Yep, every time Scott enters the Sol system he see's Luna orbiting Terra and goes "look at that moon, it is in a non circular orbit around that planet, and wow it is big compared to the size of the planet it orbits, and wow it's orbit is closer to the elliptic plane instead of the equatorial plane like most others in this system...." or perhaps when navigating takes notes and calculates based off of the relationship of the various stellar bodies but knows that every stellar relationship is unique and he doesn't need to make a big old speech about it...
The Moon (Luna) is in a mostly circular orbit around Earth. For 3 Nights a Month we have a new moon where we have a very narrow band of light reflecting off the moon or none at all.
If for 14 nights straight the Moon was in Earths Shadow that would freak me out.
A Pilot and someone who has spent time cross training as a navigator would notice something like that.
A Science officer would look at Haven see the the orbital course, speed & the Proximity to a Massive Gas Giant while on the sunward side and have more to say then yip it most get cold at night down there. (the only way I could see a moon spend 1/2 its orbit in the shadow of the Parent planet is to have its orbit slingshot out into the outer system then be pulled back in which I cannot see as being a very good environment for People to walk around on the surface. Even having atmosphere in that kind of environment doesn't make sense to me.)
I'm ignoring Ryks date structure for Haven so that I don't break my mind trying to work it out. To me Haven spends a month in the dark and seven months in the Light. and I'm happy with to agree to disagree.
The Moon's orbit is elliptical, not "mostly circular." And it's orbit moves as well to make it even more fun.
At New Moon the Moon is not in Earth's shadow at all, the Moon is at that point in time between the Earth and the Sun and is when a Solar eclipse can happen with the Earth being in the Moon's shadow. It is the Full Moon when the Earth is between the Moon and the Sun and a Lunar eclipse can happen with the moon being in the Earth's shadow. On the surface of the Moon you do have a night of about 2 Earth weeks, and a daylight time of about 2 Earth weeks to make the one moon day of about 4 Earth weeks.
Using Luna as a model for planet moon star relationships though is not the best model, since the Terra, Luna, Sol relationship is very different from the relationships of other planets and their moons within this star system, let alone others systems that we have little to no data on.
Yes when looking at the data they notice various things, but they are not going to make big speeches about it, they are going to use that data to make calculations and that's it, otherwise they would be talking about what they are seeing 100% of the time and never be able to do their work due to all the talking. As the relationships between all planets, moons, comments, asteroids, stars, spaceships.... are complex and unique.
Jumping into a system close to close to a moon could mean death. I would want to have that conversation. As to the orbit of haven - I just don't care anymore. It's magic. It's the exception.
I will make one last comment on this subject. No disrespect is intended to the OP or any other posters in this thread.
Many times, what we believe to be indisputable fact turns out to be incorrect. History is replete with such examples. Yet, many of those with science backgrounds and educations, refuse anything that does not fit into their system of understanding.
What we know to be true will always be based on our current understanding of the universe in which we live. But when we discover something new, it changes our understanding of things.
A true scientist realizes that no scientific fact is immune from being proven false. Rather than argue why something cannot be, it is both more interesting and more productive to discuss how it could exist.
The impossibility of such a system is not a matter of "current understanding", it's a matter of physically proven facts that don't match up with the described scenario.
The facts that we know about optics - in this case, geometrical optics, since the situation doesn't work for the use of wave optics - allows only one conclusion for a hypothetical system with the described cycle. However, due to the way gravity works on big, planet-sized or even stellar objects, this bowl-shaped "gas giant" cannot exist. These statements are as true in our universe with all its natural laws as the statement that 1 + 1 = 2. No matter where in the universe you go, 1 + 1 is always 2. Not 3, not 11, not any other number.
Another matter to consider - which makes the day-and-night cycle in the "sunny" half of Haven's orbit rather unlikely: Most moons in our system are in a tidal lock with their planet. Meaning that, like our moon, they always show the same side to their planet. Which means that one orbit around the planet and one "day" are (roughly) the same time on the moon. (There's a small discrepancy due to the planet moving around its parent star - but it's really minor.) And a tidal lock seems (!) to be the general case, with the (possible?) exceptions being very small, irregular moons orbiting rather big planets that are supposed (!) to have been asteroids that got caught in the planet's gravity well, and rather recently at that. (Exclamation marks in brackets show where I'm not talking about 100% verifiable scientific fact, but about theories that, although quite likely, are in no way proven.)