# Physics of gas giant and moon(s) in habitable zone.



## Vertigo (Jun 14, 2012)

Although I am asking this with regard to "aspiring writing" I'm putting the question here for a hopefully wider take up! If the mods disapprove of that please feel free to move over to aspiring writers.

I am interested in having a habitable moon orbiting a similar star to ours in the habitable zone, for simplicity lets say it is in the same orbit as Earth. I would like the moon/planet to be similar in size to Earth but maybe somwehat smaller (I don't think that is too important). However I want it to have no tectonic activity and be very old so that with no new mountains being thrown up erosion has reduced the planet surface to a fairly even altitude all round. I wonder just how long that would take after tectonic activity ceases?

Now with no tectonic activity it is likely there will be no magnetic field, so my real question is, assuming the gas giant has a very stong magnetic field (like Jupiter), would it protect the atmosphere of its moons (including my habitable one). Now I know Jupiter's magnetosphere is very large extending 7 million kilometres and almost to the orbit of Saturn. As I understand it the sun's side of the magnetosphere is is where it is smallest, so I would assume that so long as the planet's orbit lies within that distance it should be protected, right? Incidentally Io, Europa, Ganymede and Callisto (by far the most massive of Jupiter's moons) all lie within that 7 million kilometre region.

Some other things I need to consider are the effect on temperature of the planet/moon's orbit around the gas giant. If we said it orbits the gas giant at say 1 million km and assume that orbit is in roughly the same plane as the gas giant's orbit around the star, then its distance from the star will vary by 2 million km. I'm not sure how big a difference in temperature that would create (I believe our seasonal variations are more to do with how much atmosphere sunlight has to travel through rather than how far away we are). Earth's distance from the sun varies by around 5 million km so I think I can assume that my planet's 2 million km variation from orbiting the gas giant will not produce a noticeable variation in temperature.

I will also need to look at how the daylight pattern would be affected. Ganymede with an orbit (semi-major axis) of around 1 million km takes about 7 days to orbit Jupiter. So again if we assume something similar and also have the rotation around the same 24 hour one of Earth. Then, and I've yet to do calculations on this, it seems to me the planet will be in the shadow of the gas giant for maybe one 'day' in every 7, giving a 'long night' once a 'week'. I also figure that it is going to be a pretty cold and dark long night.

Thoughts anyone?


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## Venusian Broon (Jun 14, 2012)

Vertigo said:


> However I want it to have no tectonic activity and be very old so that with no new mountains being thrown up erosion has reduced the planet surface to a fairly even altitude all round. I wonder just how long that would take after tectonic activity ceases?


 
Good question (and it's something I've got to get a handle on in my WiP, so I should really think about this a bit!) 

I'd say that even when tectonic activity stops, it will take a long, long time for mountains to erode down. A good example are the mountains of Scotland - which I believe were sort of Himalaya height at one point - but now 3 billion years later are the height they are today. It's a big drop, but they're still reasonably high. Gives you some sort of handle on erosion timescales at least.



Vertigo said:


> Now with no tectonic activity it is likely there will be no magnetic field,


 
personally I wouldn't automatically assume this - a magnetic field suggests to me a molten conductor somewhere around the core (most probably of iron/nickel). Now if you are saying the whole planet has cooled off and is essentially solid, fair enough - I'd guess that tectonic activity is a function of the energy driving it below and the thickness of the crust, so yes if it's cooled off significantly it's possible that it would stop,_ but _if your moon is orbiting a Jupiter-like planet then the chances are that tidal friction would be continously pumping energy into the core and maintaining it (and possibly maintaining tectonic activity....

....however you can easily get rid of this by assuming that your world orbits the Jupiter planet in a _perfectly circular orbit_ (it's allowed!) then no tidal friction would occur and no extra heating.



> so I would assume that so long as the planet's orbit lies within that distance it should be protected, right?


 
emmmm, maybe  If the planet was quite deeply enscoused in the field then I think it would be well protected, yes. Definitely from the main 'blast' of the solar wind. But because it's going about the magnetosphere it could mean that it will wonder into regions where the various protons and electrons are being trapped (I suppose), so the planet may get a bit of a 'random buffing'. If you don't want this, then I suppose you could give your moon a weak magentic field as further protection. 



> Earth's distance from the sun varies by around 5 million km so I think I can assume that my planet's 2 million km variation from orbiting the gas giant will not produce a noticeable variation in temperature.


 
Without thinking too hard about it, I agree.



