Questions about a habitable second moon

[LadiSilverfox]

Good afternoon,
I am working on writing a story that is set on a habitable second Moon. I suppose I could easily say it's a mild planet that splits into three main seasons and make up some story about how the first Moon appears every so often for a month of phases and then vanishes. As a fantasy setting most people probably won't question too much. But that just doesn't work for me, however, I am not good at the planetary maths needed to figure out all the details. If someone were willing to help me run out scenarios to get something reasonable and still scientifically possible I would be much appreciative.
Currently, I have the following:

• Sun is either G or F white
  [*]Planet {Uranus Sized-Silicate Planet} - Volcanically active/Not life supporting
  [*]Moon 1 {Mercury Sized} - moves roughly twice as fast as Moon 2 - Not life supporting
  [*]Moon 2 {Mars Sized} - Life on this World
  

My list of questions so far has come to:

• What seasons does Moon 2 typically experience (mild-heavy)?
  [*]How does the shadow of the Planet affect the seasons?
  [*]How often does Moon 2 end up in the shadow of the Planet?
  [*]If Moon 1 travels at twice the speed around the Planet as Moon 2, how often and in what phases does Moon 2 see Moon 1?
  [*]How often does Moon 2 experience an Eclipse by Moon 1, both in and out of the shadow of the Planet?
  [*]How many hours in a typical day for Moon 2?
  [*]How many days in a typical year for Moon 2?
  [*]How are the tides changed by the gravitational pull of the Planet / at what distance from the planet would it be safe to live near the shores on Moon 2 while maintaining its orbit?
  [*]How would the tides change when adding the gravitational pull of Moon 1 to Moon 2?
  [*]How far is the Planet from the Sun? And at that distance, once the Volcanic activity settles down could it ever support life?
  

Thank you so much for your time and help. :)

 

[DaveC426913]

Don't you kind of need to tell us the size and orbits of these moons before we can answer any of these questions?

Or are you trying to retrofit the mechanics so they match the events you want in your story?That being said, some of your questions don't make sense.

• Moon 2 has no details that indicate what kind of seasons it might have. Earth seasons have to do with axial tilt. You might have seasons generated by an elliptical orbit.
• There is no reason the shadow of the planet would have any effect on the seasons. Eclipses last hours, not months.
• No way to determine how often moons are in shadow without first determining their orbital characteristics.

 

[LadiSilverfox]

I did give rough sizes of the moons by mentioning planets in our solar system I imagine as similar sizes. But I am not sure what the orbit patterns/size needs to be or even what axis angle they need to be on to have life supported on the second Moon.

 

[DaveC426913]

OK, so which way do you want to build it? Do you want to pick the orbital mechanics and see how it affects your climate? Or do you want to start with your climate and coax your moons into an arrangement that models that?

 

[LadiSilverfox]

Ideally, I think I would like to aim for a climate and coax the moons into an arrangement to fit. I think I was concerned doing that would make for something really unreasonable/unbelievable which is why I started looking into orbital mechanics.

I was thinking of something that had Earth-like qualities. Jungly-hot along the equator, moving to more moderate as you get away from the center, and cold at the poles.
Thank you so much for all your guidance.

 

[DaveC426913]

Moon 1 {Mercury Sized} - moves roughly twice as fast as Moon 2 - Not life supporting

OK, this at least tells us that Moon 1 is the inner moon and Moon 2 is the outer moon.

• What seasons does Moon 2 typically experience (mild-heavy)?

Unknown at this time.

• How does the shadow of the Planet affect the seasons?

No reason why it would.

• How often does Moon 2 end up in the shadow of the Planet?

Depends entirely on its distance and angle of inclination to the system plane.

• If Moon 1 travels at twice the speed around the Planet as Moon 2, how often and in what phases does Moon 2 see Moon 1?

Tricky.

• How often does Moon 2 experience an Eclipse by Moon 1, both in and out of the shadow of the Planet?

It surely won't. Moon1 is almost certainly too small to eclipse the star. What you will get is a transit. Venus occasionally transit the sun, but you need a telescope to see it.

You could arrange it so that Moon 1 eclipses the star but it would be quite contrived and it would constrain a lot parameters.

• How many hours in a typical day for Moon 2?

Unspecified, Whatever you want.

• How many days in a typical year for Moon 2?

