Celestia Forums

I am a writer and artist. Some time ago I did a painting of a system I have come to call the Heracles Quartet, a large gas giant with a system of 3 primary moons, one of which is inhabited.

I have some questions regarding the feasability of an earth-sized moon orbiting a gas giant that is approximately twice the diameter of jupiter.

Heracles, the gas giant, orbits at a distance of just over one AU from its sun.

The inhabited moon has an orbit both wide and highly angled relative to the planet's plane, not unlike Themisto, the ninth moon of Jupiter. This keeps the moon from ever falling behind the gas giant, so that it does not plunge into a period of freezing temperatures.

The part of the moon's orbit that brings it infront of the planet is close enough that the moon's nightside is bathed (gently, not glaringly) in the reflected light of the planet. I am not sure if this is possible, because I'm not sure how close the moon would need to be for this to occur. The moon is earth-sized and the planet nearly twice the diameter of jupiter. If the distance for this to occur is too close, then obviously the planet would be torn apart by tidal stress, or fall into the planet, destroying it.

The moon has a rotational period of approximately 26 hours.

Is what I have stated above possible for a moon of approximately earth size orbiting a planet of approximately twice the diameter of jupiter, while maintaining an earthlike environment?

PS: I am unsure of the mathematical relationship between size and mass. Given that I have the planet set at 278,900 kilometers at the equator, could someone please figure out the mass relative to Jupiter?

I'm not a professional astronomer, but here are some of my impressions about such a situation.


Unfortunately, the maximum radius of gas giants is only slightly larger than Jupiter's (~80,000 km). The increased gravity of larger planets mashes them down. See http://www.lpl.arizona.edu/grad/classes ... 1/jan_20(1).pdf

If the gas giant is rotating rapidly, it'll be oblate. The gravitational torque caused by the protruding equator tends to cause nearby satellites to migrate into the equatorial plane. I suspect for a large, habitable moon to orbit like you're suggesting, the primary would have to be tilted similarly to Uranus.

Don't forget, however, that such a sun-facing orbit would only face precisely toward the sun twice a year. Orbit orientations are fixed relative to the stars, not to the sun. (Unless the satellite is close enough to the planet that the shape of the planet's gravitational field causes the moon's orbit to precess -- this happens for some artificial satellites orbiting the Earth, for example.) There would be times a quarter-year later and about 6 months apart when the moon would go into eclipse.

Whenever the planet is up in the sky of the moon, it certainly would illuminate it, just as the Earth is illuminated by moonshine. The math for calculating the exact amount of illumination is more than I can figure out easily. Some of the factors would include the angular diameter of the planet as seen from the moon, the brightness of the solar illumination at 1au, the planet's albedo and what phase it is in relative to the moon, for example.

I hope this helps a little.

selden wrote:I'm not a professional astronomer, but here are some of my impressions about such a situation.


Unfortunately, the maximum radius of gas giants is only slightly larger than Jupiter's (~80,000 km). The increased gravity of larger planets mashes them down. See http://www.lpl.arizona.edu/grad/classes ... 1/jan_20(1).pdf

If the gas giant is rotating rapidly, it'll be oblate. The gravitational torque caused by the protruding equator tends to cause nearby satellites to migrate into the equatorial plane. I suspect for a large, habitable moon to orbit like you're suggesting, the primary would have to be tilted similarly to Uranus.

Don't forget, however, that such a sun-facing orbit would only face precisely toward the sun twice a year. Orbit orientations are fixed relative to the stars, not to the sun. (Unless the satellite is close enough to the planet that the shape of the planet's gravitational field causes the moon's orbit to precess -- this happens for some artificial satellites orbiting the Earth, for example.) There would be times a quarter-year later and about 6 months apart when the moon would go into eclipse.

Whenever the planet is up in the sky of the moon, it certainly would illuminate it, just as the Earth is illuminated by moonshine. The math for calculating the exact amount of illumination is more than I can figure out easily. Some of the factors would include the angular diameter of the planet as seen from the moon, the brightness of the solar illumination at 1au, the planet's albedo and what phase it is in relative to the moon, for example.

I hope this helps a little.

In keeping with the information about the size of planets (which I was not aware of) I've begun to scale down Heracles.

Do you folks think that 1.4 Jovian diameters is plausible? That would put Heracles at 200,177 kilometers in diameter, with some spare change.

Well, the transiting extrasolar planet HD 209458 b may have a radius of as much as 1.4 x Jupiter's so it's not too far fetched. (The radius used in Celestia's extrasolar.ssc is somewhat smaller.) Of course, HD 209458 b is a "hot Jovian", so its atmosphere is inflated by the extreme insolation.

