Could a moon orbiting a water-giant planet look like earth?

[Andreameda]

I'm a writer, damn it, not a physicist! My imagination takes me to a world where a moon can be a habitable planet that orbits the largest planet possible that could be completely engulfed by liquid water.

 

[mfb]

Large planets tend to accumulate a lot of gas, and become like the gas giants in our solar system - without oceans of liquid water. You can take a super-earth, however, something with ~2-10 Earth masses. Alternatively, two earth-like planets, orbiting each other, work as well.

 

[Andreameda]

This is helpful. Thank you. Now, another question is the rotation of the moon. For life to evolve similar to Earth on an orbiting planetoid or moon of a super-earth, would it need to rotate on it's axis as Earth does. Our moon, of course, does not. If it were orbiting a super-earth covered in water or ice, the super-earth would block out the sun for lengthy periods of time, cooling it down. The reflection of the sun from a super-earth water planet would be strong, bathing the world in reflected sunlight even at night. Lastly, for extra points, could a binary sun system have planets and if so, what kind of orbits would they be?

 

[mfb]

To get earth-like conditions (reasonable day/night temperature differences), the rotation should not be locked, so the orbit cannot be too close.

A shadow from the main planet would be rare. Just look at the moon as an example: lunar eclipses happen once or twice per year, and they do not last longer than a few hours. If you like you can make them more frequent, like once per month.

The main planet would certainly be a very important object in the sky - larger than the moon, probably with a similar brightness per area. It would have cycles similar to our moon.

 

[Bandersnatch]

Or you could have the moon tidally locked and in a very close orbit(say, 24h period). This gives you Earth-like day/night cycle, especially on the side facing away from the larger planet.
The side facing it would have much brighter nights, but I wouldn't put too much weight on the temperature rising significantly due to the reflected sunlight. Infrared albedo of snow is much lower than in the visible band, as can be seen here:
http://www.atmos.washington.edu/sootinsnow/PDF_Documents/A%20Model%20for%20the%20Spectral%20Albedo%20of%20Snow%20II.pdf
It would definitely not be another sun-like light source, as the ~0.9 visible band albedo might suggest at first glance.

Additionally, the moon having an atmosphere would mean that the temperature differences would try to equalise by creating strong wind patterns exchanging warmer and colder air between the hemispheres. This might be a good thing for the story, I suppose.

Remember that you don't have to keep the two planets orbiting each other in the same plane as the ecliptic.
Only if the orbit is coplanar, or nearly so, with the ecliptic, would there be daily eclipses on the side facing the larger planet(probably for an hour or so).
By increasing inclination by a modest amount, you can both reduce the eclipses to roughly bi-yearly occurences, and reduce the amount of light reflected from the larger planet at night(it would only rarely be a fully illuminated disc).

As for the binary system, this thread:
https://www.physicsforums.com/showthread.php?t=680386
discusses a similar setup.

 

[Andreameda]

As a writer I feel I'm cheating here not doing the work all myself, sort of like peeking over and stealing someone's notes. A fictional book or screenplay must capture the wide-eyed wonder of a mainstream audience and visual illustrations go a long way in this regard. But the physics must mesh for it to be true science fiction and not utter fantasy. The visual effect at night of an earth-like moon, tidally locked and orbiting an enormous super-earth ocean world would be fantastic visually, especially at night when the sun can be reflecting off the water like a mirror. Then a back story for how this planetoid moon came to be. I suppose it could have been a rogue planet captured by the super-earth. It could have just "dinged" off it, thus capturing much of the super-earth's water and atmosphere. Actually, I don't see any other way?

 

[mfb]

For a close orbit, tidal effects on the super-earth would be significant - I think I would give it the same day length then. Unfortunately, it is unknown (or I never saw it) how day lengths of super-Earth's look like. Well, 24 hours should be in the possible range. Just avoid the Roche limit for the orbit.

Those objects could have formed together, or after a collision (similar to earth/moon).

