Questions about a planet with two moons

[jack5000]

Hi, this is my first post - i need some help with my astrophysics.

I'm writing a sci-fi story where an Earth like planet has 2 moons. One of them is habitable and has conditions like Earth - like an atmosphere and so on (almost like a twin planet). The other moon would be smaller and more like our moon - uninhabitable and rock-like. I want the three to be as close together as possible. Some questions:

Would such a system be possible?

How large would a moon have to be to have a decent atmosphere and be habitable?

Should i size the 'Earth' planet up from our scale to enable the moons to be larger?

Are are there any factors such a system would bring up that i should be thinking about, in regards to the effects the 3 bodies have on each other?(gravity etc.)

Any idea about how the moons would orbit, and how the large moon would effect the small?

What kind of distance from the larger moon to the Earth planet is feasible?


I really don't have a great mind for astrophysics unfortunately, but I'd like the scenario to be plausible if possible, thus i need a bit a help. Thanks in advance.

 

[Nimbian]

First Welcome to the Forums, and hopefully some one here has the answers to all your questions.

Would such a system be possible?

Short Answer Yes, Stable enough that it could last million/billions of years. I don't know although there is likely an orbital solution that works. What your looking at is a Binary or Trinary planet. (Depending on the sizes) A possible situation would be as described in Rocheworld With two worlds of roughly equal mass. The Math for such a set up involve the Tug of war Principle, and the Roche Lobe. It should be possible if the smallest moon Circles perpendicular to the axis between the two larger planets.

How large would a moon have to be to have a decent atmosphere and be habitable?

Habitable by Human-Like creatures or Alien Creatures? A decent atmosphere? by Earth standards your looking at 70-90 kPa range.
ΔP=pg(Δh)
where
ΔP is the hydrostatic pressure (given in pascals in the SI system), or the difference in pressure at two points within a fluid column, due to the weight of the fluid;
ρ is the fluid density (in kilograms per cubic meter in the SI system);
g is acceleration due to gravity (normally using the sea level acceleration due to Earth's gravity in meters per second squared); (Earth G= 9.81m/s²)
Δh is the height of fluid above the point of measurement, or the difference in elevation between the two points within the fluid column (in metres in SI).

Should i size the 'Earth' planet up from our scale to enable the moons to be larger?

It all depends on how things work out in the above equations. Personalty I'd focus on the two Primary worlds and then find a stable orbit for the moon when your happy with the first too

Are are there any factors such a system would bring up that i should be thinking about, in regards to the effects the 3 bodies have on each other?(gravity etc.)

If there is liquid water on the planet there will be some major (and complicated) tides, They would only be consistent when the 3 major contributors are taken into account (The Sun, and Planet B, and the Moon), It would also cause major effects in terms of weather systems and atmospheric density. There will likely be established cycles

Any idea about how the moons would orbit, and how the large moon would effect the small?

Either the orbit of the Smallest moon will shift (relative to the Solar Plane) over time (perhaps in a cycle) or it will have to be far enough from both worlds so that the central mass is more or less equalized between the two.

What kind of distance from the larger moon to the Earth planet is feasible?

I believe the Roche equations above would best answer this.

I really don't have a great mind for astrophysics unfortunately, but I'd like the scenario to be plausible if possible, thus i need a bit a help. Thanks in advance.

I hope this helps and I'm sure others will add to it. But it would really help to have the Largest or Primary world Defined one way or another

 

[jack5000]

Thanks Nimbian, some very useful thoughts there.

I was thinking the main planet to be Earth sized, the habitable moon maybe Ganymede size and the smaller moon to be just smaller than our moon. Distance-wise to the Earth planet, maybe 70,00 km for the moon and 200,000km for Ganymede. I just ran this in universal sandbox and there were no collisions.

However, i don't know if a Ganymede sized moon would be able to have a decent atmosphere.

Yes i would want the habitable moon to be able to host humans. The physics calculations are beyond me.

If the home planet was earth, measuring by Earth mass, what kind of size of planet could have a good atmosphere? Would 0.5 Earths be able to it?

 

[Nimbian]

Ha I actuality have that "game" I'll have to do some math and punch it into the sim. get back to you in a day or two

 

[onomatomanic]

For an Earth-like atmosphere (one which can indefinitely retain relatively light molecules like methane and water), a rule-of-thumb bound is given by (R/M)*T < 2.5 R_Earth/M_Earth*T_Earth where R, M, and T are the planet's (or moon's) radius, mass, and temperature (more).

If the planet is to be "Earth-like" in composition and climate, it has to have similar density and temperature as Earth, which can be used to simplify that further to get 1/M^2 < 16 1/M_Earth^2 and thus M > 1/4 M_Earth. In other words, you really need something in the Venus/Earth range, all the other rockies in our solar system, including Mars, won't really do on evolutionary timescales. That doesn't mean they couldn't be terraformed to have short-lived (millions of years or less) atmospheres, though.

Assuming the star and orbit about it are similar to the Sun-Earth case, the mutual range within which Earth-sized bodies can orbit about each other stably is on the order of d ~ (1 AU) (M/M_Sun)^(1/3). Tidal locking timescale between such bodies is on the order of T_lock ~ (10^10 years) * (d/d_Moon)^6 / (M/M_Moon)^2 where the "Moon" subscript refers to Earth's Moon. Putting those two together gives

T_lock ~ (10^10 years) * ((1 AU)/d_Moon)^6 / (M_Sun/M_Moon)^2 ~ (10^10 years) * 400^6 / (3*10^7)^2
T_lock ~ 3*10^10 years

This value rapidly decreases as the distance between the two bodies decreases. If it's half of the allowed maximum, T_lock < 10^9 years, so the bodies will enter mutual lock after only a fraction of the age of our solar system or the time it took for life to evolve on Earth. Thus, if you want your massive bodies to be relatively close, they will almost certainly be in mutual tidal lock, as is the case for e.g. Pluto and Charon.

That being the case, you probably want to bring them together as closely as possible, just as you already said, since the day-lengths on both planet and moon is now equal to their orbital period. For a 24-hour day, the orbit equation yields about 30,000 km, similar to the height of a geostationary orbit about Earth. This is well outside the Roche limit given the relatively similar masses, so the two bodies themselves would retain their identities, though the tidal deformation would be significant, with stationary bulges with heights in the hundreds or even thousands of kilometres. If the orbit is even a little bit eccentric, this would cause vast tides - not due to motion of the tidal bulges, as on Earth, but due to changes in their heights. "Officially", their atmospheres would have merged at that distance, but the particle exchange rate would probably not signify at all. The interactions between their magnetospheres might be more interesting, but I'm not knowledgeable enough in that area to even venture a guess as to the effects.

Finally, the third component - the small moon - would have to be orbiting significantly farther out to be stable. An order of magnitude is usually assumed to be safe, which would mean 300,000 km or more. Which is still well within the range in which the planet's gravity exceeds the star's, so I don't see any problems there.