This will fall out when we set the orbital radii.

• How are the tides changed by the gravitational pull of the Planet / at what distance from the planet would it be safe to live near the shores on Moon 2 while maintaining its orbit?

It could be very large, it could be small. Would need to define more details.

• How would the tides change when adding the gravitational pull of Moon 1 to Moon 2?

It will have the effect of making the tides smaller.

• How far is the Planet from the Sun? And at that distance, once the Volcanic activity settles down could it ever support life?

Not a lot of constraint on this. Got to be large enough that the orbits two moons aren't destabilized.

 

[LadiSilverfox]

What if I was thinking 16 months with 32 hour days for Moon 2? Would that help?

 

[DaveC426913]

Clarifying Question: When you say M1 moves "twice as fast as" M2, do you mean velocity? Or do you mean period?

Period is how fast it completes one orbit of the planet. Velocity is less useful a measurement.

 

[LadiSilverfox]

Velocity.

But if Period is more useful, I am willing to alter terms. My brain and science, as much as I love it don't always meet in the middle.

 

[DaveC426913]

Velocity.

OK, that's not all that useful to observers*, but it's easier to calculate.
* because it would have to be calculated not observedWith a doubled orbital speed, M2's orbital radius will be root 2 larger than M1's.

So, if M1's radius were, say, 200,000km, then M2's radius would be 288,000km.

 

[DaveC426913]

As to setting the orbital radii, might start with how large you want the primary to be in the sky.

Can't fill the sky because the two moons need to be stable, so they can't be too close. (Esp. since the inhabitants are on the outer moon)

 

[LadiSilverfox]

Oh, definitely not too close. If it makes sense, about 8% bigger than what we see the Full Moon as? Like a Supermoon.

 

[DaveC426913]

Hm. OK.
Uranus has a diameter of 50,700 km.

To appear 8% larger than our Moon, P would have to be 5.2 million km distant from M2. That's about 18 times the Earth-Moon distance.

M1 would then have an orbital radius of 3.7 million km.

https://www.omnicalculator.com/math/arc-length

 

[DaveC426913]

You say P1 is silicate. i.e. not a gas giant. So I cant use Uranus numbers.

So you'll have to establish its mass or its density in order to work out orbital periods.

Uranus density is 1.27g/cm³
Earth is 5.5g/cm³

 

[LadiSilverfox]

Okay, I think... 9.196g/cm³

If I used this site resource correctly. https://rechneronline.de/planets//density.php
I put the diameter of Uranus, 50,700 km, under Kilogram per cubic meter. And then looked at what the density of Earth would be because Earth is a silicate.
Or am I just confusing myself at this point? LOL

 

[DaveC426913]

I am not sure a rocky planet can attain the size of Uranus. That could be problematic for your world-building.

https://en.wikipedia.org/wiki/Mega-Earth

 

[LadiSilverfox]

I was concerned with making it a gas giant due to what I was reading about radiation impacting potential life on the moons. If it was a gas or ice giant do you think that would be an issue?

 

[DaveC426913]

I was concerned with making it a gas giant due to what I was reading about radiation impacting potential life on the moons. If it was a gas or ice giant do you think that would be an issue?

Not aware that gas giants are intrinsically high in radiation, but I have no idea.

Still, at a distance of 5.2 million km, M2 is three times more distant from P1 than even the outermost Galilean moon is from Jupiter, so it would be plausible it's safe.

 

[Frabjous]

We did find a core of a gas giant.
https://exoplanets.nasa.gov/exoplanet-catalog/7643/toi-849-b/

 

[LadiSilverfox]

I found a unit converter and you're right based on the density the planet would be about 2.09 sols and from what I was reading 1.6 is really the most a rocky planet can handle.
Based on: https://worldbuilding.stackexchange...-a-theoretical-maximum-size-for-rocky-planets

And according to https://www.space.com/25185-alien-moons-habitability.html
A Gas Giant could have life-hospitable moons. So, yeah... P1 looks like it has to move to being a gas giant.

 

[Algr]

I was thinking of something that had Earth-like qualities. Jungly-hot along the equator, moving to more moderate as you get away from the center, and cold at the poles.

This is actually the most reasonable situation for a habitable planet. Star Wars has planets that are all forest or all tropical, and that is actually not possible. A planet with a breathable atmosphere will have roughly an 60°c (140°f) spread of average temperatures between the equator and poles.

