a hidden planet in a lagrange point

[MC.STEEL]

I have been thinking about a scenario for a game/comic/anyme/whatever and i have to ask tree things.

Is it possible for a small Mercury sized object to have a stable orbit in the earth-sun l5/l4 lagrange point even if all the other planets act on it?

furthermore, how bright will it be,its suposed to be a goverment coverup that silences every backyard astronomer who finds it but i dont want it to be too obvious? (btw the albedo isnt very high)

and last is it possible for this theoretical planet to have 4/5fts of earths gravity and a magnetic field?

is it possible with a very high density or is it just straight out handwavium?

[Rokker]

I have been thinking about a scenario for a game/comic/anyme/whatever and i have to ask tree things.

Is it possible for a small Mercury sized object to have a stable orbit in the earth-sun l5/l4 lagrange point even if all the other planets act on it?

furthermore, how bright will it be,its suposed to be a goverment coverup that silences every backyard astronomer who finds it but i dont want it to be too obvious? (btw the albedo isnt very high)

and last is it possible for this theoretical planet to have 4/5fts of earths gravity and a magnetic field?

is it possible with a very high density or is it just straight out handwavium?

As far as my incomplete, yet above average knowledge of orbital mechanics goes, I see no reason why it wouldn't be stable, it would likely be very bright though. I must ask, if It is going to be a top secret object discovered by public type thing why not make it an L3 orbit where such an object would be nearly impossible to see where such a discovery would be fairly hard? Lastly, as for the question over the magnetic field, of course it can have one. Magnetic fields do not depend on mass or gravity. Hell, Earth has a stronger magnetosphere than Saturn. In fact, I would say that the fact that you are making it high density makes a magnetic field all the more likely as it would mean that there are a lot of heavy elements decaying, possibly causing some large fission reactions, to keep the core hot, and that iron and nickel and other metals would be in the center of that core, likely spinning, and creating a magnetic field.

[MC.STEEL]

The problem with the other L points is that the object has to be dead center in order to stay there so thats why i chose the L5/L4,wouldt want a runaway planet now would whe.

[tntristan12]

You might want to do some research into the Trojan Asteroids that "hang out" in Jupiter's L4 and L5 zones. These are regions distinct from the asteroid belt between Mars and Jupiter, and have been stable for a long, long time. Quite possibly this is the nearest real-world analog that you could draw inspiration from for your work.

[Ralathon]

There is simply no way to keep such an object a secret. A mercury sized body at such a short distance? You'll see it with the naked eye even if the surface is covered in sooth. 4/5ths earth gravity is a tall order as well. Earth's radius is about 3 times that of mercury. So the mass of this hypothetical object needs to be 1/9th of earth. But the volume decreases by a factor 27. So your planet has a density of about 16g/cm-3. This is somewhere between lead and depleted uranium.

There is simply no way such a body can exist and go undetected. You're going to need a lot of handwaving or you need to rethink your setting. Does it have to be in L4/5? Can't you just dump it somewhere in the outer solar system?

[Kerbin Dallas Multipass]

@Ralathon

It's not particularly short distance but quite exactly the distance earth/sun

[NGTOne]

The thing a lot of people overlook about a concept like this is that the object ITSELF would destabilize L4/L5, by adding a third body to the equation. Some new equilibrium would have to be established, but that means the object might not be stable in its initial location. The reason this doesn't happen much in our system is because the Trojans are so small relative to the mass of Jupiter.

[tntristan12]

The thing a lot of people overlook about a concept like this is that the object ITSELF would destabilize L4/L5, by adding a third body to the equation. Some new equilibrium would have to be established, but that means the object might not be stable in its initial location. The reason this doesn't happen much in our system is because the Trojans are so small relative to the mass of Jupiter.

That... Makes no sense. Lagrange points are solutions to the three body problem, so adding a third body is... just part of the setup. In fact, the case of three bodies in an equilateral triangle being stable holds for *any* three bodies regardless of mass. You could have three stars, three planets, two planets and a star, two stars and a rock the size of your head... An equilateral triangle would *still* be a stable configuration, since it's independent of the masses of the three bodies. L1, L2, and L3 are mass dependent and only hold for certain mass ratios, however.

[DaveofDefeat]

Its kinda hard to hide a planet.

[Warhorse]

@Ralathon

It's not particularly short distance but quite exactly the distance earth/sun

... which is actually a pretty short distance, even by solar system standards. And at that size and distance, even if it reflected no light whatsoever, it would regularly get noticed as it occluded other celestial objects, not to mention what it would do to the trajectories of various interplanetary probes ... Sadly, Ralathon's conclusions are spot on. :-(

[K^2]

That... Makes no sense. Lagrange points are solutions to the three body problem, so adding a third body is... just part of the setup.

