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 observed


With 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.