I was concerned with making it a gas giant due to what I was reading about radiation impacting potential life on the moons. If it was a gas or ice giant do you think that would be an issue?

It's not the gas that makes the radiation, but the magnetic field from the metallic core. (Including metallic hydrogen?) So making the planet rocky or gas would not make a difference here.

Don't forget about tidal locking. Moons tend to have very long days because of this, and need to be very far or very close to their planets to have a 24 hr day.

 

[DaveC426913]

It's not the gas that makes the radiation, but the magnetic field from the metallic core. (Including metallic hydrogen?) So making the planet rocky or gas would not make a difference here.

Apparently, and I did not know this, a sizeable source of Jupiter's radiation is actually from ... Io.

 

[LadiSilverfox]

Not aware that gas giants are intrinsically high in radiation, but I have no idea.

Still, at a distance of 5.2 million km, M2 is three times more distant from P1 than even the outermost Galilean moon is from Jupiter, so it would be plausible it's safe.

So, does the change the calendar and hours per day for the M2 that we previously discussed?

 

[DaveC426913]

So, does the change the calendar and hours per day for the M2 that we previously discussed?

Did we decide to switch primary P1 from rocky to gaseous?

We'd need to fix its mass to work out the actual orbit before we know the months/years.

As to day length, that's unconstrained. With the huge orbits proposed, tidal-locking would not be an issue.

 

[DaveC426913]

If we presumed
- the mass of Uranus (14 Earths) for P1,
- the mass of Mars (.1 Earths) for M2, and
- the radius of 5.2 million km (derived post 13), then
I get an orbital period for M2 around P1 equal to 0.966 Earth years.

Anyone care to check my "math"?

 

[Algr]

If M2 is too close to P1, it will get tidally locked. If it is too far, it will drift out of P1's orbit and become a planet of its own. The latter situation depends on other planets in they system too.

 

[LadiSilverfox]

If we presumed
- the mass of Uranus (14 Earths) for P1,
- the mass of Mars (.1 Earths) for M2, and
- the radius of 5.2 million km (derived post 13), then
I get an orbital period for M2 around P1 equal to 0.966 Earth years.

Anyone care to check my "math"?

View attachment 320722

Thank you for all the work you put into this. I really appreciate the help. I'm sorry I didn't get back to you sooner, I was sick and couldn't get to my PC. (Doing better now though.)
So, M2 has fewer days per year than Earth. Do the hour per day we previously talked about on post 7 still apply?

 

[snorkack]

If the star is F or G, that dictates the orbital period of the planet in habitable zone. And that will constrain the orbital period of satellite.

 

[DaveC426913]

So, M2 has fewer days per year than Earth. Do the hour per day we previously talked about on post 7 still apply?

It's an interesting system.

What constitutes a moon's "year"? Is it the time it takes to orbit its primary planet? Or the time it takes for the planet to orbit its star?

How does one observe the orbit around the planet? You'd have to do it by looking at the stars.

Anyway, note that - by my calculations - M2 takes almost a whole Earth year just to orbit its planet, (whereas Earth's Moon only takes a month).

And with M2 being 5.2 million km from P**, its orbit around the star will be quite large - many AUs. And that means a much longer year. Hard to say what the minimum orbital radius of P is without someone to do the calculations. Jupiter has moon with a 5 million km orbit and it has a 12 year year.

M2's day would still be independent of everything else - it's simply its own axial rotation - which can be whatever you want.

 

[DaveC426913]

If the star is F or G, that dictates the orbital period of the planet in habitable zone. And that will constrain the orbital period of satellite.

That's a good point.

So we've got some tight constraints now on the system.

P can't be too close to S, or M2 (in its 5 million km orbit) will be unstable,
P can't be too far from S, or it will be outside the Goldilocks zone.

Unless ... unless M2 has an alternate heat source .... If P caused tides in M@ that would warm it
Nope. Won't work. M2 is way to far from P to be heated by tides.

The big constraint on this system - the one thing that pushes it far from the Earth scenario and toward the edge of what we think might be a viable system - is the OP's preference for the size of the primary planet in the sky of M2. That is what drives M2's orbit out to 5 million km.