See http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305277.pdf

For what it's worth, a paper by people at SWRI suggests that the total mass of a giant planet's moon system would be about 0.0001 of the planet's mass.

See http://www.swri.org/9what/releases/2006/Canup.htm
and the discussion here at http://www.celestiaproject.net/forum/viewtopic ... 3759&73759

This suggests to me that a planet that formed with a moon the size of the Earth is likely to have a mass greater than 10,000 x Earth. That's somewhat more than 30x Jupiter, which seems to be in the middle of the range of masses of brown dwarf stars (~10-80x Jupiter). Their radii tend to be slightly smaller than Jupiter's.

Of course, if an Earth-sized moon were captured somehow (formed from planetoids colliding?) maybe during the time the super-Jovian was migrating inward from the orbit where it formed, that could explain a non-equatorial orbit and its association with a planet with a smaller mass than otherwise might be expected.

The captured-moon idea was one I was already preparing to use to explain the orbit. I was not aware of the mass situation, however, it seems to fit nicely.

The paper discussing the mass of the moons of a gas giant is a theoretical paper based on the observation that the moons of the gas giants in the solar system fit this pattern. However, theory also predicted that planetary systems would have rocky terrestrial planets close in and gas giants farther out. Hot Jupiters were a complete surprise when they were found.

Perhaps the theory on moon mass is correct. I don't know. However, double stars, stars with brown dwarf companions, Pluto and Charon and Earth and the moon all exist; all of which have large companions. Why would gas giants be restricted to having small bodies in orbit when smaller and larger bodies can have companions of a substantial size compared to their own?

So I would not have qualms about an Earth-mass moon around a Jupiter-mass planet. However I wouldn't have large numbers of them because perturbations make such systems unstable. Perhaps the moons are modelled after Saturn's system with one big moon and lots of small ones.

Other notes:
* The moon would be tidelocked to the gas giant.
* The moon would have a low axial tilt in relation to the gas giant. This is important because the gas giant's axial tilt in relation to the sun would be roughly mirrored by the moon's axial tilt in relation to the sun.
* A large-diameter gas giant would have a large mass to go with it.
* The gas giant would be blue with white water clouds.
* Give the gas giant an axial tilt and this will make the moon avoid eclipse on every orbit. The larger the tilt, the shorter the eclipse seasons would be, but the more extreme the moon's seasons.

So the system I would create along these lines would be like this:
* Gas giant - Jupiter's diameter * 1.2, Jupiter's mass * 2 to 5. This would make the moon orbit quickly.
* Axial tilt of gas giant - between 20 and 30 degrees
* Axial tilt of moon in relation to gas giant - less than 1 degree
* Axial tilt of moon in relation to sun - between 20 and 30 degrees
* Tidelocked moon - would have locked in less than 1 million years

The world would have seasons like the Earth with one exception. The hemisphere that faces the giant would experience eclipses around the equinox. These eclipses would last about 5% to 10% of the day at their longest and would be like a short night. The other hemisphere won't experience eclipses.

If modelled after Saturn's moons, this moon is the largest moon of the planet by a fair margin. Its orbit would influence the orbits of the other moons. Thus the nearby moons would be in a stable orbital resonance with it.

bdm wrote:The paper discussing the mass of the moons of a gas giant is a theoretical paper based on the observation that the moons of the gas giants in the solar system fit this pattern. However, theory also predicted that planetary systems would have rocky terrestrial planets close in and gas giants farther out. Hot Jupiters were a complete surprise when they were found.

I've heard this sort of comment a lot, but it's not really helpful IMO. At least, there's no reason not to use an existing theory/model just because it's likely or possible that it'll be proved wrong in the future. We've got to use the data we've got now - and the understanding that we have now based on that data - otherwise we won't get anywhere because we're waiting for the 'perfect model'.

Perhaps the theory on moon mass is correct. I don't know. However, double stars, stars with brown dwarf companions, Pluto and Charon and Earth and the moon all exist; all of which have large companions. Why would gas giants be restricted to having small bodies in orbit when smaller and larger bodies can have companions of a substantial size compared to their own?

Because they don't form the same way. My understanding is that the large satellites of gas giants form out of the material that's left over in the circumjovian disk, but after the gas giant has mostly formed. Companion stars form out of the protostellar cloud while the primary is still forming, so there's still enough material there to allow them to get very massive. I think it's mostly about the timing really.

Pluto/Charon and Earth/Luna don't count here because they're not gas giants - those satellites were born from giant impacts on their primaries, not by accretion from a disk while the planet was forming. So those models in the paper that Selden linked to don't apply to the terrestrials.

