Defining moons

[metaphor]

Hmm, the equation for the Stern-Levison parameter is L = M^2/a^(3/2)*k, where M is mass and a is semi-major axis, and k is a constant. It seems that if you express mass in Earth masses and semi-major axis in AU, k is about 1.5e5.

Applying that to moons, and dividing by the square root of mass of the primary compared to the mass of the Sun, you would get something like this:

[table=width: 500]

[tr]

[td]Satellite[/td]

[td]Stern-Levison parameter[/td]

[/tr]

[tr]

[td]Moon[/td]

[td]3.0e2[/td]

[/tr]

[tr]

[td]Phobos[/td]

[td]5.5e-10[/td]

[/tr]

[tr]

[td]Deimos[/td]

[td]2.7e-12[/td]

[/tr]

[tr]

[td]Metis[/td]

[td]6.7e-9[/td]

[/tr]

[tr]

[td]Amalthea[/td]

[td]1.3e-5[/td]

[/tr]

[tr]

[td]Io[/td]

[td]6.9e3[/td]

[/tr]

[tr]

[td]Callisto[/td]

[td]1.1e3[/td]

[/tr]

[tr]

[td]Himalia[/td]

[td]1.1e-7[/td]

[/tr]

[tr]

[td]Sinope[/td]

[td]1.2e-11[/td]

[/tr]

[tr]

[td]Pan[/td]

[td]6.6e-11[/td]

[/tr]

[tr]

[td]Mimas[/td]

[td]2.3e-3[/td]

[/tr]

[tr]

[td]Enceladus[/td]

[td]1.3e-2[/td]

[/tr]

[tr]

[td]Tethys[/td]

[td]3.1e-1[/td]

[/tr]

[tr]

[td]Dione[/td]

[td]6.7e-1[/td]

[/tr]

[tr]

[td]Rhea[/td]

[td]1.8e0[/td]

[/tr]

[tr]

[td]Titan[/td]

[td]1.7e3[/td]

[/tr]

[tr]

[td]Iapetus[/td]

[td]6.3e-2[/td]

[/tr]

[tr]

[td]Phoebe[/td]

[td]1.9e-7[/td]

[/tr]

[tr]

[td]Puck[/td]

[td]1.7e-5[/td]

[/tr]

[tr]

[td]Miranda[/td]

[td]4.8e-3[/td]

[/tr]

[tr]

[td]Ariel[/td]

[td]1.1e0[/td]

[/tr]

[tr]

[td]Umbriel[/td]

[td]5.1e-1[/td]

[/tr]

[tr]

[td]Titania[/td]

[td]2.2e0[/td]

[/tr]

[tr]

[td]Oberon[/td]

[td]1.0e0[/td]

[/tr]

[tr]

[td]Proteus[/td]

[td]2.6e-3[/td]

[/tr]

[tr]

[td]Triton[/td]

[td]1.2e2[/td]

[/tr]

[tr]

[td]Nereid[/td]

[td]4.1e-6[/td]

[/tr]

[tr]

[td]Charon[/td]

[td]6.0e-1[/td]

[/tr]

[tr]

[td]Hydra[/td]

[td]6.6e-9[/td]

[/tr]

[tr]

[td]Hi'iaka[/td]

[td]9.9e-6[/td]

[/tr]

[tr]

[td]Dysnomia[/td]

[td]1.7e-2[/td]

[/tr]

[/table]

Here's a graph:

The yellow line is where the Stern-Levison parameter equals 1 with respect to the Sun. Moons are all on the top of the black line. There should be a lot more moons to the left of the yellow line, but I didn't graph the smaller ones.

Edited November 8, 2014 by metaphor

[Camacha]

the Stern-Levison parameter

We discussed this at length in the Pluto thread and I would loathe to repeat myself, but I just fail to see why the Stern-Levison parameter or any other variable that attempts to measure orbit clearing counts for anything. It seems too arbitrary, especially since we know next to nothing about how indicative it is. Not only is it one of many values you can choose to categorize things, it might be totally different in other solar systems. We just don't know yet.

That is also the reason why I have been advocating the hierarchy option, since there is bound to be a hierarchy in pretty much any system.

[metaphor]

We discussed this at length in the Pluto thread and I would loathe to repeat myself, but I just fail to see why the Stern-Levison parameter or any other variable that attempts to measure orbit clearing counts for anything. It seems too arbitrary, especially since we know next to nothing about how indicative it is. Not only is it one of many values you can choose to categorize things, it might be totally different in other solar systems. We just don't know yet.

That is also the reason why I have been advocating the hierarchy option, since there is bound to be a hierarchy in pretty much any system.

It's a measure of how long it takes a body to clear its orbit, and is based on easily measurable parameters (mass and orbital radius). For moons it doesn't really work well since there's other important forces that determine a moon's orbit, like solar tides.

