It doesn’t seem very complicated at all to face Mecca wherever you might be in the world.
There was a minor plot point in the novel Artemis about the main character’s father, who is a devout Muslim engineer living on the moon (along with the main character who is secular, leading to quite a bit of headbutting) building a pivoting device that allows him to pray facing the Earth and thus Mecca wherever the moon happens to be in its orbit.
Wouldn’t that always be the same place?
ETA: @Alesan made the same point much more succinctly while I was typing.
Given that the Moon is tidally locked to the Earth, wherever the fellow’s quarters are on Moon, the Earth always hangs in (almost) the same place in the sky. What changes over time is the illumination phase of the Earth, which part of the Earth is facing the Moon, and whether it’s sunny or dark at his quarters on the Moon.
But if facing the Earth as a whole is accurate enough, no need for moving parts at all.
If they spent much time traveling around on the back side of the Moon, the side not facing Earth, they’d need a bit of math, or a machine, to know where beneath their feet the Earth might be found. But as long as they stay in one spot, that direction won’t change over time. If they travel around on the back side, of course it’ll be a different direction at each location.
Because the moon is tidally locked? Hmmm, good point…
Looking it up, I misremembered the book (it was a Yom Kippur read quite a few years ago so not too surprising). The platform doesn’t rotate, it’s just tilted so that you can look up at Earth which was high in the sky instead of just looking in the vague direction of West where the Earth was directionally.
I don’t know if real Muslims living on the moon would feel the need to do that, given that Muslims living on the opposite side of the world from Mecca don’t pray facing down? But I guess even in the book most Muslims in the city just face west, it’s just the main character’s dad who feels the need to face upwards.
But that’s the difference between treating the Earth as opaque, so “The direction of” amounts to “The direction of over the surface”, rather than “Direction of though the body of Earth”.
Space isn’t spherical, neither is it opaque. With very few exceptions, any “compass” direction you face parallel to your local lunar surface won’t point anywhere near Earth.
I look forward to seeing how actual Muslims answer this question once we have large scale human habitation on the lunar surface 
maybe someone can bump this thread in a few decades.
I can’t answer from the perspective of the moon, but the practical rule my fellow Muslims in America follow is when in a moving conveyance (airplane, ship, vehicle), face forward.
Leaving aside the facing toward Mecca issue…
I’ve never flown with a Muslim pilot (that I know of). But regardless of faith type, I would find it bizarre for a pilot to pause during flight in the cockpit and tell me they were going to stop what they were doing and pray.
At my airline we weren’t even allowed to read a book during flight. However, FAA regs do allow for a pilot to leave the cockpit for “physiological needs”, ie, using the lavatory. We have procedures for that and, of course, I would have no way of knowing if they prayed while in the bathroom, nor would I care.
We also have procedures for taking meals in the cockpit and I have flown with a few people who routinely said a quick prayer before eating. But I never had anyone call my attention to their doing it during flight (I only knew about it from eating with them at restaurants).
I don’t know much about practicing Islam, but one hopes they are not compelled to perform a required prayer during a critical phase of flight.
Edit: Back in my CFI days I did have one rather devout student. He always stopped and did a short prayer before we took off. We were friendly enough that I kidded him about it sometimes and also cautioned, somewhat seriously, that he might not be able to do this sort of thing at a busy airport.
The prayer doesn’t have to be at a very specific time and regardless of that any rules would be waived in an emergency or where it would cause harm. I was told that there’s a procedure if you happen to miss one where you can combine a couple of the daily prayers.
Is there a section for being dismissed for having radical political and religious convictions? I haven’t read everything about this case, but I don’t recall any evidence that this person was banned for incompetence as a pilot.
AFAIK there is not within that system. But I would expect that the FBI, TSA, whoever in the federal government that does counterterrorism would notify the FAA of pilot people they’re worried enough about. Or maybe give FAA access to that “worried enough about” list and let them run it against their pilot roster? But where is that “enough” threshold? I sure don’t know.
And at least historically, the idea that the federal government could do any such spying on the legal activities of US citizens would have been horrifyingly outré. Not widely praised as a darn good idea.
I was also writing about US domestic practice in response to a direct question upthread from somebody. Just as I’m writing now. Yes, which answer(s) amount to perpetuating a kinda hijacking of a thread about a hijacking.
All of the info about US practice is potentially interesting background, but ultimately has no direct relevance to whatever processes or cooperative agreements the Omani and Dubai governments may or may not have in place.
I also think those prayers are pretty quick. When i was helping a Syrian refuge learn English, his wife sometimes laid out a rug and prayed. Other that laying out the rug and rolling it up again, it didn’t take long. I have to think a quick prayer break is routine on airlines in the middle east. And you’d check with the other pilot to make sure that it’s not a bad time, and that the other pilot knows not to depend on you for a couple of minutes.
Muslims living in Avarua Island (antipode of Mekka) … for them, every direction will do …(any direction is equidistant from Mekka, although SD nitpicking would not surprise me, with the earth not being a perfectly perfect sphere and so)
Yeah, the Islamic rules (at least, under most interpretations) are fairly practical-minded, and make accommodations for extraordinary circumstances that basically amount to “just do the best you can”. If your prayer time falls during the flight, and it’s a quiet, routine part of the flight where your copilot can easily manage things, then you’re expected to pray. If it’s right in the middle of landing or heavy turbulence or something that you need to attend to as a pilot, then take care of that and don’t stop for prayers until it’s safe to do so.