* The moon would be tidelocked to the gas giant.

Correct.

* The moon would have a low axial tilt in relation to the gas giant. This is important because the gas giant's axial tilt in relation to the sun would be roughly mirrored by the moon's axial tilt in relation to the sun.

If it was tidelocked, it shouldn't have any axial tilt relative to its orbit around the gas giant at all.

* A large-diameter gas giant would have a large mass to go with it.

1.4 Jovian radii is too big, unless it's a very young (less than a few hundred million years old) or so close to its star that its atmosphere becomes extended. They won't be much bigger than Jupiter... brown dwarfs range from about 77% to 120% of Jupiter's radius, depending on their mass and age.

* The gas giant would be blue with white water clouds.

Why?

* Give the gas giant an axial tilt and this will make the moon avoid eclipse on every orbit. The larger the tilt, the shorter the eclipse seasons would be, but the more extreme the moon's seasons.

Correct. Though an eclipse wouldn't freeze the satellite, it's be more like a brief night. It wouldn't spend THAT long in the shadow of the giant.

* The gas giant would be blue with white water clouds.

Why?

Because of that :

Heracles, the gas giant, orbits at a distance of just over one AU from its sun.

the subject have already been discussed if I remember, and jovian planets at such a distance of a sun-like star would have this appearance.
But I can be wrong...

Malenfant wrote:

bdm wrote:The paper discussing the mass of the moons of a gas giant is a theoretical paper based on the observation that the moons of the gas giants in the solar system fit this pattern. However, theory also predicted that planetary systems would have rocky terrestrial planets close in and gas giants farther out. Hot Jupiters were a complete surprise when they were found.

I've heard this sort of comment a lot, but it's not really helpful IMO. At least, there's no reason not to use an existing theory/model just because it's likely or possible that it'll be proved wrong in the future. We've got to use the data we've got now - and the understanding that we have now based on that data - otherwise we won't get anywhere because we're waiting for the 'perfect model'.

I've made the comment here before and you may have read it. The weakness of the theory is that it is formulated from only four data points. That does not invalidate the theory, but increases the probability of a flaw.

The theory probably assumes that Uranus and Neptune formed in the same way as Jupiter and Saturn. However, attempts to model planetary formation in computer simulations often cannot form planets like Uranus and Neptune. So theories that treat all four solar system gas giants the same should be understood in this context and therefore taken with a grain of salt.

The primary reason why I feel it's important to raise it is because the fictional planet under discussion has a moon comparable in size to the Earth. If the theory has some merit - a reasonable assumption - one Earth-sized moon may be possible but not large numbers of them. Large numbers of Earth-sized moons in close proximity also have stability issues such as perturbations. Thus I suggested modelling the moons after the moons of Saturn - one large moon and lots of smaller ones.

Besides, if the large moon was impossible, it would go against the purpose of this thread. And that would spoil the fun.

Malenfant wrote:

Perhaps the theory on moon mass is correct. I don't know. However, double stars, stars with brown dwarf companions, Pluto and Charon and Earth and the moon all exist; all of which have large companions. Why would gas giants be restricted to having small bodies in orbit when smaller and larger bodies can have companions of a substantial size compared to their own?

Because they don't form the same way. My understanding is that the large satellites of gas giants form out of the material that's left over in the circumjovian disk, but after the gas giant has mostly formed. Companion stars form out of the protostellar cloud while the primary is still forming, so there's still enough material there to allow them to get very massive. I think it's mostly about the timing really.

Pluto/Charon and Earth/Luna don't count here because they're not gas giants - those satellites were born from giant impacts on their primaries, not by accretion from a disk while the planet was forming. So those models in the paper that Selden linked to don't apply to the terrestrials.

Are there sound theoretical reasons why giant impacts cannot form large moons for gas giants in the same way? Gas giants may initially form at well-spaced distances, but during the planetary ejection phase when orbits of planets tend to cross, a collision between two gas giants is not a remote possibility. Could a large moon accrete from the debris of such a collision?

Malenfant wrote:

* The moon would have a low axial tilt in relation to the gas giant. This is important because the gas giant's axial tilt in relation to the sun would be roughly mirrored by the moon's axial tilt in relation to the sun.

If it was tidelocked, it shouldn't have any axial tilt relative to its orbit around the gas giant at all.

By "low axial tilt", I was thinking of a tilt of less than one degree. I should have stated this. For the purposes of building the world, the exact magnitude of the angle was not important. What is important is that the larger the tilt of the primary to the sun, the larger the tilt of the moon would be to the sun because the small axial tilt of the moon would make the magnitudes of the axial tilts comparable.