 

[Algr]

What constitutes a moon's "year"? Is it the time it takes to orbit its primary planet? Or the time it takes for the planet to orbit its star?

Good question. For an inhabited planet, they would probably want to refer to a full change of seasons as a year. Since that is based on the sun's angle to the moon, it would be the same as the planet's year. The moon-to-sun distance would change based on the orbit around the planet, but that would be (guessing) 200 million km ± 5 million km. Not as big a deal as a tilted-axis seasons.

 

[LadiSilverfox]

Good afternoon, everyone.

I have spent some time thinking about the information you previously provided and how that would work or might look from the surface of the M2. Dave, as you mentioned some of these calculations came out of some tighter restrictions.

Let's say we start over? My restrictions are that M2 is comfortably habitable, has a 32-hour day, and is tidally locked to P. P (inhabitable) still has M1 and M2. (Bonus: M1 was habitable but now is not.)

You're free to alter sizes, planet types, distances, tilt, etc to make a realistic and stable living situation for M2.
Please and thank you. ^~^

 

[DaveC426913]

Let's say we start over?

You're free to alter sizes, planet types, distances, tilt, etc

How can we alter anything if we're starting over?

So far, your requirements are far too broad, and they put the onus on us to invent it from whole cloth.

 

[LadiSilverfox]

Basically, before it was stated that the restrictions were too tight.
For instance; picking what type of Sun forced the Goldilocks zone to be in a particular area. Or The planet's size in the moon's sky helped with the distance the moon was from the planet. But that made the path borderline unstable, right? Also, it was so far from the planet it didn't have tidal locking.

That's why I am saying maybe starting over is best. Since I don't know things like what percentage of the sky the planet should take up to be tidally locked but not pull into the planet's gravitational field or what the axis tilt should be, that's why I said make any alteration you believe is practical to the scenario.

Like; originally I had wanted the planet to be a silicone core and we realized at that size it wouldn't work so we altered to an ice giant. Maybe you realize to be tidally locked and in the Goldilocks range, and you realize an ice giant won't work for some reason? So you are free to change it to something that will.

I'm sorry if the requirements seem very broad but me taking guesses at decisive information that might get us where it needs to be didn't really seem to work before. If you have other suggestions about how to streamline this for both of us, I am all ears.

 

[hmmm27]

originally I had wanted the planet to be a silicone core

That's going to influence my visualization of the planet, somewhat.

How much scientific accuracy is necessary for the storyline ?

 

[Bandersnatch]

Let's say we start over? My restrictions are that M2 is comfortably habitable, has a 32-hour day, and is tidally locked to P. P (inhabitable) still has M1 and M2. (Bonus: M1 was habitable but now is not.)

Potential habitability of the satellite, to a good approximation, should be determined by the distance from the star. I.e., if the parent planet is in the habitable zone, so are its satellites.
Other reasons than solar irradiation can still affect habitability, though. So you can e.g. say M1 used to be habitable, but being small has lost too much of its atmosphere by now. While M2 being larger has retained its atmosphere and is habitable just fine.
This also suggests the parent planet should not be an ice giant, as the ices should melt/sublimate at the distance from the star where the moon can be habitable.
Energy from tidal stretching or otherwise received from the parent planet could alter this picture, but IMO it's better to ignore these for clarity.
Similarly, I'd handwave away any radiation concerns. You can always say it's remarkably low, or the moon happens to orbit away from the main belts, or itself has a strong magnetosphere.
Or, you could say that while M2 orbits away from the radiation belts, M1 has at some point drifted (due to tidal interactions) into one of the belts, which accelerated atmosphere loss and is the reason M1 is uninhabitable. Maybe it still has enough atmosphere to survive on, but it's now too strongly irradiated to support life? There are options here.

Here, use this spreadsheet.
(Google Docs; use the hyperlink and make a copy to edit - otherwise it's viewing only)

There are two sheets in there.
The first is for the star and its habitable zone. The data should be left alone here, unless you really need more/different masses. But it already spans the range of masses corresponding to G and F-type stars. If you really want to, the masses can be extended on either end by a bit, and the table should still make sense.
Pick a star you like, and an orbit within its HZ, and copy the mass and the desired orbit into the second sheet.

