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Two Moons

nathan said:
An interesting fact about this is that the moon's orbit is always concave to the sun -- I think that also implies it is never retrograde either, but I've not done that calculation.
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You mean the Moon's orbit is always convex, and never concave. That's true. And yes, it implies that it never moves retrograde as seen from the Sun (but the opposite implication is not true).

Goshawk said:
Well, just for the sake of argument, and to give a starting point, let's stipulate that it's one Earth-sized planet, and two moon-sized moons, with the current size, shape, density, etc. of the current earth-sized planet and moon-sized moon. Would celestial mechanics allow those two moons to orbit around the planet?
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I think the question is similar, although not identical, to this question: can three stars of comparable mass form stable systems?

Well, there are systems like that that are reasonably stable. The general rule of thumb for stability in such cases is hierarchy: if masses are too similar to establish a clear hierarchy, distances can do - meaning that two of the objects will be relatively close and the third one farther away.

In the case of one Earth and two Moon-sized moons, there are two main ways to arrange that: either one of the moons could orbit much lower than the other, or the two moons could orbit each other closely at a high orbit around the Earth. (This is of course only a basic recipe for long term stability; a general guideline of where to start further search for actual self-correcting orbital resonances.)

The presence of the Sun adds another layer of complexity, but its great mass and distance already offers hierarchical separation; in essence, it makes the situation conceptually equivalent to a quadruple star system (with a certain ratio of constituent masses) - and even those are in general known to exist.
 
The two moons could orbit each other and obit the Earth around their center of mass.
 
Thabiguy said:
You mean the Moon's orbit is always convex, and never concave. That's true. And yes, it implies that it never moves retrograde as seen from the Sun (but the opposite implication is not true)
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Oh, yes, I see I was defining things wrongly. Thanks for the clarification!
 
If the moons were much smaller than Earth's moon then that would simplify things. The inner moon could be close in, say orbiting once every two or three days and the outer one maybe twice as far away and slightly bigger in size. This would make it slightly smaller as seen from the planet. The big issue here is tides, because the size of tides are very sensitive to distance from the moon. Much more than gravity.

There are certain orbits where this is stable. Just check out Jupiter's moons for what I mean. Because I do not know what I am talking about.
 
rjh01 said:
If the moons were much smaller than Earth's moon then that would simplify things. The inner moon could be close in, say orbiting once every two or three days and the outer one maybe twice as far away and slightly bigger in size. This would make it slightly smaller as seen from the planet. The big issue here is tides, because the size of tides are very sensitive to distance from the moon. Much more than gravity.

There are certain orbits where this is stable. Just check out Jupiter's moons for what I mean. Because I do not know what I am talking about.
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Yes. If the moons are much smaller than the planet you can certainly have two or even more in stable orbits. Jupiter is a great example, or just the small artificial satellites we have put around the Earth. What made be wonder is that Elfquest, Warhammer etc take place on approximately earth-sized planets, with moons seeming to be about the same size as ours. Technically, they actually tend to be depicted as much bigger than our moon, but I have interpreted it as being mainly artistic license. Even people painting the real moon tend to make it seem much bigger than it is.
 
Travis said:
One must consider the unique circumstances that formed Earth's moon. Would it be possible for such a rare event to happen twice? Sure, but the odds of it happening are pretty low.
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I wish the moon that crashed into Mars had been further away. Mars would have a magnetic field and the water would stil be liquid.
 
Travis said:
I'm not sure and would guess that such a system might be unstable in the long run.
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My understanding is that the Earth-Moon system is also believed to be unstable 'in the long run.'

In other words, 'in the long run' is probably longer than the inhabitants of Elfquest care.
 
drkitten said:
My understanding is that the Earth-Moon system is also believed to be unstable 'in the long run.'
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All orbits are unstable in the long run, because (if nothing else) there is always gravitational radiation to carry energy away.

About the OP, my guess is that most such configurations will be very unstable (i.e. if you randomly pick some initial data for the orbits, there will almost always be a collision or ejection within a few orbital periods). But that doesn't mean there aren't any long-lived ones - there probably are - and the question boils down to how small a region of initial-condition space they're confined to.
 
sol invictus said:
But that doesn't mean there aren't any long-lived ones - there probably are - and the question boils down to how small a region of initial-condition space they're confined to.
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What does "long-lived" mean in this context?

Humans have had astronomy for approximately 5000 years.

If someone claimed that in 50,000 BCE, the Earth had no less than four additional Moon-sized satellites that were stolen by Space Gypsies on or about the night of 45,000 BCE, I'm not sure I could disprove them. I don't even know where to look for fingerprints....