 

[snorkack]

As a writer I feel I'm cheating here not doing the work all myself, sort of like peeking over and stealing someone's notes. A fictional book or screenplay must capture the wide-eyed wonder of a mainstream audience and visual illustrations go a long way in this regard. But the physics must mesh for it to be true science fiction and not utter fantasy.

Precisely. People have thought about habitable, tidelocked satellites before. I think it is good to check the physics and verify that you are not getting anything wrong.

Say that what you have is a hot Uranus - mainly water, but missing the hydrogen-helium atmosphere of cold Uranus. Say, 14,6 times Earth mass, and 3 times Earth diametre. This gives 54% Earth density, or about 3 - much denser than water, but such amount of water can be expected to be compressed by gravity. There are some works that quantify such compression - leaving it for your homework to look up the numbers for what you want.

Anyway, the combined mass of the giant and moon is 15,6 Earth masses. Then the synchronous orbit distance for 24 hour period is 105 000 km. The diametre of the giant was 38 000 km, so its radius spans about 10 degrees, and its diametre about 20 degrees in sky. 40 times the linear size of Moon (coming together from being about 11 times bigger, and 3,5 times nearer) and thus about 1600 times the area.

If your planet has 23,5 degrees of axial inclination then the eclipses will occur less than 2 months in spring and autumn each - but every day during that period - and then not at all for a bit over 4 months of summer and winter each. This applies on suburanian point: towards either pole, the eclipses will occur earlier in spring and later in autumn, so the eclipse-free period in winter is shorter and that in summer is longer.

and reduce the amount of light reflected from the larger planet at night(it would only rarely be a fully illuminated disc).

Yes, but not by much.
Consider that a gibbous moon 45 degrees from full is 85 % illuminated. The dark crescent spans just 15 % of the width of the disc. At smaller inclinations, even less... 23,5 degrees from a fully illuminated disc is 96 % illuminated.

 

[Andreameda]

This is assuring in the sense I'm covered, physics wise. What I'd need to inform an illustrator who, like me, cannot decipher or make heads or tails of what you just said, is approximately how big "Uranus" would appear in the sky? Say, as compared to the our own moon. The larger the better I'd think for visual "awe". Also, I was thinking, as another suggested, it would be less than a gas giant like Uranus, warm enough for liquid water, compresed by gravity ... and more like a super-earth rocky planet. If both are possible, then perhaps I could have both. The waterworld super Earth and the earth-like moon orbiting the giant? Imagine how cool it would be to have satellites orbiting the water world -- only they're aren't really orbiting, they are floating on the water. Whether I'd want perilous sea creatures underneath is under consideration.

 

[Bandersnatch]

What I'd need to inform an illustrator who, like me, cannot decipher or make heads or tails of what you just said, is approximately how big "Uranus" would appear in the sky? Say, as compared to the our own moon.

As snorkack said, with that setup, the disc's diametre on the sky would be ~40 times as large as that of the Moon(or the Sun), or approximately the width of a handspan at arm's length, or 1/9th of the East-West arc across the sky.

 

[snorkack]

"Floating on the water" is absurd. Rock would sink.

Roche limit will limit the size of the planet in sky.

If you want to depict it, remember 2 basic things:
1) The moon is tidelocked. Anywhere on near side, the planet hangs immovable in the sky, depending on where on the moon you are.
2) It is a sphere illuminated by distant sun. If Sun is near, it is a crescent with horns pointed away from the Sun - wherever the Sun is, near or far from the planet, above or below horizon, the phase of the planet is always given by the direction to the Sun.
And the direction to Sun will vary in a consistent manner depending on the time of day, season of year, location on the moon...

 

[Andreameda]

Snorkack -- is this forum for astrophysicists only? "Absurd" is rather harsh, isn't it? How was I to know that you couldn't have a floating "space station" on a water planet?

 

[mfb]

You can put boats on a water planet, of course. Unless you propose some advanced technology, they are probably too small to be visible from the moon without a really powerful telescope.