> Then, and I've yet to do calculations on this, it seems to me the planet will be in the shadow of the gas giant for maybe one 'day' in every 7, giving a 'long night' once a 'week'. I also figure that it is going to be a pretty cold and dark long night.


 
This might be a killer. Very roughly (I've got some Excel'ed equations that calculate approximate temperatures of arbitary planets orbiting arbitary suns in arbitary distances, so modifing them...) 

If you cut out 1/7th of the energy that the moon receives because the big world is blocking the sun light, then instead of an average global temperature of an Earth-like world of ~14 deg C (with an atmosphere mixture like ours today), you get an average of _minus 22_ deg C . 

There will be ways around this of course - a high concentration of greenhouse gases, don't know off hand how much CO2 you'd need to cover the gap, but I think it wouldn't be too much.



Hope the above was helpful.


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## Ursa major (Jun 14, 2012)

Vertigo said:


> Some other things I need to consider are the effect on temperature of the planet/moon's orbit around the gas giant. If we said it orbits the gas giant at say 1 million km and assume that orbit is in roughly the same plane as the gas giant's orbit around the star, then its distance from the star will vary by 2 million km. I'm not sure how big a difference in temperature that would create.


Doesn't that assume the gas giant's orbit is circular, i.e. it is always the same distance from the star?


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## Vertigo (Jun 15, 2012)

@VB Thanks for the response. Comments on your comments (in order )

A few billion years I can live with and I'm proposing nothing higher than the Scottish hills, so that's workable.

Interesting about the tidal friction and of course a circular orbit or one very close to it would just about elliminate it. On the magnetic field, however, my understanding is that a magnetic field needs a 'dynamo' to drive it and that dynamo is the circulation of the molten core (or molten part of the core). Also as I understand it you _can_ have a molten core but without circulation (or significant coherent circulation). I believe Venus is thought to be an example. So no tectonic activity means either no molten core or no circulation in that core and so no magnetic field.

...I think!

Re the magnetosphere, my understanding is that if Jupiter's is at least 7 million km then an orbit well within that at say one or two million km should stay well within it at all times. Mind you I'm not too sure what the impact of the magnetic field would be on the moon!

On your last point that's a little worrying, however possibly manageable. I have some similar software that I haven't tried this out with yet (to bo honest I haven't really figured out how to use it yet ) so I will have to have a play. I'm thinking the further out I place the moon's orbit (staying within the gas giant's magnetosphere) the smaller the proportion of time in eclipse. And I still need to do the trigonometry to figure out just how long it would be in eclipse anyway!

@Ursa, yes very true but we still have a fair bit to play with considering there is no noticeable effect from our own 5 million km eccentricity. I suspect you would have to shift orbit by quite a significant amount to get a big change in temperature.


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## Venusian Broon (Jun 15, 2012)

Vertigo said:


> On the magnetic field, however, my understanding is that a magnetic field needs a 'dynamo' to drive it and that dynamo is the circulation of the molten core (or molten part of the core). Also as I understand it you _can_ have a molten core but without circulation (or significant coherent circulation). I believe Venus is thought to be an example. So no tectonic activity means either no molten core or no circulation in that core and so no magnetic field.
> 
> ...I think!


 
My thinking was it _may_ be possible to have a situation where, say the core remains molten enough for a magnetic field, but say because the crust was just too thick there wasn't enough energy to drive the plates about. 

Interestingly (because I believe the ESA have just Ok'd a mission to go there) Ganymede, the biggest moon in the solar system does have a magnetosphere but doesn't have tectonic activity - which was what I was thinking about. Possible though it was because of its eccentric orbit causing heating (although no one really knows). 



> Re the magnetosphere, my understanding is that if Jupiter's is at least 7 million km then an orbit well within that at say one or two million km should stay well within it at all times. Mind you I'm not too sure what the impact of the magnetic field would be on the moon!


 
Regarding this, again this came from real findings, that the aurora around Jupiter is linked to a moon's orbit (can't remember which one off hand) - that somehow one of it's moons triggers certain big events. But as the aurora are the effects of the solar wind slamming into the other particles inside the magnetosphere, I believe, then the moon may be going through these regions of space as well - hence getting a secondary bombardment, (it would be like being in a neon tube!) The magnetoshere is quite a complex force shield.




> And I still need to do the trigonometry to figure out just how long it would be in eclipse anyway!