Lagrangian points derivation assumes point-object. A large object can modify the solution.

But that's not the real problem. The real problem is that L4/L5 aren't really stable. An object can stay there quite a long time, but it will be shaken loose eventually. One of the hypotheses for the large impact that formed the Moon is a body that came from Earth's L4 or L5. It's just not stable enough for something to still be there. Though, a recent capture is not impossible.

As for the object remaining undetected, that's very unlikely.

[Kerbin Dallas Multipass]

... which is actually a pretty short distance, even by solar system standards. And at that size and distance, even if it reflected no light whatsoever, it would regularly get noticed as it occluded other celestial objects, not to mention what it would do to the trajectories of various interplanetary probes ... Sadly, Ralathon's conclusions are spot on. :-(

Just wanted to mention that a mercury object in L4/L5 would have the same visibility to the naked eye as actual mercury at its best visibility. The distance and illumination would be relatively similar.

OP mentioned this is scifi and a government coverup. So, yea, astronomers from 1500 B.C. would indeed notice the object, to John Doe the nightsky would just look normal.

[Kerbin Dallas Multipass]

One of the hypotheses for the large impact that formed the Moon is a body that came from Earth's L4 or L5.

Whow, you're saying a planet sized trojan existed for about a billion years? Thats not a good point to disprove the hypothetical object we're discussing XD

[Rokker]

Lagrangian points derivation assumes point-object. A large object can modify the solution.

But that's not the real problem. The real problem is that L4/L5 aren't really stable. An object can stay there quite a long time, but it will be shaken loose eventually. One of the hypotheses for the large impact that formed the Moon is a body that came from Earth's L4 or L5. It's just not stable enough for something to still be there. Though, a recent capture is not impossible.

As for the object remaining undetected, that's very unlikely.

Don't bring moon creation theories into this man. There are like a million of those and each one is almost pure speculation.

[Rokker]

The problem with the other L points is that the object has to be dead center in order to stay there so thats why i chose the L5/L4,wouldt want a runaway planet now would whe.

I think L3 would be fine, especially if they are in the exact same orbit, because then they'd share the same orbital speed and period and everything.

[Rokker]

... which is actually a pretty short distance, even by solar system standards. And at that size and distance, even if it reflected no light whatsoever, it would regularly get noticed as it occluded other celestial objects, not to mention what it would do to the trajectories of various interplanetary probes ... Sadly, Ralathon's conclusions are spot on. :-(

Well, it is a govt coverup and interplanetary probes tend to be a government thing. I dont think word about it would get out very easily.

[K^2]

Whow, you're saying a planet sized trojan existed for about a billion years? Thats not a good point to disprove the hypothetical object we're discussing XD

Young Sol system was a much different place. When a lot of the junk is orbiting in all sorts of weird trajectories, perturbations average out a lot better than when you have fully formed planets which have thoroughly cleared their orbital neighborhoods. Furthermore, the best way for an object to stay as perfectly at L4/L5 as possible is to have it form there. Junk would be falling in from various quasi-stable orbits to form a planetary body, which would allow it to stay put at the L4/L5 much longer than a fully formed rigid body would. Basically, this particular flavor of large impact hypothesis gives you the best possible scenario for an object to stay in Earth's L4/L5, and it still fell out of there pretty much as soon as it finished forming. There is just zero chance of an object from early system formation to still be there.

Like I said, capture isn't all together impossible, but it'd have to be a very recent one.

Don't bring moon creation theories into this man. There are like a million of those and each one is almost pure speculation.

And? We aren't talking about whether that actually happened or not. We have no sufficient evidence to confirm even the large impact, even though it is most consistent with observations, let alone say where the body came from. But that's entirely tangential here. We are discussing if a body could exist at these locations. The hypothesis of large impact caused by an L4/L5 object is studied well enough so that we know what sort of dynamics to expect from such a body. Whether it existed or not, this is how a body in L4/L5 would behave. That's all we need to know for this discussion.

P.S. If you really need a good hiding place for a planetary body, I'd go with L3. Now, an object there, one that's small enough not to cause significant gravitational disturbance, can stay there undetected by anyone who doesn't have a telescope in interplanetary space. So for a science fiction work, one which assumes a gov't conspiracy, that'd make for a plausible location. It's hard to picture something with .8G not to cause enough disturbance to be indirectly detectable, though.

