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I seek to build a habitable moon of a giant planet, thus I looked at the Rouche Limit Equation to figure out how to get the biggest possible Hill Sphere for my moon to exist in.

$r_H = a(1-e)\sqrt[3]{\frac{m}{3M}}$

$r_H$ = radius Hill sphere

$a$ = semi major axis satellite

$e$ = orbital eccentricity satellite

$m$ = mass satellite (planet)

$M$ = mass central object (sun)

If I interpret the formula right I want to set the secondary objects orbital eccentricity as low as possible, the mass of the star has high a possible, making the lifetime and the spectrum of the star along with the impossibility of planet formation around O and B stars due to photoevaporation the limiting factors. Since the mass of the star is related to its temperature and so to the position of the habitable zone I included this in the calculation of the optimal stellar mass.

This leaves me with the mass of the planet which should be as high as possible. For a gas giant, this would mean 13,8 Jupiter masses. However brown dwarfs offer a much higher mass of up to 0,08 Solar masses before turning into red dwarfs. Given the formula above it is obvious why it seems tempting to use a brown dwarf instead of a gas giant. I´m somewhat at a loss at classifying this system since brown dwarfs are neither planets nor proper stars, so any clarification on whether this is a binary star system or a planetary system would be appreciated.

I have come up with a number of potential benefits and issues by myself, yet I would appreciate it if someone who is more knowledgeable on the subject would check my assumptions and point out what I missed.

  • Deuterium and/or Lithium burning should be over within a few million years, so it won´t mess with the system in the later stages. During the formation process, however, the radiation pressure of the active brown dwarf should create a secondary frost line around it. This isn´t necessarily a bad thing since it will make the formation of a big planet much more likely and could inhibit the formation of a radiation belt pumping Io equivalent.

  • The mass of a brown dwarf will make keep the orbit of the planet/moon much more stable, as it can provide a stronger counterweight to the suns influence than any gas giant could.

  • The additional heat won't be much of a problem since orbits can be adjusted to account for it.

  • Some Brown Dwarfs seem to be capable of flaring, which would be bad for obvious reasons. Is this a rare occurrence or do all Brown Dwarfs flare?

  • Would the magnetic field of the Brown dwarf deliver any benefits or cause any problems? I assume that a situation similar to the one with Ganymedes magnetosphere will occur.

In the end, I´m interested in whether a Brown dwarf is superior to a gas giant as the host planet for a habitable moon.

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    $\begingroup$ Would you mind sharing why you want a giant hill sphere? There might be other ways to solve whatever the underlying requirement is. $\endgroup$
    – Starfish Prime
    May 8, 2019 at 10:53
  • $\begingroup$ @Starfish Prime I want it so I can have a huge moon system along with my habitable moon. For the habitable moon scenario a captured one in an eccentric orbit seems most plausabile, yet this capture event would wreak havoc on the rest of the moon system if there is little space aka a small hill sphere. Additionally there's the astetic aspect of either having a Sudarsky Class 2 or 3 Gas Giant vs having the red glow of an L-type or the reddish purple of T-type Brown dwarf. On this front I want to know if the second set of options is even plausabile. $\endgroup$
    – TheDyingOfLight
    May 8, 2019 at 11:43
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    $\begingroup$ Ahh, moons of moons. I think they've popped up on here multiple times in the past, and they're quite problematic. Honestly, given how awesome it would look to be orbiting a gas giant, it seems almost greedy to want your own moons as well. $\endgroup$
    – Starfish Prime
    May 8, 2019 at 11:55
  • $\begingroup$ @Starfish Prime Ups I meant that differently. The habitable moon is not supposed to have any moons, but to be the biggest moon in the gas giants moon system insted of the only one. $\endgroup$
    – TheDyingOfLight
    May 8, 2019 at 12:43

2 Answers 2

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One possible problem with just a plain ol' Gas Giant is... radiation.

From Quora: Jupiter’s magnetic field is the largest out of all the planets in the solar system. It probably has a huge metallic hydrogen core (still a mystery). The magnetosphere extends millions of kilometers into space all the way to Saturn on one end and millions of kilometers in other directions. It's because Jupiter’s magnetic field is so intense, which would not be that dangerous in on itself, that a much greater amount of the deadly charged particles get trapped, be it from the Sun or Io’s volcanic activity. Those particles literally keep accumulating and residing within the Jupiter’s magnetic fields, forming the so-called radiation belts.

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    $\begingroup$ Are you aware of the function of the hard-science tag? I´m looking for the technical reasons behind a Brown Dwarfs inferiority or superiority. $\endgroup$
    – TheDyingOfLight
    May 7, 2019 at 21:58
  • $\begingroup$ Updated to focus just on radiation. Hard-science enough, or do you need numbers? $\endgroup$
    – rje
    May 7, 2019 at 22:07
  • $\begingroup$ Numbers would be nice, but having researched the subject myself I´m fairly sure that removing Io would make Jupiter way more pleasant radiation wise. So simply not including an Io equivalent cloud do the trick. Additionally, your answer feels quite narrow and does not really cover my actual question. Thank you for answering, but without meaning to offend you this answer won't work unless you expand it a lot and provide some data and formulas. $\endgroup$
    – TheDyingOfLight
    May 7, 2019 at 22:13
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    $\begingroup$ @TheDyingOfLight This answer could be considered a frame challenge, which is permissible. However, as you've stated, the lack of sources and/or equations does not satisfy the requirements of the hard-science tag. $\endgroup$
    – Arkenstein XII
    May 8, 2019 at 0:58
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Gas giant moons are easy. For scale, Jupiter's outermost big moon (Callisto) is within 5% of Jupiter's Hill radius. Move Jupiter in to the Sun's habitable zone means dividing its orbital distance from the Sun by about 5. So if Jupiter was in the Sun's habitable zone (and all its moons too), Callisto would still only be at about 25% of the Hill radius, meaning that all four Galilean moons would be perfectly stable. When I wrote a blog series called "Building the Ultimate Solar System", I argued that five large moons around a gas giant was a conservative number. (Blog post here: https://planetplanet.net/2014/05/22/building-the-ultimate-solar-system-part-4-two-ninja-moves-moons-and-co-orbital-planets/)

Brown dwarfs are a little tricky. They start off burning deuterium (and giving off plenty of energy), then they cool off and fade in about a few hundred million years (see image below, with inward-moving habitable zone as the BD cools off). Why does this matter? Because if you want a planet to end up receiving the right energy from the star (assuming the BD is in orbit around a star), then the planet will necessarily be roasted for the first several hundred million years of its life. Will that mean its water will be lost to space? Maybe -- it's hard to calculate precisely.

(See https://planetplanet.net/2014/10/09/real-life-sci-fi-world-4-earth-around-a-brown-dwarf/)

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