# Earth-like planet the size of Callisto with Io-like moon. Plausible?

Good afternoon! I'm working on a fantasy series set on a very small planet, roughly the size of Pluto or the Moon. I've already read some topics on the small earth-like planets, but mine's a bit unique. Here's why:

(Few parts edited)

The Planet

• Roughly the size between Pluto and Callisto (2370-4800km diameter)
• Same gravity (maybe a bit less) as Earth
• Slightly warmer temperatures than on Earth
• Slightly shorter days and years
• Geologically active (= moving plates and active volcanos)
• Able to sustain intelligent life

The moon

• The size of Io
• Geologically active like Io
• Similar surface like Io
• Basically the same as Io

I have changed few things since the last post. The planet may be upscaled, Pluto-sized planet was maybe an overkill.

I will be very thankful for any answer!

• Welcome to WorldBuilding! If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! Jun 19, 2017 at 13:38
• Hello! I have read that amaizing article. I am ok with using artificial materials for this planets, if it turns out it will not be able to exist in real world. Though the first thing I want is to know if it could exist without them, and with the moon it's supposed to have. From your edited comment and from the discussion you've linked, I see that if the moon was indeed upscaled to 3,700 km, which is about 100 km more than Io has, there would be a possibility of such world's existence? If yes, what about the other things a habitable world has to have? Thank you for answering so quickly! Jun 19, 2017 at 13:42
• I replaced science-based with reality-check because you are just presenting a situation and ask for plausibility. reality checks should use real science in the same way science base answers would, with two caveats: it explicitly allows for "no" as an answer, and allows skipping science if you can prove something in more obvious ways (i.e. by pointing to a real example, nothing proves an idea more than the fact that such thing exists). Jun 19, 2017 at 13:59
• You could not have a body like Io in orbit around a small planet (unless it was really, really close, and that would probably put it inside the Roche limit). Io is the way it is because of tidal heating from Jupiter's gravity. Jun 19, 2017 at 16:55

A body the size of Callisto with a surface gravity equal to Earth's would have to have an average density of 14.57 g/cm³. Since gravity at a given distance from a body of a given mass is proportional to the mass and inversely proportional to the square of the distance, the mass of your Callisto-sized planet must be

$$M = { M_E \times \left(r_C \over r_E \right)² } = 8.548 \times 10^{23} kg$$

where $M_E$ = mass of Earth, $r_C$ = mean radius of Callisto (2410 km) and $r_E$ = mean radius of Earth. That gives about a seventh of Earth's mass, because anything on the surface of your planet will be much closer to its center than anything on the surface of Earth.

The density of your planet can then be calculated by dividing its mass by its volume (which is the volume of Callisto). If you don't want to introduce any more parameters you can calculate the volume using the radius, which after some simplification gives

$$D = { {3 M_E} \over {4 \pi \times r_C \times {r_E}²} } = 14.57 g/cm³$$

That's about three times the average density of Earth, or twice the density of iron, or a bit more than the density of mercury. I don't think a planet like that could form naturally in any way, but even if that were no problem, its chemical composition would probably preclude the existence of anything like plate techtonics or any of the common geochemical cycles that we know.

I would suggest allowing for a much smaller gravity and a bit larger size, but in that case you might as well go and make your planet a clone of Mars. If you cut the gravity by half (by reference, Mars gravity is 1/3 of Earth's) you could have a "cannonball" planet made almost entirely of iron and other heavy metals, with a very thin lighter crust and mantle; I'm no geologist so whether this would work I cannot say.

As for the satellite: you can have anything you want, really, if your model is an existing natural satellite. Just bear in mind that two bodies of similar sizes orbiting close to each other will raise mutual tides and will probably become tide-locked in a short span of time.

• Thank you very much for your answer! This is what I've been looking for. So, if I want to have a planet like this, I would have to replace iron with a different, artificial metal, and still, there would not be any volcanic activity on the planet. Either that, or just go with an Earth-clone. About the tides the Io moon would cause, I was thinking that the higher density of the Planet would cause the moon to have lesser effect on the tides. Though either way, thank you very much for your answer! I really appriciate the work you've put into it! Jun 19, 2017 at 16:06