Designing a Fantasy World - physics advice needed

[CordaHed]

Hey Guys,

Very new to this forum - signed up as it seemed it might be possible to get some answers and advice as I'm designing a world (actually two worlds - two exomoons) and want to try and pay at least some attention to the constraints and realities of physics, as much as possible! My knowledge of physics is limited to a very basic understanding of the major concepts - that's where I'm hoping some of you much more learned members might be able to offer a bit of advice if you have the time!

Broadly speaking, I'm creating a Fantasy World which I imagine would consist of a solar system with around 4-6 planets (the precise number isn't really an issue) orbiting a star or orbiting binary star system in a circumbinary fashion.

One of those planets would be a gas giant, orbiting in the habitable zone. I'm setting the world across two separate moons, both of which are orbiting this gas giant (although I appreciate there would likely be many more moons in this gas giant's system).

Now, I don't necessarily need everything to be 100% accurate in a physics sense (I appreciate that's probably impossible anyway), but I'd at least like to try and keep things sensible and create a fairly realistic, feasible system so that the idea doesn't become outlandish or ridiculous from a scientific point of view.

I guess it's easiest to post my "criteria" in terms of how I'm hoping my world will look and then if you learned guys have any major red flags or thoughts I'd love to hear them and it would really help the overall development of my World:

• A solar system (single star or binary) of between 3-6 planets (doesn't really matter but I'd like to have a firm idea of the total number of planets and keep it fairly small if possible).
• A gas giant somewhere in the inhabitable zone (approximately 1AU).
• At least two moons orbiting that gas giant - I presume there would be a lot more but two habitable moons "next" to each other and the other moons can be fairly arbitrary.
• Both moons to be around Earth size (I presume from a physics point of view they could not be smaller and habitable).
• I presume both would be tidally locked so I'd be hopefully looking for them to have orbits that give them a "day" similar to Earth - around 24-36 hours. This, I'm presuming, may be tricky, but ideally they can't have the issue of having light/dark periods on the far side being days at a time. I'm trying to keep the basics of the moons fairly similar to Earth so that a humanoid style life could realistically have evolved there.

I guess my questions are - are there any major physics problems that make that kind of scenario ridiculous and, if not, what might be the idiosyncrasies of those particular moons? I know there could be issues such as tidal heating but I'm hoping that it would ultimately be realistic to have two fairly Earth-like moons in orbit around a gas giant.

I also know that due to tidal locking one half of the moon would see a much more irregular day/night pattern and be subject to shine from the planet, which is fine so long as the other half can experience a relatively normal day/night pattern if possible.

I'm just not experienced enough in astrophysics to be able to begin working out issues related to axis, distance from the gas giant etc. and how they will impact on the overall system. Broadly speaking, I know what I want, and I just want to make sure it's at least partially feasible and how it might affect things like seasons, earthquakes/volcanoes, day cycles, weather etc. as best as possible.

The whole thing doesn't have to be completely watertight when it comes to the physics. I fully imagine there will always be a little bit of license, but I'd like to think I at least did some research and put some thought into it all before creating any arbitrary system that made no sense.

Any input, thoughts, critique, random observations from those who know a lot more about this would be very interesting and greatly appreciate! Thank you.

 

[phinds]

What do you mean when you say two moons "next to each other"? This could be a serious issue in terms of possible orbits.

 

[CordaHed]

Sorry phinds, I realized that was a bad way of phrasing it!

As in, if you have multiple moons in the planetary system, one of those moons would be the inner moon on an orbit closer to the planet and the other moon would be on the next orbit out - so not immediately next to each other on the same orbit but on adjacent orbits (in other words not separated by the orbits of one or more other moons). In other words they're in relatively close proximity to each other (analagous to, example, Io and Europa in the Jovian system).

Hope that clears it up!

 

[phinds]

OK, you should be able to make that part of it work at least. I have no idea whether they would necessarily be tidally locked as that's not something I've paid much attention to.

 

[Bandersnatch]

Why do you need them tidally locked anyway? They can be rotating at a similar rate to Earth and thus have similar day/night cycle lengths.

