Understanding orbital characteristics of a moon of a gas giant

Kirshy

Hi,

I am doing research for a story and would like to set it on a habitable moon in orbit around a gas giant. I've done a bit of research on this and understand that the moon would likely be tidally locked, so that only one face of the Moon would ever face the gas giant. I understand that axial tilt affects the seasons more than distance from the sun, and that's about it. I'm having trouble finding the information I want and am hoping that someone on here might be willing to take some time to answer a few questions.

I'm thinking the easiest solution to figuring some of my questions will be to use Jupiter or Saturn as the basis for the gas giant in my story but transplant it to a fictional solar system and place them in a closer orbit to the star. With that in mind, here are my questions.

Question 1: What distance from the sun would the gas giant need to be orbiting in order for one of its Moons to be within the goldielocks zone? Would the gas giant itself generate enough friction and heat to extend that range?

Question 2: What type of tidal/gravitational effects would the gas giant and other moons orbiting the gas giant have on the Moon in question?

Question 3: What would the day/night/year/season cycle be like on a Moon like this. Would you count its year from its orbit around the gas giant or the gas giants orbit around the sun. How long would the days be? How much light would it get? It is difficult to conceptualize how this would work.

Question 4: Would both sides of the Moon get equal daylight? How would this work?

Question 5: What would gravity be like on the Moon? Would the moon need to be the same size as Earth to have similar gravity?

I want the Moon to be Earth-like. Similar gravity and atmosphere, but still alien. If there is anyone out there willing to help, I would greatly appreciate it. I look forward to hearing from you.

Thanks.

Simon Bridge

See wikipedia for relying on the star alone. You can get tidal heating (qv. Io) as well, yes.Depends on the mass of the Gas Giant and the size of the moon. If you pick the Saturn or Jovian system just googling will give you lots of information on particular Moons to extrapolate from.You'll have to decide what would be important to the inhabitants. Certainly the orbit about the giant would be important to them (eg. the moon will likely pass through the giant's shadow regularly) but the orbit about the star would contribute to the overall seasons.

On Earth - the solar and lunar periods had differing importance - to figure out what people would use, you should research the history of the calendar.

The actual time periods are fairly straight forward to calculate from the orbital equations.Depends on the distance from the star, the inclination of it's orbit about the giant, and how reflective the giant is. The Moon is tide-locked to the Earth but both "sides" get about the same light because, as it goes around the Earth, the Moon rotates wrt the Sun. This is why the Moon has phases.Depends what it is made out of.You mostly want good gravity to keep the atmosphere in place ... though, see Titan and Niven's "Smoke Ring" for alternatives.

The most useful resource I've seen for this sort of writing is actually GURPS: Space - it has reasonable tables and rule-of-thumb equations for most of the stuff you want to know. You do not need the rest of the system to use the data.

Kirshy

Thanks Simon, this is super helpful. I'll check into the links you provided and see if I can't figure this out.

onomatomanic

True for Earth, not necessarily true for planets in general, and likely nothing that simple can be said about seasons on a moon.

It could, but you probably don't want it to: If the moon has a surface structure similar to Earth, which is the only obvious way to get anything like Earth-like surface conditions, then non-negligible tidal heating implies continual non-negligible deformations of that surface. In other words, the world would be subject to tremendous earthquakes, order of magnitude more extreme than those we get on Earth.

Those can get really complicated, but they don't have to. In the simplest case, once the moon is tidally locked and the orbit has circularized, with no other major moons close-by, the planet would have no variable effect at all, and the Sun and the far-away major moons will cause variable tidal stresses of a magnitude similar to those on Earth. Anything much bigger than that is trouble, per the above, so that's probably the case you want anyway. As on Earth, those stresses would principally register as ocean tides - if there are oceans, that is. Ground and air tides don't really register at that point, by comparison.

