Reality Check: Habitable moon around earth-like planet

Question

For a complex world-building scenario I want a habitable moon orbiting a habitable earth-like planet. The habitable moon should allow for flora, fauna and landscape as similar to earth as possible. The same goes for the habitable earth-like planet it is orbiting.

I have checked the various topics concerned with habitable moons:

• What would a habitable moon most probably look like?
• Habitable moon of a gas giant: working out the sizes and distances
• Naturally making a gas giant moon habitable
• How would an earth-like planet with a habitable moon work and how to get there?

Based on what I read there, especially Jim2B's answer here, I have created the following moon with this calculator:

• mass: 0.33 of earth’s mass (around 3 times the mass of mars)
• density: 1.3 of earth's density (because I want a higher surface gravity)
• radius: 0.6332 of earth’s mass (calculated by the application using mass and density as a given)

This is all calculated by the program:

• Diameter = 8070 km
• Density = 7.176 g/cm³
• Surface Area = 204.5 million square km
• Roche Limit = 1000 km (nearest possible natural satelite)
• Surface Gravity = 0.83 Gs
• Geosynchronous orbital distance = 24820 km, or miles (from surface of planet)
• Geosynchronous orbital velocity = 2.13 km/s , or miles per second

Maximum surface* temperature to hold onto an atmospheric component for billions of years, for each type of gas:

• Carbon Dioxide? 2972 °C
• Oxygen? 2087 °C
• Helium? 22 °C
• Hydrogen? -126 °C

Could such a moon possibly exist? And if not what changes would be needed to make this moon around an earth-like planet possible?

Please consider the following points particularly:

• Density of the moon: I need it as high as possible to have the surface gravity of the moon approximate 1 g. Playing around with the calculator I have settled on 1.3 times the density of earth, which gives a surface gravity of 0.83 Gs. This means a density of 7.176 g/cm³. Is this density achievable by still keeping a similar elemental composition to earth's? If not, could that be achieved by replacing some of the iron with a denser element? What properties would such an element have to have?
• Atmosphere: Could this moon sustain the necessary atmosphere considering the surface temperatures?
• Earth-like planet the moon is orbiting: This planet has the roughly same mass and radius as earth. If a larger mass and/or surface is necessary to have such a moon, that would be ok, as long as the density of the earth-like planet could be lower to keep the surface gravity of said planet at 1 G.
• Distances between planet and moon: No specific requirements. Can be anything to make this planet-moon relationship work.
• Size relations between planet and moon: Apparently accretion disk formations would make such a large moon compared to the planet unlikely, but would it be impossible? Could there be any other scientifically explanation for a planet having such a large moon, for instance a "rogue moon" captured by the planet (Theia captured instead of a collision), the moon being debris from the planet itself or something else? This alternate explanation can be unlikely, as long as it is scientifically sound and possible at all.

Answer 1

It's definitely within the realm of possibility.

Real quick first, defining terms to make comparison easier (I really do hate the pronoun game):
Earth: Our planet.
Luna: Our moon.
Terruh: The planet your moon orbits (since it's definitely not Terra, get it? Okay, tough crowd.)
Lunuh: Your moon (since it's... okay, fine.)

Density: You need Lunuh to have an average density of around 7.2 g/cm3. That's workable. Here is a list of the approximate density of various "layers" of Earth - crusts, mantle, etc. For Lunuh, you'll want either the higher-density layers to be thicker/bigger (relatively speaking) OR the densities themselves to increase. Density increase is probably easiest - for example, the inner core of Earth is an iron-nickel alloy which is about 80% iron, but nickel is denser than iron so an increase in the amount of nickel would lead to an increase in density. You could also try, for example, reducing the thickness of the mantle, but I don't have enough geological experience to know what would happen if you tried that. But, on the bright side, the iron-nickel core will give Lunuh a nice magnetic field, which is good for habitability.

Atmosphere: Yes, it could definitely hold on to a breathable atmosphere if the necessary gasses were there. Note that the numbers given are for maximum temperature. The higher the temperature, the faster the molecules are moving, so the more likely they are to escape into space. Since Lunuh won't be reaching temperatures of 2000 C (since we, you know, don't want to melt when we visit), it will definitely be able to hold an oxygen/nitrogen atmosphere.

The Planet: Terruh can exist no problem. Its existence is its own problem outside of having Lunuh orbiting it. There are side effects of having such a large moon, such as significantly bigger tides and brighter nights, but those aren't existence problems.

Distances: It's a good thing that you don't have any requirements for the distance between Terruh and Lunuh, because this moon will have to be quite a bit further away from Terruh than Luna is from Earth. You specified that Lunuh will be 1/3 the mass of Mars, which means that it will be about nine times the mass of Luna (WA link). In order to get the same gravitational force between Terruh and Lunuh as between Earth and Luna, Lunuh would need to be triple the distance from Terruh that Luna is from Earth. More on that in a sec.

Size Relations: As @HenryTaylor said in a comment, it would be more likely to have been captured than formed via impact or accretion disk. My best hand-wavy explanation would involve Terruh capturing Lunuh during the tumultuous early life of the solar system, but given that planetary formation in general is still largely in the realm of hypotheses, I can't say too much as far as scientific rigor is concerned.

So all in all it looks okay. We can have large moons, though at a certain point we have to ask ourselves if it's really just two planets orbiting each other.

The main problem I'm seeing is the issue of tidal locking. Luna is tidally locked to Earth, which is why we only ever see one side of it. If Lunuh got tidally locked with Terruh, things could get problematic as far as the habitability side of things is concerned. Remember that it's triple the distance from Terruh that Luna is from Earth, so it's orbital distance (relative to the planet) is six times that of Luna. Assuming the same orbital velocity (not sure whether/how much it would have to change to make a stable orbit), that means it would have a day-night cycle of six months (in Earth time). That's not exactly conducive to life, so it absolutely cannot be tidally locked. But other than that, it seems like it would work fine.

Answer 2

What you have here is really a double planet. I'd recommend just going for that, and have two quite similar planets orbiting their mutual centre of gravity. That lets you get rid of the density problem, and makes it easy to accept they both have fairly fast rotation and hence magnetic fields and reasonable atmospheres.

Having such a double planet form is quite unlikely, but it's only unlikely, not impossible.

As a bonus, having two potentially life-bearing planets so close makes it positively plausible that life could spread from one to the other via bacteria carried on debris from impact events on one planet, which happens to hit the other planet.

Addition: there isn't any fundamental difference between a large moon, with a fraction of the planet's mass, and a double planet. In both cases both of them orbit a barycentre, it's just that a larger moon means the barycentre is further from the centre of the planet. But that doesn't make any very major difference.

If the moon is going to blow up, you need to consider what happens to the debris. If the moon is blasted apart and disperses in all directions, the chunks that hit the planet will be more than adequate to cause an extinction event.

If you remove the moon in some way that doesn't damage the planet, the loss of the moon will perturb the planet's orbit, in a way that depends on their positions relative to the sun when the moon goes away.

Answer 3

This sounds plausible to me. Large moons are sometimes formed in hydrodynamical simulations of giant impacts between protoplanets in the late stages of planet formation. The hardest part to buy is the density. Mercury has a lot more iron than Earth but its density is about the same because, with less gravity it is less compressed. We also don't know of any exoplanets with densities that indicate a much more iron-rich composition than Earth (although they are very hard to measure).

UPDATE: There is now a 2.6 Earth-mass exoplanet known with a Mercury-like composition -- see https://en.wikipedia.org/wiki/K2-229b