The moons may not be Earth-sized, or have an Earth-like density
As it happens, someone has looked into this exact question (among many others). All quotes are from that article unless otherwise noted.
The article notes that the biggest requirement, of course, is that the planets must be liveable:
As a matter of fact, the most limiting canon information regarding the
size of Qresh and its moons is that they are all of the appropriate
mass-to-radius size to support reasonably-comfortable human existence
- and that’s one hell of a requirement.
They use some astrophysics programs to determine suitable m and r for the various bodies. They need to satisfy several requirements: gravity within human tolerance, stable orbits, and stable (and solid) bodies. This may not be a unique determination, but as long as such values exist it demonstrates that the Qresh system is feasible.
In the case of the astrophysics fandom, this means online simulators.
We combined the mass/r ratio constants with a thorough exploration of
the simulations to figure out what combination of masses, r values and
orbits could be stable. The results were one set of sizes (mass and r,
the combination of which determines density and g) and two possible
sets of orbits.
Basically, one should not assume that the moons are Earth-sized bodies. The density of the moons can be very different from that of Earth (or Qresh), since they could be made of relatively exotic materials.
Sizes. As mentioned in the Goldilocks’ planet paragraph above, Qresh
is approximately twice as wide as Earth and 4 heavier to satisfy both
density and gravity requirements. Based on the simulation, it seems
like likely dimensions of Qresh are twice times Earth’s width and 4.5
times its mass, yielding half the density and a g 12% higher (that is,
a person weighing 50kg on Earth would weigh 56kg on Qresh). The likely
dimensions for the three moons are as follows:
Leith: just under 1/3 Qresh’s width and 8% its mass, yielding 2.5
times the density and 80% of its g.
Westerly: almost 40% of Qresh’s
width and 14 times its mass, yielding 2.6 times the density and an
effectively identical g.
Arkyn: a sixth of of Qresh’s width and just
under 3% its mass, yielding 6 times the density and an effectively
This gives each planet a gravitational constant (relative to Earth g), of:
- Qresh: 1.12 g
- Leith: 0.9 g
- Westerly: 1.12 g
- Arkyn: 1.12 g
According to this article, it is possible that humans could adapt to gravity over twice that of Earth, so 1.12 times should not make life unliveable (though it might make it uncomfortable). As for a somewhat lower gravity, humans have spent over a year in zero-g environments without dying, so I suspect a 10% lower gravity would be very survivable.
Here are the relative sizes of the moons and planet, according to their calculations:
The moons may not even have spherical orbits around Qresh
They note that of course, in this case, the center of gravity will differ appreciably from the center of Qresh, and the orbits of some of the moons will not be centered around Qresh. There are apparently two classes of orbit, one of which is shown below:
All that said, of course, the show (being filmed on Earth), presumably doesn't depict these somewhat different gravities as accurately as possible.