km, or 4-ish times the distance to the Moon.

What would be stable orbital distances

I'm not entirely sure if having six sizeable satellites within the aforementioned distance is stable, and don't know of a way to calculate this other than putting the setup into a gravity simulator.
Other than that, a reasonably plausible arrangement, IMO, would be to shave off maybe 10-20% on either end of the 1.5 million km range, and spread the satellites more or less equally within that.

appearances, and likely effects on their parent planet's tides be?

I don't know what you have in mind re. appearances, other than the aforementioned apparent size. Maybe that they'd all likely be locked in synchronous rotation with one side facing the planet, as Scott mentioned above.

As for the tides, you can again use proportionality starting with the lunar tides - any satellite that is x times closer than the Moon will cause x^3 times larger tides (and vice versa). At the same time, a satellite being y times less massive, will cause y times smaller tides.

So, e.g., if you take Titania - it's approx. 2.5 times smaller than the Moon (let's round it to 3 for convenience), and approx. 20 times less massive. If we were to put it towards the inner edge of the proposed range, roughly three times closer than the Moon. Then it'd look just about the same size in the sky, and produce 27 times larger tides due to its proximity, divided by 20 times due to lower mass, for the total of approx. 135 percent the magnitude of lunar tides.
While if you were to put it 3 times further than the Moon, towards the outer edge of the plausible range, it'd look 9 times smaller, and produce negligible tides of some couple percent of a lunar tide (i.e. 27*20 smaller).

Would it be possible for such a moon system around an Earth mass planet to form under these conditions?

For a planet like Uranus, having the Roche limit a bit further out, a plausible mechanism is tidal disruption of a larger moon as it is drawn too close, broken into pieces, which then spread out into a ring system and re-coalesce into a number of moons. With an Earth-like planet, the disruption region is almost at the surface, but maybe it could work here as well. It would be more catastrophic, having the satellite break down this close. But then again, not any more catastrophic than how the Moon is thought to have formed. And, maybe a straight-up collision could just as well form a ring system instead of what we've got.

I think the current thinking is that moons coalescing from rings like that form hierarchically, where those further out tend to be larger than those closer in. You can take that into consideration when arranging the system.