I can't improve much on Simon's answer on that point. You can pretty much pick and choose the values you want for those, and then work backwards to figure out the orbital data. Seems counterintuitive, but picking the orbital data arbitrarily as likely as not leaves you with a moon that's not very well suited for life, despite being roughly at the right distance from the Sun.

One interesting and not immediately obvious circumstance here is that if civilizations evolve on this moon similar to the way the human ones did on Earth, then those on the far side (as seen from the planet) will never even know that the planet exists until their "Columbus" discovers it in the skies above their "America". Not knowing about it, their cosmological models and religions and calendars created before that time thus won't take the planet into account in any way.

If there are other major moons nearby, I guess they ought to in principle be able to figure things out, but the mental leap required might well be too vast, and they'd end up explaining all celestial motions with some silly epicycles-upon-epicycles model even so.

Probably, the far side will get more insolation and be noticably warmer. The reasoning goes like this: If the moon is tidally locked, then the length of the day is determined by the orbital period about the planet. The day can't be too long, otherwise temperatures get too hot during the day and too cold during the night. A relatively short day requires a relatively tight orbit. That, in turn, means that the planet subtends quite a big part of the sky, like several tens of degrees. If no major upheavals intervened, which they can't have for evolution to have taken place at an Earth-like pace, the orbital inclination can't be large enough to move the moon out of the shadow cone cast by the planet, as it passes behind it. Thus, the near side will experience a total eclipse lasting a non-negligible fraction of every day, in addition to experiencing the ordinary night as the moon passes in front of the planet. Thus, less insolation is received here over the course of a full orbit. Thus, lower temperatures.

Earth is pretty dense, for a rocky body. So, you can't really make the moon much smaller without reducing gravity. You can make it a bit bigger by changing the composition to one that has more light and less heavy elements; however, that automatically means a metal-poor world, which would impact the post-paleolithic development of indigenous cultures.

Czcibor

Realistically you would have a longer day. Io orbits Jupiter in is 1,77 Earth days long and has terrible volcanoes because of tidal heating. Presumably realistic day for habitable moon would be longer... which would cause awful temperature changes between day and night.

Seasons? You have your moon tidally locked, thus they are the same as on the planet. It all depends on axial tilt. You might have them but you don't have to.

Assuming that moon orbit is coplanar with planet and the star (no seasons), and we use Io and Jupiter as example. Jupiter equatorial radius 71 492 km, Io orbit radius 670 900 km. We assume that star that provides light is a point that is infinitely far. I calculate in degrees (90 - arccos(71492/670 900))*2=12,3 degrees. So under perfect conditions the side facing its planet would be in shadow during its midday for 6,7% of day. Matters a lot...

... as long as we don't assume that everything is tilted. If its tilted by more than mentioned 12 degrees, then we get a moon that is rarely eclipsed. Earth is tilted by 23 degrees.

So effectively you have to choose between seasons or one side less heated than the other.

EDIT:
The moon must have almost perfectly circular orbit, however that's not required for the gas giant. It can have elliptical orbit what would cause something like seasons for its moon anyway.

EDIT2:
A question that you haven't raised but I think that's interesting - the color of the planet:
http://en.wikipedia.org/wiki/Sudarsk...:_Water_clouds

Kirshy

All of these links and replies have been a great help, and given me a lot to think about. Is there anyway you guys could provide me with the formulas I will need to figure this stuff out? Namely distance from the planet to the sun, orbital radius of the moon, and then I will need to figure out orbital time, and how to figure out how often the moon would be eclipsed by the planet and such.

onomatomanic

Formulae only turn values into other values. As in, v = d/t only gives you a speed v if you know the distance d and the time t already; otherwise, it's nor very useful, except in the conceptual sense. That's behind what we've been saying above: First of all, you need to make up some values to begin with. For example, turn the general statement "I want the Moon to be Earth-like" into a concrete temperature range. How cold is it allowed to get during the night, and how hot during the day? Et cetera.