You can have the moons smaller than Earth, if you increase their density relative to our planet. Otherwise a smaller moon means lower gravity and that introduces lots of problems with atmosphere and Earth-like habitability.
Use the following simple formula for designing your moons:
$g=\rho R$
where:
g is the surface gravity as a fraction of Earth's; use 1 for exactly what we've got, or +/- maybe 10-20% if you want to experiment with different gravity. I.e., g=1.1 for 10% stronger gravity etc.
R is the radius as a fraction of Earth's
$\rho$ is the density as a fraction of Earth's

For example, a planet with twice the density $\rho=2$ and the same surface gravity as on Earth (g=1) would need to have $1=2R => R=1/2$ or half the Earth's radius.For moon placement, let's base it on Jupiter's system: http://en.wikipedia.org/wiki/Galilean_moons
Use the following simple formula:
$T^2=R^3/M$
where:
T is the orbital period as a fraction of one of the Moon's (let's use here and hereafter Io; so, 1.7 days means T=1, 3.4 days means T=2 and so on)
R is the orbital radius as a fraction of the selected Galilean satellite's
M is the mass of the gas giant as a fraction of Jupiter's mass

You can increase the mass of the gas giant by as much as about a factor of 10 (M=10) to allow for faster obits at the same orbital distance. More than that and the planet will start fusing hydrogen (will turn into a brown dwarf sub-stellar object).

Try not bringing the moons any closer than about 3-4 times the radius of the gas giant (you can treat it as approximately equal to Jupiter's radius regardless of mass). Any closer and tidal forces might break the moon apart.

Keep the moons reasonably spaced - maybe a 0.5 - 1 million km difference in orbital radii. This should make it somewhat more plausible to have two very massive moons in stable orbits. Throw in a half-arsed orbital resonance in there for extra plausibility - meaning, make one moon's orbital period a multiple of the other's. As in, for example, one does one orbit, the other does exactly 2 o 3 at the same time.
As a side effect of the resonance, the moons will return to the same configuration in the sky after every orbit of the outer one.

Don't put the moons farther than about 5 million km (i.e., more than 10 times the orbit of Io). You want them to stay firmly in the gas giant's gravitational well.Most of the numbers are approximates, and you could do with some more fiddling, but they should be good for you needs.

A word of advice - make yourself an excel spreadsheet and put it the equations in there. It'll calculate a range of values for your system.
Let us know if you should need a hand with that or if anything of the above needs a bit more explaining.

 

[CordaHed]

Thanks so much for your feedback/comments!

I presumed it was common for moons to become tidally locked to their planets within a few million years? Certainly before there was a serious chance of sentient life evolving at least?

 

[Bandersnatch]

I presumed it was common for moons to become tidally locked to their planets within a few million years? Certainly before there was a serious chance of sentient life evolving at least?

It's true, but I think you could get some leeway here by placing the moons in high-radii orbits, as the tidal-locking time scale is very strongly dependent on the distance from the primary. Also, dissipation factors for bodies other than the Moon are largely unknown, and there's some extra room to fiddle with in the initial angular momentum (initial rotation) of the moons. What I'm saying is, you could probably get away with it.

If you'd rather keep to the tidal lock, though, you'll end up having the day/night cycle lengths being very different between the two planets. These will be equal to the orbital period T you'll get from the above equations. You will not be able to have similar day lengths on both planets.

You could marry the two approaches, by having the closer planet tidally locked, and the farther one still rotating to produce similar day lengths on both planets.

 

[CordaHed]

Thanks again for all this great help! I don't need to be too scientific about everything but those equations will really help and it's just good to know I'd be creating a system that wasn't completely incongruent with physical law.

That's interesting regarding the tidal locking issue - some flexibility with that would be welcome given the problem you highlighted with vast differences between day and night on both moons. Although technically speaking the moons do not need to be especially similar it would probably be silly to have one moon with a day around 24-30 hours and another with a day that lasted for a week or more (as well as not entirely congruent with the idea of sentient life similar to ours evolving).