The second one is for the planet-moon system. It's a bit more messy (sorry), just remember that green fields want you to enter something, while blue fields tell you something. It calculates things like the sizes of the two planets, how large the parent planet would look on the sky, if the orbit is not too large for the moon to fly away, or what the period has to be given the radius (or vice versa). A few other things.
The data already in place is for a Sun-like star, Earth-like orbit of the parent planet, a Uranus-like parent planet, and an Earth-like moon tidally locked on a 32h orbit (which sets the length of a day in this case).

There's precious little room for another moon on an even lower orbit, so either raise the orbit of M2, or place M1 on a higher orbit than M2. (M1 is not included in the spreadsheet)

There's nothing there about orbital inclination or axial tilt (yet). If you decide to have axial tilt AND tidal lock, then the orbital inclination will have to be equal to the axial tilt (and vice versa). Without tidal lock the tilt and the inclination can be uncorrelated.

With the current setup, and without inclination, significant daily eclipses would be commonplace. These are not taken into account when deciding habitability, or anything else for that matter.

Try playing with it a bit and see if any of it makes sense. Some cells have comments telling you what's what, but let me know if you need clarification or want something added that you can't do yourself. Or if the link doesn't work for some reason.

Also, I can't guarantee everything's put in correctly. Comments welcome.

 

[LadiSilverfox]

That's going to influence my visualization of the planet, somewhat.

How much scientific accuracy is necessary for the storyline ?

Basically, I am trying to figure things out like how often they see M1 from M2, if possible, in what phases. When/How often M2 experiences eclipses or other such events, it will tie into how certain outer spiritual realms will interact with M2.

 

[snorkack]

Consider then the three systems of densely packed big satellites in Solar System.
Jupiter: 317,8 Earth masses
Inner large satellites:

1. Io 422 000 km +1,7627 d
2. Europa 671 000 km +3,5255 d (2:1 resonance to Io)
3. Ganymede 1 070 000 km +7,1556 d (2:1 resonance to Europa)
4. Callisto 1 883 000 km +16,69 d (out of resonance)

Saturn: 95,2 Earth masses
Inner large satellites:

1. Mimas 186 000 km +0,9424 d
2. Enceladus 238 000 km +1,3702 d (not resonant to Mimas)
3. Tethys 295 000 km +1,8878 d (2:1 resonance to Mimas, not to Enceladus)
4. Dione 378 000 km +2,7369 d (2:1 resonance to Enceladus, not to Tethys)
5. Rhea 527 000 km +4,5715 d (out of resonance)
6. Titan 1 222 000 km +15,9454 d (out of resonance)

Uranus: 14,5 Earth masses
Inner large satellites:

1. Miranda 129 000 km +1,4135 d
2. Ariel 191 000 km +2,5204 d
3. Umbriel 266 000 km +4,1442 d
4. Titania 436 000 km +8,7509 d
5. Oberon 584 000 km +13,4632 d

no resonance for Uranus.
Your quoted 32 hours for M2 is close to what Enceladus and Miranda have. And there is the major satellite Mimas inwards of Enceladus, as well as minor satellites inwards of all of the aforesaid.
What do you mean by "twice faster" for M1? Velocity? Or maybe period, as in being in a 2:1 resonance to M2? There are 4 pairs of 2:1 resonances among the 15 major satellites listed, so a likely if not inevitable arrangement.
What is "Uranus-sized" for your "silicate" planet P? Mass, or radius?

Also a question for the astronomers/celestial mechanics here...
Precisely what are these 4 2:1 resonances precise to?

This ties to the question of what phases will M1 be seen.
If M2 and M1 are out of resonance than M1 will be seen in all phases.
If M2 and M1 are close to resonance but not precisely then M1 will also be seen in all phases, but over a long time period.
But if the resonance is "precise" then precise to what?
Consider near side of Europa. Jupiter is visible at all times and all phases. In one orbit (3,5255 days), Sun circles the sky so half of the time it is night and some of the rest, eclipse. But at the same time, Io completes 2 orbits around Jupiter - thus catching up with Jupiter just once.
In a long term, do conjunctions of Jupiter and Io as seen from Europa happen always in the same constellations of fixed stars? Then they happen in all phases over 12 year orbit of Jupiter. Or is the resonance exact in synodic terms, so the conjunctions are always in the same phase? Or neither?
Same question about the other 3 pairs (Ganymede-Europa, Tethys-Mimas, Dione-Enceladus).