 
I just gave it a thought, and I got a bit of a shudder! To answer it well, is I think is not a trivial. Working out the shadow of the Jupiter on the moon is easy enough when you've plugged in your orbit radii of both Jupiter-Sun and World-Jupiter...but then of course the Jupiter planet is moving at the same time as your world, so the direction your world is going relative to the orbit of the Jupiter will probably have an impact...




> @Ursa, yes very true but we still have a fair bit to play with considering there is no noticeable effect from our own 5 million km eccentricity. I suspect you would have to shift orbit by quite a significant amount to get a big change in temperature.


 
The thing about solar radiation incoming on a planet in an elliptical orbit its that, the elliptical orbit is an elongated circle - so yes there are moments in the orbit when it's quite a distance 'extra' away, but then at other moments it closer and it receives more. Shifting the eccentric for a planet so close to the sun shouldn't really have much of a noticeable effect for those living on the planet. But as you further out and really boost the eccentricity it would start to get a problem as your orbits are very long time-wise, so that'll give the planet very pronouced hot and cold periods, depending on where the planet is. 

[For the record, I calcuated that for an earth-sized planet orbiting in a _perfect circle_:
at perhelion distance (147M k) average temperature is ~16 deg C.
at aphelion distance (152M k) average temperature is ~12 deg C.]

In your case, the average distance this moon is (assuming a near-circular orbit) is the orbit of the Jupiter planet. Just to complicate things further though, the sun is always getting blocked by the big gas giant _when the planet is furthest away from the sun_ therefore it actually boosts the average temperature a little i.e. be careful when doing your averaging of solar fluxes! Again watch about orbital period - if you give your moon a very high period, then there should be a big winter as the moon would remain far away for a long while, but also to balance it out there will be a long and big summer. On the other hand if you are orbiting every 7 days then I think it's not a problem.

Drat, now you've got me thinking about that sun blocking orbit problem


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## Vertigo (Jun 15, 2012)

Venusian Broon said:


> My thinking was it _may_ be possible to have a situation where, say the core remains molten enough for a magnetic field, but say because the crust was just too thick there wasn't enough energy to drive the plates about.
> 
> Interestingly (because I believe the ESA have just Ok'd a mission to go there) Ganymede, the biggest moon in the solar system does have a magnetosphere but doesn't have tectonic activity - which was what I was thinking about. Possible though it was because of its eccentric orbit causing heating (although no one really knows).
> 
> ...


 
That is some interesting stuff - so much for us still to learn eh. I have also noticed that Venus interestingly _does_ have a weak magnetosphere but no internal dynamo generating it. Instead it is created by the interaction of the solar wind with the ionosphere.





> I just gave it a thought, and I got a bit of a shudder! To answer it well, is I think is not a trivial. Working out the shadow of the Jupiter on the moon is easy enough when you've plugged in your orbit radii of both Jupiter-Sun and World-Jupiter...but then of course the Jupiter planet is moving at the same time as your world, so the direction your world is going relative to the orbit of the Jupiter will probably have an impact...


 I have done my sums now (gasp - see below) and I have come up with a much more acceptable figure for the period of the eclipse. The orbital period of the moon (Eden) around the gas giant (Goliath) is 18.41 days and the eclipse will be approximately 0.95% of that time lasting 4.2 hours. I agree that the direction and speed of rotation of Eden will have an effect on that figure but I don't think it is enough of an effect to worry about. This figure being so much smaller than my original guess means that I think the moon's climate should be very stable.


For the record here are the figures I'm using (and yes the gas giant and moon names are horribly corny but they are just working names for now!):

*Star*
Mass – 1.00547 (sol)
Radius – 1.0044 (sol) = 698,560.2 km
Luminosity – 1.0193 (sol)
Spectral class – G2V

*Goliath*
Orbit – 147,382,541 km
Period = 355.95 days
Eccentricity – 0.021
Inclination – 1.2 deg
Rotation – 12.64 hrs
Radius – 72,146.756 km
Density – 0.25
Surface gravity – 2.83 g
Mass – 361.833 (* Earth)
Geostationary orbit – 196,416 km
Albedo – 0.6

*Eden*
Orbit – 2,107,365 km
Orbit period – 18.41 days
Eccentricity – 0.0017
Inclination – 0.002 deg
Rotation – 22.63 hrs
Radius – 5841.23 km
Density – 0.98
Surface gravity – .897 g
Mass – .7528 (* Earth)
Geostationary orbit – 36,962 km
Albedo – 0.25

And here's the calculation and of course the diagram is not even approximately to scale!!!!


