3
$\begingroup$

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)

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

  2. 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...)

  3. 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

Could a habitable planet with lower gravity have a thick atmosphere?

How do you get a thick atmosphere with less than earth-like gravity?

Making a planet habitable for humanoids: The planet

Making a planet habitable for humanoids: The star

What's the smallest reasonable natural planet or moon with Earth-like surface gravity?

Habitable environment on a big moon of a gas giant lacking magnetosphere

Can a habitable moon rely on the magnetosphere of its parent planet for radiation protection?

How small could an Earth-like planet be while still realistically being able to sustain human life?

Habitable moon of a gas giant: working out the sizes and distances

Naturally making a gas giant moon habitable

Smallest possible habitable planet? (also taking density into account)

What parameters are necessary to generate a plausible star in line with a spectral classification?

Increased Luminosity in Stars

What is the maximum orbital time for my moon around my planet?

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?)

$\endgroup$
  • $\begingroup$ 1.5 Jupiter radius (with only 1.5 times the mass)? That's 3.375 times as voluminous, and 2.25 times less dense. Fluffy Jupiter :) $\endgroup$ – Alexander Oct 10 '18 at 18:00
  • $\begingroup$ @Alexander Yes, I was trying for that, though I'm not sure I 'should have' tried for it. The idea being a large radius to create a large angular size when viewed from the moon's surface. I tried to base it, somewhat, on 'known' exoplanets, and at the same time keep it away from weird extremes in 'known' exoplanets which might turn out to be errors in our abilities to measure them. But that radius/mass/density relationship is exactly the kind of thing I'm not sure I understand well enough, and which prompted this question $\endgroup$ – Dalila Oct 10 '18 at 18:08
  • 1
    $\begingroup$ Non-hot "fluffy" Jupiters is not what we were able to observe so far, but there is no hard science that forbids it. If you need it for your story, that should be Ok. $\endgroup$ – Alexander Oct 10 '18 at 18:15
  • $\begingroup$ @Alexander Answers to this question will probably be the deciding factor on final changes to the system before going in to the story. 1.0 Jupiter radius is acceptable, if it comes to that, but I'd like it a bit more, if there's a plausible explanation for making it bigger, that doesn't cook the moon. "no hard science that forbids it" is good enough for now :) $\endgroup$ – Dalila Oct 10 '18 at 18:20
3
+50
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Thanks. I went through my numbers again, and I think I found the decimal I missed earlier (shifted over about 6 decimal places somehow, I think) I've edited the Moon's mass accordingly. Does that work out better? $\endgroup$ – Dalila Oct 17 '18 at 13:04
  • $\begingroup$ @Dalila That's certainly an handwavium core density I'll run the whole answer again and we'll see what we get. $\endgroup$ – Ash Oct 17 '18 at 13:08
  • $\begingroup$ I'm expecting a core density roughly 3 times more dense than earth (just over 16000 kg/m^3 if I got my math right this time, obviously it's very possible I botched it again), though not quite dense enough to be a solid pure osmium marble in space ... though a solid pure osmium marble 'core', with earthlike outer layers is kinda the density I was trying for ... $\endgroup$ – Dalila Oct 17 '18 at 13:20
  • $\begingroup$ @Dalila So apparently I had the first surface gravity number wrong somehow, even though everything else using that number still checks out the same as it did before and I'm using all the same calculators. Have a look at the new results anyway and I think I've linked all the calculators I've used, the data I feed in came direct from Wikipedia. $\endgroup$ – Ash Oct 17 '18 at 13:45
  • $\begingroup$ On that site you referenced for the gravity calculation, I think you entered the radius in KM, instead of Meters. I provided KM in my question, but the site uses meters in it's calculation. Does that check out? $\endgroup$ – Dalila Oct 17 '18 at 14:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.