Kirshy

Fair enough. Lets keeps this simple. We'll make the moon in question have the same mass, density, and volume as Earth, and hopefully the same gravity. Temperatures about the same as Earth, but probably 5-10 degrees Celsius warmer on the hot side, and 5-10 degrees Celsius cooler on the cool side. Mean temperature of 25 degrees Celsius, max temp of 65 degrees Celsius, lowest temp -50 degrees Celsius. We established earlier in the thread that because it was tidally locked one side would be warmer than the other by some margin, I hope that is enough. I want the world to be about 80% water with one super continent and several micro-continents and many volcanic archipelagos scattered throughout the vast oceans.

I like that Jupiter has two inner moons, Io and Europa, and would want something similar for my world. I think it would influence the culture that faces the gas giant. And at least one additional moon further out from my Ganymede that is visible to those on the outward facing side. Czcibor mentioned the colour of the gas giant. I didn't fully understand the article but again for arguments sake lets make it a Class I gas giant like Jupiter and Saturn.

If we make the star that this gas giant orbits the same as our Sun, then I believe the orbit would have to be within 3AU. Do we use the numbers above to figure this distance out or is this something I can state here?

I would think that in order for the gas giant to have a moon the size of Earth it would need to be bigger too. How much bigger? Ganymede is several times smaller than Earth in volume, mass, and surface area. So how do I figure this out? Or am I wrong about this? Can we say for now that the gas giant is twice the size of Jupiter and the orbit of my Ganymede is 16 days. Will that give us all the information we need?

Then the other thing to figure out is how often my Ganymede will be eclipsed by its parent planet, and how long those eclipse periods will last.

Kirshy

16 days might be too long an orbit to make it habitable. But until I know how big the gas giant should be I won't be able to get this information.

Czcibor

That's a bit too harsh to call it inhabitable...

Oceans would remain habitable. :D However, on the land you would have a hot day in the Arabic Peninsula (for Americans: Death Valley) during a day, and a cold day on Greenland during a night. (approximation, I'm curious whether anyone can give exact numbers? Maybe some papers concerning climate on tidally locked planets can be used as general idea?)

Land flora would be either primitive (lichens), very durable for temperature changes (something like conifers) or able to fold back their leaves for night (and maybe also for midday).

Land fauna would be able to hide in water or in holes for night (and midday).

The best place for any land life would be places next to big water reservoirs which would mitigate such violent weather.

The situation can be partially saved by already mentioned high water cover and maybe some very dense atmosphere. That should spread the heat around a bit.

Any intelligent specie that lives inland should occupy caves.

Executive summary: if the moon is supposed to have temperature that should make it habitable, the planet should absorb enough heat to have water clouds, thus the planet would look white. Just a color.


EDIT: Assuming that the star is supposed to be as big as the Sun, than proper orbit radius is somewhere around 1 AU for a habitable planet. (tidal heating should be a minor source of heat)

You don't need a bigger gas giant. (actually you wouldn't have a planet with much bigger diameter than Jupiter as such, because more massive planet would be simply denser) You might have the gas giant heavier or lighter, pending what you like, it would not be a problem to move it in any way.

Kirshy

Thanks Czcibor. But that is not the kind of world I was hoping to build :P

I would hoping it would be warmer, more of a jungle world. I know that no world is just one type of climate though despite what Star Wars has taught us. But because I want the planet to have one large super continent and that continent would stretch horizontally across the equator it would be mostly the same climate so it could support a large homogenous forest. To get those kinds of temperatures it would need a closer orbit to the gas giant parent?

Czcibor

Exactly. However, if the orbit is too close you will get very active volcanism.

Kirshy

A little active volcanism might be fun.

So if the Moon orbit the gas giant every 7 days. Sits about 1.6 AU from a star like our sun. Can I safely assume describe it as a warm garden world. Filled with jungle and temperatures similar to a South American rain forest?