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## Venusian Broon (Jun 15, 2012)

Vertigo said:


> For the record here are the figures I'm using (and yes the gas giant and moon names are horribly corny but they are just working names for now!):


 
Cool - maths geeks strike again!

I quickly did the calcuation another way (approximated the sun's light to be perpendicular to the planet...good enough!) and I got that the Goliath eclipsed the sun completely for Eden for ~1.1% of it's journey.

The effect of the motion of Goliath around sun is so much slower than Eden's orbital speed around Goliath so there is virtually no extra impact on Eden because of this. 

I don't have me solar flux sums with me right now - but a 1% drop in total radiation is not going to have too much of an impact on overall temps. Perhaps a reduction of degree or thereabouts from an Earth-like world at Goliath's position. So as you say not too bad at all!


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## Vertigo (Jun 15, 2012)

Venusian Broon said:


> Cool - maths geeks strike again!
> 
> I quickly did the calcuation another way (approximated the sun's light to be perpendicular to the planet...good enough!) and I got that the Goliath eclipsed the sun completely for Eden for ~1.1% of it's journey.
> 
> ...


 
I had originally planned to just go with the approximation of the sunlight being perpendicular, making the gas giant's shadow the same as the gas giant itself. But, actually I was surprised, just how much smaller it turns out to be. Almost 18,000 km smaller from a full size of just under 150,000 km. So over 10% smaller which is where you will have got a slightly longer eclipse time than me. I guess moving the gas giant so much closer to the star than Jupiter is has quite a significant effect.

Still the main thing I wanted was to have the moon have no tectonic activity and still retain it's atmosphere and also not get fried by stellar radiation which is actually probably a more significant worry, since I want life on the planet, and I think this is a workable solution for that. Though I accept there are others such as Ganymede having a magnetosphere without tectonic activity. Though if I've done my sums right it's not a very strong magnetic field (around 30 times less than Earth's) so I'm not sure if would provide much protection on it's own.


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## Venusian Broon (Jun 15, 2012)

Vertigo said:


> So over 10% smaller which is where you will have got a slightly longer eclipse time than me. I guess moving the gas giant so much closer to the star than Jupiter is has quite a significant effect.


 
To my inner (experimental) physicist 10% of 1% is nothing and should be ignored. Our answers were identical 



Vertigo said:


> Still the main thing I wanted was to have the moon have no tectonic activity and still retain it's atmosphere and also not get fried by stellar radiation which is actually probably a more significant worry, since I want life on the planet, and I think this is a workable solution for that. Though I accept there are others such as Ganymede having a magnetosphere without tectonic activity. Though if I've done my sums right it's not a very strong magnetic field (around 30 times less than Earth's) so I'm not sure if would provide much protection on it's own.


 
One of the things that this site has taught me is that, most imaginative SF settings we writers come up with, even many freak-out day-glo ones, are theoretically allowable to our current understanding (and perhaps even quite likely to be present somewhere in this universe), yes they sometimes needs pretty bizarre starting conditions and the odd balant coincidence, but hey the universe is a big, big place....


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## Vertigo (Jun 15, 2012)

I agree! I enjoy taking an end condition "I want a planet (or whatever) with such and such a feature" and then figuring out a plausible way to get that feature.


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## RJM Corbet (Jun 16, 2012)

Vertigo said:


> Thoughts anyone?





Why do you want world without mountains, Vertigo?

How are you going to amuse yourself there?


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## Vertigo (Jun 16, 2012)

This is very true RJM; I'll have to fine other amusements


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## Metryq (Jun 17, 2012)

As RJM Corbet suggested in another thread, there is another mechanism for a moon of a gas giant to have low-mountain terrain: Lightning-Scarred Planet Mars, Part two

A plasma mechanism (like the Io flux tube?) might also be a way to warm and "power" the planet—all-day auroras, even when the sun is out. Make it a very "active" system with a bright blue or white star.


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## Vertigo (Jun 17, 2012)

Yeah but I need it to be full of life as well, so I can't have anything too dramatic flattening it.


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## RJM Corbet (Jun 18, 2012)

Metryq said:


> As RJM Corbet suggested in another thread, there is another mechanism for a moon of a gas giant to have low-mountain terrain: Lightning-Scarred Planet Mars, Part two ...


 
Thanks for bringing that one back Metryq.

To me it's still a very convincing explanation for the Martian terrain, and scary too. Where do such huge electrical arcs originate from?

The universe is a very strange place ...


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