I quite like the idea of a tidal lock affecting the innermost moon, with the gas giant obscuring the sun partially or completely for a few hours every day. My inkling was to have a 'day' of around 30 hours, approximately 15 hours of daylight and 15 hours of night, with an additional 2-3 hour period of darkness in the late morning/early afternoon as the star passed behind the gas giant. I also quite like the idea that one half of the moon would be unaware of the gas giant in the night sky, which could help inform mythology and religion.

With the outermost moon not tidally locked I'm guessing I could have a day of around similar time (22-30 hours) and place it on an orbit that would mean the star was only partially obscured in daylight, giving the the effect of a partial eclipse each day.

 

[Bandersnatch]

My inkling was to have a 'day' of around 30 hours, approximately 15 hours of daylight and 15 hours of night, with an additional 2-3 hour period of darkness in the late morning/early afternoon as the star passed behind the gas giant.

That sounds about right. A bit too high.
30 hours for a 1 Jupiter masses gas giant would place the moon at a distance roughly corresponding to where our Moon is. From such distance, the gas giant would look 20 times larger (diameter-wise) than the Moon looks from Earth. It would take about 50 minutes for the star to pass behind the disc of the gas giant.
You could 'puff-up' the giant by about 50% (largest discovered is 70% larger than Jupiter) to push it to about an hour and a half, but not more.

This is assuming the moon orbits in the same plane as the gas giant orbits the star - a rather unlikely occurrence, but it could happen. If you were, however, to make it more inclined, the eclipses could become more of a seasonal event. Twice a year for a few days they'd take the full hour/hour and a half, getting shorter on the tail ends, an be non-existent for the reminder of the year.

 

[Czcibor]

Try not bringing the moons any closer than about 3-4 times the radius of the gas giant (you can treat it as approximately equal to Jupiter's radius regardless of mass).

I think the gas planet should be much bigger (diameter) than Jupiter. Wiki:

Despite this, Jupiter still radiates more heat than it receives from the Sun; the amount of heat produced inside the planet is similar to the total solar radiation it receives.[29] This additional heat radiation is generated by the Kelvin–Helmholtz mechanism through contraction. This process results in the planet shrinking by about 2 cm each year.[30] When it was first formed, Jupiter was much hotter and was about twice its current diameter.[31]

http://en.wikipedia.org/wiki/Jupiter#Mass_and_size

This planet receives lots of heat (yeah, habitable zone) from its mother star so it should not shrink so much.

That's interesting regarding the tidal locking issue - some flexibility with that would be welcome given the problem you highlighted with vast differences between day and night on both moons. Although technically speaking the moons do not need to be especially similar it would probably be silly to have one moon with a day around 24-30 hours and another with a day that lasted for a week or more (as well as not entirely congruent with the idea of sentient life similar to ours evolving).

Why would it be a so big problem for life similar to our?

Just living at interior of continents would be a challenging idea. (can be partially moderated by water bodies and dense atmosphere)

With the outermost moon not tidally locked I'm guessing I could have a day of around similar time (22-30 hours) and place it on an orbit that would mean the star was only partially obscured in daylight, giving the the effect of a partial eclipse each day.

If you put it on not locked orbit, then it should be really far away. So realistically eclipse would be rare.

EDIT: Planet should have formed in a cooler place and later migrate inward. It implies that satellites actually should have lots of water / volatiles, unless they've lost if later. (loss through tidal heating is somewhat likely for the more inward planet)

 

[Durakken]

Earth-sized moons around a gas giant in the habitable zone of a star being "habitable" doesn't work.

Firstly, you need to move the gas Giant out as the Gas Giant produces heat and such as well.
Secondly, the moons are likely going to be more volcanic and have tons of earthquakes due to it's proximity to the Gas Giant
Thirdly, the moons are not going to have anywhere near similar year to Earth...

I don't have the right words to quite describe the problem... What you have to understand is that a day/year is going to be really weird, because the moon going around the planet and it being tidally locked (just to make it easier) will result in something like...
midnight = all dark
midnight to 6 am = You have the sun coming over the horizon to the point of twilight
6am to noon = farside: similar to Earth day / nearside: twilight reverses and the sun recedes.
noon = farside: all light / nearside: all dark
noon to 6pm = farside: similar to Earth day/ nearside: the sun comes over the horizone on the other side
noon to 6pm = farside: similar to Earth day/ nearside: twilight reverses and the sun recedes.

