Feasible star + planet + moon combo? Did I miss anything that makes this system wildly unstable or otherwise impossible?

Question

Here's what I've come up with:

The star:

1. A main sequence star, roughly a sol analogue

2. Younger than Sol (say 3-3.5 billion years old)

3. roughly the same starting mass as Sol, but has had less time to burn off mass, so is slightly more massive than current Sol mass (1.05-ish Sol masses)

4. is also slightly hotter, again due to younger/more mass/burning hotter (maybe the hotter side of G2, or maybe it's a G1).

The planet:

1. Gas Giant

2. Jupiter-like elemental composition (roughly 74% hydrogen, 25% helium, 1% other, by mass)

3. total mass of 1.5 Jupiter masses

4. 1.5 Jupiter Radius

5. I believe this mass + radius combo gives a density of about about 550kg/m^3

6. Semi-major axis of about 1.04 AU

7. I believe this semi-major axis, plus the 1.05 Sol masses of the star, yields an orbital period of about 378 days

8. I also believe this puts the planet within most common definitions/boundaries of habitable zones/goldilocks zones/CHZ/etc for the described star.

The moon:

1. Rocky (metal/silicate) crust

2. Semi-major axis of about 4 million km

3. Radius of 2142 km

EDIT 4. Mass of 6.594e^23 kg (was previously listed as 6.594e^17 kg)

5. I believe this semi-major axis, and the mass of the parent planet, yield an orbital time of about 42 days

6. I also believe this radius and mass yield earth-like gravity (yes, I know this requires a core made of handwavium, or at the very least a handwaved explanation of how a core of osmium/platinum came to reside at the center of this moon...and in this manner the hand has been waved...)

7. No matter how I try, I can't seem to wrap my head around atmospheric retention ... I'm hoping this moon can hang on to an Earth-like atmosphere for at least a few million years, if not for the full evolutionary time range, but ... wow the info on that confuses me ...

Factors I tried to take in to account, and related links/articles/answers:

Stellar formation, stellar evolution (age/mass/temperature relationships), stellar luminosity, main sequence, Gas Giant formation/location (formed beyond frostline and migrated in later), gas giant composition, gas giant densities and radius based on those compositions(especially that if a gas giant of more than amount 2 Jupiter masses is likely to be crushed by its own gravity down to about jupiter radius, rather than increasing it's radius any more), hill spheres, formation methods of terrestrial planets, roche limits, magnetosphere and atmosphere effects on stellar winds and radiation, and the reverse effects of radiation stripping atmosphere, radiation on the moon from the gas giant planet

https://astronomy.stackexchange.com/questions/8440/maximum-and-minimum-gas-giant-ice-giant-densities

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So my question has 2 main parts:

1. Is there something I should have considered, but didn't, that makes my system unstable in a time frame of a few million years (preferably a few billion), or impossible to begin with (other than the handwavium core of the moon)?

2. Assuming that I didn't fail to consider all applicable aspects, did I make any glaring mathematical or conceptual mistakes? (did I miss a digit or decimal, and my planet is actually inside my star? Did I entirely misunderstand a concept, like Hill Spheres or roche limits, such that even though I attempted to take them in to consideration I utterly failed to apply it properly?)

Answer 1

As you've already discussed with Alexander in the comments observed super-Jovian worlds tend to start shrinking in diameter and growing in average density once they top about +5-10% over Jovian mass, so your Gas Giant is maybe a bit on the fluff-ball side, it maybe could happen but we've never seen in. A possible mechanism would be to have a very hot, dense, radioactive core with a thick pure hydrogen/helium atmosphere that's kept highly active and buoyant by convective currents caused by the heating of the lower layers, not stable over geological time, but nothing ever is. Currently the mean density is 589kgm^-3 and it's orbiting well outside it's stellar Roche Limit of approximately 2,250,000 km so it should be all good. The planet has a hill sphere of about 1.2x10¹⁰km or almost exactly 80 AU, so it will definitely capture the moon in question.

The moon is indeed handwavium heavy now, I ran an average density calculation with the new numbers and came out with 16.018gcm^-3. Apparently the surface gravity will be 0.97, just about right where you want it. The moon's proposed orbit is well within the gas giant's Hill Sphere so it should be in a stable orbit and well outside its 85000km Roche Limit so the moon itself should be stable enough.

The Roche Radius calculations were done with the Excel formula on this page.

In short it should be a stable system but there's something weird with the surface gravity calculation for the moon that I can't work out.