Edited January 25, 2014 by K^2

[Kerbin Dallas Multipass]

P.S. If you really need a good hiding place for a planetary body, I'd go with L3. Now, an object there, one that's small enough not to cause significant gravitational disturbance, can stay there undetected by anyone who doesn't have a telescope in interplanetary space. So for a science fiction work, one which assumes a gov't conspiracy, that'd make for a plausible location. It's hard to picture something with .8G not to cause enough disturbance to be indirectly detectable, though.

Oh comeon. You're trying to pick on the L4/L5 idea by saying "this will only last a billion years" and now you come up with L3?

You're just making up your own scifi reality which is even more improbable

[Rokker]

Young Sol system was a much different place. When a lot of the junk is orbiting in all sorts of weird trajectories, perturbations average out a lot better than when you have fully formed planets which have thoroughly cleared their orbital neighborhoods. Furthermore, the best way for an object to stay as perfectly at L4/L5 as possible is to have it form there. Junk would be falling in from various quasi-stable orbits to form a planetary body, which would allow it to stay put at the L4/L5 much longer than a fully formed rigid body would. Basically, this particular flavor of large impact hypothesis gives you the best possible scenario for an object to stay in Earth's L4/L5, and it still fell out of there pretty much as soon as it finished forming. There is just zero chance of an object from early system formation to still be there.

Like I said, capture isn't all together impossible, but it'd have to be a very recent one.

And? We aren't talking about whether that actually happened or not. We have no sufficient evidence to confirm even the large impact, even though it is most consistent with observations, let alone say where the body came from. But that's entirely tangential here. We are discussing if a body could exist at these locations. The hypothesis of large impact caused by an L4/L5 object is studied well enough so that we know what sort of dynamics to expect from such a body. Whether it existed or not, this is how a body in L4/L5 would behave. That's all we need to know for this discussion.

P.S. If you really need a good hiding place for a planetary body, I'd go with L3. Now, an object there, one that's small enough not to cause significant gravitational disturbance, can stay there undetected by anyone who doesn't have a telescope in interplanetary space. So for a science fiction work, one which assumes a gov't conspiracy, that'd make for a plausible location. It's hard to picture something with .8G not to cause enough disturbance to be indirectly detectable, though.

Well, generally speaking, using pure unproven speculation to back up a point in a discussion is looked down upon.

P.S. Yup, L3 all the way. hi-5

[K^2]

(In)stability of Lagrangian points is not speculation. It's well-studied fact. Possibility of proto-planetary body forming at such points is also a well-studied fact. That's what we are talking about. Whether such an object actually existed is besides the point. The reason the hypothesis exists is because it is physically viable. Again, all we care about in this discussion.

Oh comeon. You're trying to pick on the L4/L5 idea by saying "this will only last a billion years" and now you come up with L3?

You're just making up your own scifi reality which is even more improbable

L3 can be made stable by resonances with other objects. L4/L5 cannot. The 8:13 near-resonance of Earth-Venus motion could have been offset into a true resonance with a planetary body at L3.

Now, feel free to remove your foot from your mouth.

[Kerbin Dallas Multipass]

Now, feel free to remove your foot from your mouth.

I'm not familiar with that idiom, sorry I don't know what it means.

And are you now moving Venus all over the place to make things happen?

[ZetaX]

L3 can be made stable by resonances with other objects.

I could not find anything on that, do you have a link¿ For all I know more objects generally only make it less stable.

[PakledHostage]

I'm not familiar with that idiom, sorry I don't know what it means.

According to the Leo online German-English dictionary, it means:

ins Fettnäpfchen treten

[K^2]

I could not find anything on that, do you have a link¿ For all I know more objects generally only make it less stable.

I can't find anything on L3 specifically right now. Here are some slides for a talk on L4/L5 resonances. The approach would be exactly the same. You'd start with a rotating frame, and try to figure out which resonances are going to be stabilizing and which are going to be de-stabilizing.

But in a nutshell, consider a very simple picture. Two objects of equal mass at each other's L3. Introduce a third object which is in 1:2 resonance with one of these. It is, obviously, in the 1:2 with the other body as well. This means that any drift of one of the two bodies results in interaction with the resonating body, which both restores the original perturbation and adjusts the second body to match it. Now, all you have to do is make sure that stabilizing effect of the 1:2 is greater than de-stabilizing of 1:1.

Now, it's entirely possible that I jumped the gun on 8:13 being capable of stabilizing an object in Earth's L3. It might depend on a huge number of factors. But it'd be interesting to investigate, at least.

[DJEN]

Don't bring moon creation theories into this man. There are like a million of those and each one is almost pure speculation.

Not really. But true somewhat.