We're trying to see if there's a good way to subdivide natural satellites into classes instead of lumping them all together (which I guess is what you mean by hierarchy option?).

[Camacha]

It's a measure of how long it takes a body to clear its orbit, and is based on easily measurable parameters (mass and orbital radius).

It's the ability to clear its orbit, right? That is a subtle difference, I guess. I understand what the value is supposed to signify, but like I said, I fail to see why exactly this value is relevant or universally telling. It rather feels like a pretty random line drawn in the sand.

We're trying to see if there's a good way to subdivide natural satellites into classes instead of lumping them all together (which I guess is what you mean by hierarchy option?).

The hierarchy option is what I outlined in this post. It's classifying bodies based on their relative position in a system, much like a family tree in biology. When you talk about a moon, you know that you are talking about a spherical object that orbits a planet which orbits at least one star. Maybe the current setup of that system is too simple for now, as it needs to be able to cope with nesting situations, but that should not be a major issue.

[metaphor]

So from the data I've looked at there are really two families of moons. The moons in prograde circular orbits that start out small near the planet and get bigger up to a point, and the (usually) retrograde irregular orbit moons that are much smaller and farther away. There is a large gap without moons between these two regions. The prograde closer moons probably formed together with the planet, while the irregular outer moons probably were probably captured.

Jupiter's moons. The outermost regular moon, Callisto, is at 1.9 Gm, while the innermost irregular moon, Themisto, is at 7.5 Gm.

Saturn's moons. The outermost regular moon, Iapetus, is at 3.6 Gm, while the innermost irregular moon, Kiviuq, is at 11.1 Gm.

Uranus's moons. The outermost regular moon, Oberon, is at 0.6 Gm, while the innermost irregular moon, Francisco, is at 4.3 Gm.

Neptune's moons. Neptune has Triton, which is retrograde and probably captured, but still in a circular orbit close to equatorial, at 0.4 Gm, while the innermost irregular moon, Nereid, is at 5.5 Gm.

It seems like planetary moons have this kind of size distribution:

[K^2]

I just want to jump in here to cause even more confusion and question status of the Moon as an actual moon, and suggest that it is a part of the Earth-Moon double planet system instead.

Now, I know that Moon fails a barycenter test, but I consider it to be a silly one, since barycenter location isn't a fixed thing. It fluctuates for any realistic orbit, and indeed, moves out further and further. And in fact, Earth-Moon's barycenter will eventually be outside of Earth's radius. But that's not a huge problem, since that won't happen for a while. However, as we are discovering more and more exoplanets, we are bound to find some that have orbits elliptic enough that barycenter moves in and out of heavier planet's radius. I do not want to have to adjust status of an object as a Moon or a Planet depending on what time of the month it is. That's silly.

Is there something else that will let us distinguish moons from planets? But of course! Gravitational pull of a parent planet on the moon is always stronger than gravitational pull of the star. This is true of every moon in the Solar system. That is, except for the Moon.

Indeed, Moon orbits the Sun, not the Earth. The proof positive of that is Moon's trajectory around the Sun. It is convex everywhere. In layman's terms it always accelerates towards the Sun. Never away. Unlike all other parameters, convexity of the orbit will not change, except over the-age-of-the-star-system kind of scales. Even if the orbit of the moon/planet is highly elliptical, the orbit around the star either is or is not totally convex.

This is a variation on the tug-of-war definition, which uses relative distances and masses, but it is a more general one, because tug-of-war parameter can also change for elliptic orbits. Convexity is fixed.

There are three possible outcomes of the convexity test, and I propose distinct names for all three.

Both pass: Double planet. Both bodies orbit the star first and foremost, and they happen to stick around because of secondary attraction to each other.

One passes, one fails: Planet and its moon. Not much going on here.

Both fail: Binary planet. Both bodies orbit primarily each other, and as a single unit, move around the star.

Based on the above definition, Earth-Moon system is a double planet, and in 1969, we put people on a planet and not a moon.

[KerikBalm]

Indeed, that is worth considering, I did make reference to it in my OP.

We do need a way to distinguish a moon from just orbiting "stuff", and a moon from a planet.

Although that defintion seems less pressing, because the Earth-Moon system is the only one where this question even applies.

Then there is also Pluto-Charon, but those aren't real planets .

The mass ratio there is about 10:1

For Earth-Moon, its about 100:1 I have a hard time considering them a double planet with a mass differnece of 2 orders of magnitude, but there are good arguments for it.

In the case of Mars, Jupiter, Saturn, Uranus, Neptune, it is very clear that there's no double planet - but what to call a moon... that is very unclear.