But 50,000 years in astrophysical terms is barely time enough for a quick smoke break.
 
drkitten said:
What does "long-lived" mean in this context?
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I've never thought about the 3-body problem in any depth, but I would think that if one ignores gravitational radiation (i.e. treats the Newtonian 3-body problem), there should be some infinitely long lived orbits.* If so, initial conditions close to those configurations could have an arbitrarily long lifetime. Those long lived orbits might be a set of measure zero, but sometimes dynamics (tidal forces, for example, or "friction" from other small bodies) can drive you towards such special points.

But 50,000 years in astrophysical terms is barely time enough for a quick smoke break.
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In a sense, yes - but it's also many orbital periods.


* Does anyone know if that's been proven or disproven? I suspect with some masses equal there are examples, but what about with all three different?
 
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Dictator Cheney said:
it is my understanding that the world cannot "support" its moon.
isnt the moon drifting away from the earth, 4 centimeters every year?
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No. It isn't that the Earth cannot "support" the moon; the moon pulls on the oceans (tides, natch) and they cause friction that brakes the Earth's rotation by very small amounts. However, as it slows it looses rotational momentum, and that *must* be conserved. The only give in the system to absorb it is the moon moving farther out in it's orbit and absorbing the excess momentum. It will continue with this until the Earth's rotation stops relative to the moon's orbit. This is effected through gravitational coupling.

The two "stable" Lagrangian points don't help; they are only stable while the mass at the point is minor compared to the Earth; as the L4/5 objects increase in mass, they begin orbiting around the points and eventually collide with Earth. This is one of the hypotheses of the creation and destruction of Theia in The Big SplashWP, that led to the creation of the moon.

The barycenter off the earth/moon system (the location around which the both rotate; the common center of gravity) is within the earth, and so the moon is considered a satellite. If it were outside the earth, then they would be considered twin planets, though that is just an arbitrary definition among astrophysicists and has no physical significance.

There are orbits that would work for dual moons - one would be where he orbits of the moons are identical but on opposite sides. If ne of the moons starts gaining or slipping back relative to the other, though, they would start interfering with each other. Other possible orbits are orbits with resonances, which is how Jupiiter keeps it's moons disciplined.
 
Thabiguy said:
nathan said:
An interesting fact about this is that the moon's orbit is always concave to the sun -- I think that also implies it is never retrograde either, but I've not done that calculation
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You mean the Moon's orbit is always convex, and never concave. That's true. And yes, it implies that it never moves retrograde as seen from the Sun (but the opposite implication is not true).
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You're right that it's never in retrograde. The moon's orbit would look a bit like a spirograph.



Steve S
 
shadron said:
Yeah, there aren't many with moons as big as Earth's is; we could almost be considered as a double world.
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You mean in our solar system only, right? We really don't know how common a large moon (double world) is elsewhere. (For that matter, before Pluto/Charon got demoted, it would qualify as a double planet.)

From the evidence of our solar system, we do know that the early history of it was quite violent. Pretty much all the rocky planets and moons show the scars of frequent, and sometimes very large impacts. If our moon was formed by a very early, very large collision, it could be that large moon formation is not so terribly rare.
 
UncaYimmy said:
Appearing to be about the same size, I believe, is going to be a factor. The sun and the moon appear to be about the same size from our vantage point (consider an eclipse).
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Also, art typically takes liberties with moons, partly because of the optical illusion about the size of the moon when it is close to the horizon. People seldom clue into the fact that the moon in movies is usually vastly larger (and/or closer) than the real moon.
 
steve s said:
You're right that it's never in retrograde. The moon's orbit would look a bit like a spirograph.

[qimg]http://www.internationalskeptics.com/forums/imagehosting/thum_81544a1cc7a64e884.jpg[/qimg]

Steve S
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I assume the diagram is a picture of the moon's orbit around the sun.

I would have thought it would look more like a sine wave that had been bent into a circle. The way you have this at the moment the moon suddenly changes velocity with a huge acceleration. However the acceleration of the moon is almost constant.
 
rjh01 said:
I assume the diagram is a picture of the moon's orbit around the sun.

I would have thought it would look more like a sine wave that had been bent into a circle. The way you have this at the moment the moon suddenly changes velocity with a huge acceleration. However the acceleration of the moon is almost constant.
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That diagram is not to scale. The cycloid SteveS shows has concave parts. Hm, I also think it's inside-out. The moon's orbit around Earth is in the same direction as the Earth's orbit around the sun, so the apexes of the cycloid (were there to be any) would be on the inside.
 
Who built the Moon? It's speed is 1k per second and is neatly placed to hold the earth stable. It is 400 times closer than the sun making it just right for complete eclipse, appearing the same size. The maths are astounding and all laid out in the book "Who built the moon". Plenty on Google too.
 
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