If it's not tidally locked it's even more crazy as what is and isn't farside/nearside is different.
This is assuming a pretty close orbit too. I doubt you'd get such a close orbit and you want 2 moons fairly close but small differences in orbits can still result in large differences in speeds going around the planet/star.

As far as the seasons go... I have no idea how that would work itself out because you didn't mention the tilt of the moon which is what determines seasons, but also because the heat the gas giant and the tectonic plates could make it so there are no seasons at all...

 

[CordaHed]

Thanks for your input! So you don't think it would be possible to have, for example, a gas giant roughly the same as Jupiter approximately 1.3AU from a Sun fairly similar to our own?

Here's what I have been tinkering with as a basic idea/premise, so I can get critique. A gas giant approximately 152,000km, orbiting approximately 1.3AU away from a Sun that's essentially the same as ours (say pretty much identical mass), with a near identical mass to Jupiter. I'm calculating that would give the gas giant an orbital period of about 550 days, give or take.

Let's say the main moon had a mass similar to Earth but a diameter slightly smaller, around 10,000km, and that it orbited around 400,000km from the gas giant. I'm calculating it would have an orbital period of about 1.6 Earth Days (and an identical rotation period presuming tidal locking).

The link below is to a rough (apologies for the low quality) video mockup of what a day cycle might look like nearside. The parameters are not identical - the gas giant is about 154,000km and the distance between the moon and the planet is around 460,000km, so the planet would appear slightly bigger in the sky on my 400,000km moon compared to this. The sun would also be bigger - the sun here is about 3 times smaller than my envisioned sun, but around twice as far away as depicted here, so all in all it would be slightly bigger in the night sky. The moon here has an axial tilt of about 92 degrees.



From the position of the camera here, I'm calculating you'd have, from the nearside perspective, broadly speaking a normal day cycle of about 19 hours sunlight and 19 hours, with a period of darkness in the day as the sun dips behind the planet lasting somewhere around an hour, give or take (and depending on your exact position on the moon). If that's the case, that would be fine with me - I'm not necessarily looking for something that similar to an Earth Day, just so long as I don't end up with a day/night cycle lasting days or more - but if there's irregularity or a mildly longer day/night cycle that's fine with me - I can essentially "bump up" the sleeping patterns of my humanoids to sync with that, so they're just sleeping a little longer and staying awake a little longer.

Now, ultimately I think I'm going to want and need some artistic license in terms of making this moon fairly Earth-like, as you've pointed out. Increased volcanic activity on the moon is fine but I don't want it to be extreme - ultimately I don't think I'm ever going to get something that seamlessly balances with the laws of physics for reasons you've pointed out, but as long as there is some nod to physical laws and the major elements of the moon are couched a little in reality, I'm OK if I have to bend some rules as I'll never need to go into much detail about them. It's a medieval inspired fantasy world so the astronomy will be in its infancy - I'd like it to have some nod to realistic day/night cycles and seasons but if I'm doing a bit of rule-flexing it's not going to matter too much - a la Pandora in Avatar or something (but with a little more detail and thought gone into it).

That having been said, the more I can make it realistic, the better, without changing the world into something unrecognisable I guess!

 

[Durakken]

Well, you could download Unity 3D and program in a decent model if you really wanted to see what it would work like... that's probably the easiest way to see. But an idea on how to get it more earth-like might have it so that the orbit around the planet by the moons is Perpendicular to the orbit around the star. You could then make the moons orbit further out and make the orbit around the planet to last a pretty long time which would probably give seasons similar to earth. How realistic this is to happen I have no clue, but Neptune is tipped on its side like this, but I don't know about the moons surrounding it.

 

[CordaHed]

Thanks, Durakken! That's my plan eventually - to model the system in an engine and see how it works. But it's really helpful having more knowledgeable people on this subject giving me a bit of warning on what to look out for.

Incidentally that video was made on a free piece of software called Space Engine, if anybody is interested. It's not customisable but it's a really cool and well thought out way to navigate around the known and unknown universe and see what you come up with!