[K^2]

Just for my 2c on the "orbiting stuff" point, we have a term "natural satellite". Given that, I'd recommend classifying as moons only stuff that's roughly round in shape. Same as we require for planets. Yes, I know that it'd drastically cut down on moons in the system, but that seems like a good idea with gas giants.

[Camacha]

All right, this might sound like a silly question, but if the Moon is orbiting the Sun rather than Earth and experience more of its influence, why is the moon not tidally locked to the Sun?

If I understand things correcly, it somewhat (but not quite) reminds me of the interaction between Epimetheus and Janus pushing and pulling on each other to form some sort of coherent non circular pattern.

Based on the above definition, Earth-Moon system is a double planet, and in 1969, we put people on a planet and not a moon.

I already see huge discussions arising if that ever gets accepted. The US will have put the first man on the Moon, but the next nation to visit it (bar the US) will have put the first man on a planet. Or, at least, according to people from that nation for sure.

Edited November 9, 2014 by Camacha

[metaphor]

All right, this might sound like a silly question, but if the Moon is orbiting the Sun rather than Earth and experience more of its influence, why is the moon not tidally locked to the Sun?

Because tidal forces are proportional to 1/R^3 while gravitational forces are proportional to 1/R^2, so closer objects will experience more tidal force compared to gravitational force. Tidal acceleration is dr*2GM/R^3. The tidal acceleration of the Sun acting on the Moon is about 1.3e-7 m/s^2, while the tidal acceleration of the Earth acting on the Moon is about 2.5e-5 m/s^2. The gravitational acceleration due to the Sun is 5.9e-3 m/s^2, and the gravitational acceleration due to the Earth is 2.8e-3 m/s^2.

It's not really like Janus and Epimetheus since those two are on opposite sides of their Saturn orbit most of the time.

[Camacha]

However, as we are discovering more and more exoplanets, we are bound to find some that have orbits elliptic enough that barycenter moves in and out of heavier planet's radius. I do not want to have to adjust status of an object as a Moon or a Planet depending on what time of the month it is. That's silly.

That's solved easily enough - just make it a requirement that the barycentre lies outside of the two bodies for at least the last full orbit/year to be a double (...).

It's not really like Janus and Epimetheus since those two are on opposite sides of their Saturn orbit most of the time.

I know, hence the somewhat but not quite, but it helped me painting a mental picture of what the relation actually is, since it is not a true orbit. It is more pushing back and forth than swinging around, apparently.

Because tidal forces are proportional to 1/R^3 while gravitational forces are proportional to 1/R^2, so closer objects will experience more tidal force compared to gravitational force. Tidal acceleration is dr*2GM/R^3. The tidal acceleration of the Sun acting on the Moon is about 1.3e-7 m/s^2, while the tidal acceleration of the Earth acting on the Moon is about 2.5e-5 m/s^2. The gravitational acceleration due to the Sun is 5.9e-3 m/s^2, and the gravitational acceleration due to the Earth is 2.8e-3 m/s^2.

Right, I had not realized that tidel forces are much different from gravitational forces, I assumed they were simply a direct result of gravitational forces.

Edited November 9, 2014 by Camacha

[K^2]

That's solved easily enough - just make it a requirement that the barycentre lies outside of the two bodies for at least the last full orbit/year to be a double (...).

That's a very artificial solution. And if planet severely loses tug-of-war, the mutual orbit can take much longer than a year to complete. So your definition would still change from year to year.

The convexity is a very elegant mathematical principle, and it simply either holds or it does not.

I already see huge discussions arising if that ever gets accepted. The US will have put the first man on the Moon, but the next nation to visit it (bar the US) will have put the first man on a planet. Or, at least, according to people from that nation for sure.

Nah. US will claim right away that they've already put a man on the planet. It's not like something about the Moon changed, just the definition.

Edit: Though, if there is an ongoing mission when new definition is adopted, "The men who went to a moon, but came back from a planet," has a nice ring to it.

[Camacha]

And if planet severely loses tug-of-war, the mutual orbit can take much longer than a year to complete.

Can you elaborate? I can't quite picture this.

"The men who went to a moon, but came back from a planet," has a nice ring to it.

That sounds like a neat 50's movie

[K^2]

Can you elaborate? I can't quite picture this.

Take Mars, drop it on Mercury's orbit. Put Moon on orbit around Mars. Drop periapsis to 30k km. Apoapsis at 1M km, just within Hill Sphere. The Moon would go around Mars in 130 days, during which the barycenter will spend a couple of days inside Mars' radius. A year at Mercury's orbit is 88 days. So there will be a lot of "years" where barycenter stays completely out, and a lot of years where it would cross into planet's radius.

This arrangement would require interior star system to be pretty barren to be stable, but there is no reason why it can't exist.

That sounds like a neat 50's movie

I was actually referencing a 90's movie. But with that title, 50's might be a better decade for it.