Two moons in tidal lock orbit: phases, tides, axial tilt?

[TheDarkFrontie]

Consider the following;

We have Earth with two moons in orbit (discounting the existence of our own moon for the sake of this hypothetical scenario). One moon is the size and mass of Pluto, orbiting around 70,000km from Earth. The other is the size and mass of Pluto's moon, Charon, orbiting around 7,000km from Pluto. For the sake of the scenario, seen as they're exactly the same as Pluto and Charon, I'll just refer to them as such.

"Pluto" is tidally locked with Earth, orbiting the same as our moon - around once every 29/30 days. "Charon" is tidally locked with "Pluto", orbiting it every 7 days. From Earth, what would this look like? How would the two moons appear from Earth's surface in terms of their phases and position? Pluto's would remain the same as our moon does anyway (right?), but how would Charon look? Would their orbits be stable in relation to each other and to Earth? How would this affect tides on Earth, with two moons in orbit? Would it affect axial tilt (and thus, seasons) of Earth in any way given the mass and distance of the objects? Would this even be possible, to have a moon tidally locked to another body, which is tidally locked to a large planet?

 

[rootone]

Calculating orbits of multiple bodies is difficult and highly dependent on the masses, distances and velocity involved.
In some cases you can get stable orbits, others produce chaotic orbits, and some result in a body being ejected from the system.

It is possible though to have a situation where a body A is orbiting B, and B is orbiting C.
This is in fact the case for planets in the solar system which have moons orbiting them.

I don't think tidal locking can affect axial tilt, but not certain on that point.

 

[TheDarkFrontie]

So in a case where body A (smallest) is tidally locked to body B (medium), which is in turn tidally locked to Body C (large planet), how would body A appear from the planet (body C), if it's orbit around body B is 7 days?

 

[rootone]

It will be highly dependent on the speed of the orbits, (and orbital inclination ).
I don't think being tidally locked would enter into it much, that is to do with rate of spin of a body on it's own axis.
I suppose the most likely scenario is that an observer on the largest body would see the smallest body passing in front of the medium body,
then disappearing behind it, and later reappearing on the other side.

 

[TheDarkFrontie]

I gave the duration of the orbits in the original post:

Body A is tidally locked to body B, completing one orbit in 7 days
Body B is tidally locked to body C, completing one orbit in 29 days

Body B would look to an observer on body C like our moon, as the orbital duration is unchanged. It's how body A would look to an observer on body C that I'm interested in (considering it is tidally locked to body B, completing an orbit in 7 days). What would it's phases look like?

 

[rootone]

Ah, sorry I missed the figures you gave.
OK, well let's keep things simple and forget about orbital inclinations.
Let's assume all three bodies are nicely lined up in the same plane.

Standing on the largest body C, you will see the medium body B appearing directly overhead once every 29 days.
We can forget that C might itself be rotating, it most likely is, this doesn't affect the overall picture, just the timing.
Since it is tidally locked you always see the same side of B.

When B is directly overhead of the observer standing on C, the small object A can be at any point in it's orbit around B.
If it so happens that A is is directly in front of B as seen from C, then C will always see the same side of A as well.
If it is at some other point in it's orbit the observer on C will get to see some part of the other side of A.
or they might not see it at all because it is behind B at that stage.

To see phases we need to introduce a fourth body D, a light source, and now the math gets hellish
It could all be calculated precisely, but I leave that to the math experts if you are looking for that much of a high level of detail.

 

[Bandersnatch]

There's nothing all that hard about visualising phases in this situation. The two satellites would have both the same phases as seen from the planet at all times.

However, this setup is impossible. For a 30 day orbit of the pair you'd need an orbital radius almost the same as that of the Moon. At 70Mm the orbit would be much faster (use Kepler's 3rd law to get a number on it).

Furthermore, even at the 380-ish Mm separation, or anywhere within the gravitational influence of Earth, the setup is unstable - you can't have two moons orbiting each other this close to another massive body. There's a reason no moons in the solar system have their own satellites.

 

[rootone]

Our Moon does!, (have satellite orbiting it) ...
but these are insignificantly small compared to the Moon, and don't play any part in the orbits of the Moon or Earth.

You are right though about phases.
Whatever the light source is, both satellites will appear with the same phase as seen from the planet.

Problem is, the light source is a star in all probability, and that might make the orbit stability of the setup even trickier.

 

[Bandersnatch]

Our Moon does!, (have satellite orbiting it) ...
but these are insignificantly small compared to the Moon, and don't play any part in the orbits of the Moon or Earth.

Even those artificial satellites are in unstable orbits. You need to consider the timescales involved - we're talking millions of years.
The only long-term stable orbits in a restricted three-body system have the third (approximated as massless) body librating in L4 and L5 Lagrangian points.

 

[TheDarkFrontie]

Ah, that makes sense. How about a set-up similar to Mars, with two moons in orbit around the planet? As opposed to one moon in orbit around another moon which orbits the planet.

Say these two moons are tidally locked too, however one is much further out. The larger moon (Moon A) takes, say, 28 days to orbit, the smaller moon (Moon B) twice as long at 56 days. As they're both tidally locked to the planet, would Moon B just appear to have phases that last twice as long as Moon A?

As you can tell, I know very little of astronomy or astrophysics, I'm asking as I'm writing a book and I'm going for as much realism and accuracy as I can. It's a very minor detail in the book, but I still want it to be there!

 

[Bandersnatch]

would Moon B just appear to have phases that last twice as long as Moon A?

Yes. It would also move across the sky twice as fast. You'd have periods when only one moon is visible. When next to each other, they'd have the same phase.Incidentally, there are some free planetarium programs out there that allow you to mod in a planetary system and then have a look at how it works from space or from the surface. It requires a bit of work (not a whole lot, though) to learn how to do that, but there are helpful tutorials on their websites so it shouldn't be that much of a hurdle for a driven writer.

I've heard good things about Space Engine:
http://en.spaceengine.org/
you might want to check it out.

Celestia is another one, albeit simpler and somewhat clunky.
http://www.shatters.net/celestia/

If modding is too much of a hassle, you can always find a random system that resembles what you need (Space Engine generates planets procedurally).