 

[Bandersnatch]

I don't agree with @Durakken on most of the points he made.

The heat from the gas giant is of no consequence, as it just changes the habitable distance (by not much at all), not habitability as such.
Volcanism is going to be an issue only if the moon is subject to changing tidal forces such as Io is.

I don't know what he means by year/day not being similar. A tidally locked moon will have days just like Earth does, with the period equal to its revolution period. Seasons likewise are not going to differ, as long as the axis of inclination is kept similar to Earth's. But you've found out that yourself as I can glimpse from your mockup (thanks for mentioning the Space Engine, I've never heard of it and it looks useful) and calculations.

The perpendicular orbit of moons is most certainly a bad idea - these are unstable.

 

[Durakken]

The heat from the gas giant is of no consequence, as it just changes the habitable distance (by not much at all), not habitability as such.
Volcanism is going to be an issue only if the moon is subject to changing tidal forces such as Io is.

Cumulative heat would make the moon uninhabitable, that's why you need to back the planet out of the habitable zone... it would have to be balanced with the distance of the moons to the planet too.

I don't know what he means by year/day not being similar. A tidally locked moon will have days just like Earth does, with the period equal to its revolution period. Seasons likewise are not going to differ, as long as the axis of inclination is kept similar to Earth's. But you've found out that yourself as I can glimpse from your mockup (thanks for mentioning the Space Engine, I've never heard of it and it looks useful) and calculations.

The rotation of the moon and the revolution of the planet cannot be balanced to be close to Earth's 24 hour day, 365 day year.
Likewise trying to get anything like Earth climate while trying to produce the same 4 seasons will not work, even more so if the perpendicular set up isn't followed as the sunlight hitting the moon would be different. You might get similar some places and not others though. I'm just saying that you're not going to get the north and south having opposite seasons in a continuous order of Winter > Spring > Summer > Fall > Repeat

 

[Bandersnatch]

The habitable zone for the Sun extends from about 0.95 to 1.65 AU according to this calculator:
http://depts.washington.edu/naivpl/sites/default/files/index.shtml
(the paper it's based on by Kopparapu et al. linked at the bottom of the page)

The wattage received from a Jupiter-like gas giant is so low (1/14th of the insolation at 1AU), that all you need to do to get exactly the same energy balance as Earth's is to push the orbit back to 1.03 AU.

This is most definitely not pushing it away from the habitable zone.

The rotation of the moon and the revolution of the planet cannot be balanced to be close to Earth's 24 hour day, 365 day year.

I have no qualms with this. Although the 38h/500days setup the OP came up with is rather close.
I have issue with your description in post #11 - that the sun would dance a crazy dance on the sky. It would move just like it does here, with days just as we've got here, only longer - as can be seen in the visualisation the OP provided.

Likewise trying to get anything like Earth climate while trying to produce the same 4 seasons will not work,

Why would that be? The inclination of the rotation axis (in the case of the non-tidally locked outer moon) would produce exactly the same seasonal variation, providing the orbit around the giant is coplanar with the ecliptic.
With the inner, synchronous moon, the seasons could only be achieved by having the orbit inclined to the ecliptic. This achieves exactly the same effect of having the northern hemisphere more exposed to sunlight for half a year than the southern one.

 

[Durakken]

The reason you seem to not see a problem with the seasons is because it seems like you're not taking into account that the big planet in the way.
Unlike here on Earth where the Sun/moon are far enough away/small enough to not block a significant amount of light and the moon just happening to be always on the the night side, on this fictional world every revolution around the planet the moon will be completely over shadowed by the planet giving it that wonky day pattern that i described.

Perhaps the moon is out far enough for this not to happen, but I'm not sure that's possible or probable... and even if it were the less stable the moons would be in their orbits as the farther they are from the center of the gravity well the less stable their orbits become... and that's ignoring the second planet that would likely push the other farther in, if not block out light from time to time as well causing all sorts of weird day night cycles.