Malenfant wrote:

* A large-diameter gas giant would have a large mass to go with it.

1.4 Jovian radii is too big, unless it's a very young (less than a few hundred million years old) or so close to its star that its atmosphere becomes extended. They won't be much bigger than Jupiter... brown dwarfs range from about 77% to 120% of Jupiter's radius, depending on their mass and age.

I agree, 1.4 Jupiter radii was too large. However, my intention was to suggest that if the planet was larger than Jupiter in radius, it would likely be more massive as well.

Malenfant wrote:

* The gas giant would be blue with white water clouds.

Why?

The planet would likely be cooler than this one:
http://www.extrasolar.net/planettour.as ... lanetID=72

and would probably resemble this one:
http://www.extrasolar.net/planettour.as ... anetID=158

Malenfant wrote:

* Give the gas giant an axial tilt and this will make the moon avoid eclipse on every orbit. The larger the tilt, the shorter the eclipse seasons would be, but the more extreme the moon's seasons.

Correct. Though an eclipse wouldn't freeze the satellite, it's be more like a brief night. It wouldn't spend THAT long in the shadow of the giant.

If a planet or moon had an axial tilt of 60 degrees relative to its sun, it will have extreme seasons regardless of eclipses. I did state that the eclipse was likely to last between 5% and 10% of the day.

Wow, thank you for your very indepth and informative responses.

As for the planet's color and appearence - I never intend to get too indepth on Heracles' composition; it simply isn't an important matter to the story. Heracles is blue, so it is up to the reader - should they be curious - to find out that this is because of a large quantity of methane, etc.

Interestingly, the entire idea of this system of mine stemmed from artwork first before any sort of writing became associated with it. I've been painting spacescapes in Photoshop for years now. One of the earliest pieces I made was of a gigantic terrestrial planet, with two moons akin to our own, but smaller.

Of course, I learned that a terrestrial planet could only be so large before being crushed by it's own gravity - and gas giants are just so much more aesthetically pleasing, so it became a large, very bland teal giant (such as Uranus, but far more blue than cyan) with three moons, and a very visible ring.

In its current state, the Heracles Quartet consists of-

Heracles - A blue gas giant approximately 1.2 Jovian diameters in size. The length of its day is in question, as the planet stems from artwork, and in some pieces the planet is bland while in others, it is banded akin to Jupiter.

and its three primary moons, which (much like the Galilean moons) are called Jordanian, name after the man who discovered the system.

-Jordan, the planet's largest moon, slightly smaller than Earth in diameter. Also named after the discoverer.
-Achilles, a smaller moon comparable to Earth's moon in size.
-Odysseus, similar to Achilles in size and composition, suggesting they may have once been the same body, or formed from the same material.

In its current state, it is really a very plain system. The Quartet is the only presense of bodies within the inner solar system. To my knowledge, the system also has a large ring of bodies at its edge, much like the kuiper belt, although I've not expanded on such an idea at all.

And, should anyone be curious, this is the most recent image of the Heracles Quartet: http://img228.imageshack.us/img228/2163 ... 600hn4.jpg

Stellatus,

The artwork seems quite well done. Obviously you've had some experience doing it. Of course, the crescents that are illuminated should be a lot thinner, but that's reasonable artistic license

Is the partial halo supposed to be an illuminated cloud of dust or distant stars?

selden wrote:Stellatus,

The artwork seems quite well done. Obviously you've had some experience doing it. Of course, the crescents that are illuminated should be a lot thinner, but that's reasonable artistic license

Is the partial halo supposed to be an illuminated cloud of dust or distant stars?

I'm not sure what you mean by the halo. Do you mean the patches of green and blue lights? Those are just distant stars. Most of the time, I feel it is best - in space art - to forsake the necessarily realistic in favor of the artistic.

If you mean the very faint ring around the sun - I'm not even sure that's supposed to be there I made this piece on a different monitor than the one I am currently using (19" widescreen, this was made on a 15" fullscreen) and while I may have intentionally made that ring and simply don't remember (it happens) it may simply be an artifact that I was not aware of on the old monitor.

I was referring to the bright patches that seem to surround the sun. Artistic is good

selden wrote:I was referring to the bright patches that seem to surround the sun. Artistic is good

Ah, just distant stars then.

That's a nice picture, but what bugs me about it is that the moons appear to be arranged somewhat randomly around the planet... they should all be in roughly the same orbital plane, but some look well above or below Heracles' equator.

They are essentially arranged randomly. Whenever you have more than one moon it is difficult to place them without it looking like they're all aligned in a straight set which, while it may be realistic, isn't particularly pleasing to look at, I find.