How do I figure out Year Length, season length, and how often there would be an eclipse and for how long the eclipse would last?

Czcibor

Year lenght:

What about:
http://en.wikipedia.org/wiki/Kepler'...tion#Third_law
If you have Sun sized star - distance in AU ^ 1.5 *365,25 days

So 739,2 days.


You want usual seasons caused by axial tilt or often eclipses?

First I wanted to say that with 7 days long day and 1.6 AU from its Sun-like star, you are going to get a cold planet that's friendly only during those long days. However, when I thought for a while... it might work, but with very dense atmosphere that would distribute the heat more equally and with very strong greenhouse effect that would make the planet warmer during nights.

There would be some side effects of very dense atmosphere. Like for example water boiling in round 150 Celsius degrees. (5 atm)

onomatomanic

Sorry, I lost track of this thread.

1) To get a rough estimate of how much the day-night temperature gradient changes with day-length, we need an estimate of the equilibrium difference, that is to say, the difference between dayside temperatures and nightside temperatures if Earth were tidally locked to the Sun. The former would theoretically be above 400 Kelvin; practically, it seems unlikely that it would exceed actually exceed 100 Celsius, since cloud formation due to the massively increased evaporation of water would have the effect of reflecting much of the sunlight straight back into space before it gets to that. The latter should be in the same region as polar winters in the real world, 200 Kelvin (there are various major differences, of course, but some would act to increase and some to decrease this value, therefore the result shouldn't be far off). So, let's call that a 150 Kelvin gap.

2) The typical difference between day and night for a 24-hour day is perhaps a tenth of that, 15 Kelvin.

To a good approximation, a thermal effect of this kind can be modelled as an asymptotic exponential of the form a*(1-r^t), where a is the asymptotic value, t the time variable, and r the rate of approach. We know a from (1), and can find r by requiring that the expression works for (2). Thus, the day-night temperature difference DT is given by

DT ~ (150 K)*(1-0.9^(t in days))

DT ~ 15 K for t ~ 1 day
DT ~ 50 K for t ~ 4 days
DT ~ 80 K for t ~ 7 days
DT ~ 120 K for t ~ 16 days

Habitability becomes problematic if night frost is a global phenomenon, I suspect, and for a mean temperature of 25 Celsius, that means we need a DT of below 50 Kelvin and thus a day-length of 4 Earth-days at most. A DT in the region of 100 Kelvin, such as in the 7 days and 16 days cases, does not seem remotely feasible to me.

What do you think?

Czcibor

I wanted to whine that 100 C is too hot, however after reading:

"Extraordinary climates of Earth-like planets : three-dimensional climate simulations at extreme obliquity"

Where they reached in worst conditions round 80-90, that's possible guess.

So I would ask the following question - how to modify the formula what you brought here (BTW: thanks!) to take in to account denser atmosphere?

onomatomanic

Well, the formula would still be the same, you'd just have to find a new way of calibrating it. The easy way to do that would be to look at typical temperatures for a real planet with the appropriate conditions, just as I looked at Earth. Unfortunately, there isn't any such planet, that I can think of. Venus' day is far too long to be of any use, and Titan doesn't seem to get enough sunlight for day and night to register much.

The hard way to do that would be to look at the physics involved and try to estimate how the thermal properties of the atmosphere (primarily, heat flow, secondarily, heat buffering) would increase with density. Can't help you there myself, but if you want to invest the necessary research, this should be tractable even without much in the way of a physics background.

As a compromise, you might try to estimate daytime and nighttime temperature on a waterworld. Looking at the differences between continental and ocean climates, and at the differences in the temperature gradients between equator and pole for our atmosphere on the one hand and our oceans on the other hand, should be sufficient to get a handle on that. A dense atmosphere would then be somewhere between an Earth-like atmosphere and a liquid like water. If you get somewhere with that and post it here, I'll be happy to provide feedback, at least.