 

[Bandersnatch]

As detailed in earlier posts in this thread, the eclipses in the scenario discussed take only 2 hours of the 38h day of the inner moon, assuming its orbit is coplanar with the ecliptic. If it isn't, then the eclipses are reduced to rare occurrences similar to what we get on Earth.

 

[CordaHed]

You make a good point about the perpendicular orbit. Unfortunately that's just the way this moon was programmed in Space Engine and to my knowledge that can't be changed (I'll check that though).

I'll probably alter the moon's orbit to make it more realistically stable. This would affect the day/night and probably mean eclipses were rarer, as you say, although I'm quite happy to have the eclipses happen fairly often, even daily if needs be, as this interrupted day/night cycle would be an interesting peculiarity for the world itself (at least on the nearside of the moon). I'll see if I can mock that up and see what we get.

Seasons are less of an issue for me. I'm guessing (?) that if I wanted fairly recognisable seasonal patterns I could just put the gas giant on an elliptical orbit that pushed it further back from the star for a section of its orbital period, or else I could put the moon on an axis similar to Earths?

I may be wrong but I'm guessing the planet's effect on the overall temperature of the moon would be fairly negligible? If You have approximately 18 hours of daylight and 20 hours of darkness (18 hour night and around 2 hours eclipse) I'm imagining the nearside may be overall marginally cooler?

 

[snorkack]

Seasons are less of an issue for me. I'm guessing (?) that if I wanted fairly recognisable seasonal patterns I could just put the gas giant on an elliptical orbit that pushed it further back from the star for a section of its orbital period, or else I could put the moon on an axis similar to Earths?

Just put the axes of gas giant rotation, moon orbit and moon rotation on a suitable angle to gas giant orbit. There is nothing improbable about presence of earthlike seasons on a gas giant: the axial tilts in Solar System are Earth 23,45 degrees, Mars 25,19, Saturn 26,73, Neptune 28,33. On the other hand, there is nothing improbable about lack of seasons either: Jupiter 3,12 degrees, Venus 2,64 degrees.

I may be wrong but I'm guessing the planet's effect on the overall temperature of the moon would be fairly negligible? If You have approximately 18 hours of daylight and 20 hours of darkness (18 hour night and around 2 hours eclipse) I'm imagining the nearside may be overall marginally cooler?

Yes, and coolest in the dead middle of near side.
The gas giant hangs immovable in sky, basically like a geostationary satellite. The duration of day during equinoxes is constant over the length of the nearside equator that sees the whole disc of giant - but the middle of the near side will miss the heat of the noon sun normal to ground, while the edges of near side equator are eclipsed of morning or evening slanting rays.

 

[Czcibor]

As detailed in earlier posts in this thread, the eclipses in the scenario discussed take only 2 hours of the 38h day of the inner moon, assuming its orbit is coplanar with the ecliptic. If it isn't, then the eclipses are reduced to rare occurrences similar to what we get on Earth.

2 hours of the highest luminosity out of 19 (assuming everything being coplanar)

EDIT: so something like 10,5% of light less, so on equator it would get as much light on equator of eclipsed side on one side as on 26th parallel of the other side. (assuming that I haven't forgot the basic trigonometry that I had)

 

[snorkack]

2 hours of the highest luminosity out of 19 (assuming everything being coplanar)

EDIT: so something like 10,5% of light less, so on equator it would get as much light on equator of eclipsed side on one side as on 26th parallel of the other side. (assuming that I haven't forgot the basic trigonometry that I had)

You did forget integration. 10,5% time, but these are 10,5% of highest luminosity, so rather more than 10,5% light less.
For example, Jupiter has Io at 42 hours orbit and then Thebe at 16 hours orbit.
Suppose Jupiter sized planet had a satellite at 24 hour orbit. By my estimate, the orbital distance should be 290 000 km, and Jupiter should span 28 degrees of sky along equator. Meaning that daily eclipse (assuming no inclination) should last 1:52 - about 1,86 hours out of 12 hours daytime being 15,5% time and a bigger share of light.
A satellite at 8 times the orbital period - 8 days, slightly longer than Ganymede - would see Jupiter span 7 degrees of sky. An eclipse would last about 3,7 hours, out of 96 hours daytime.