a hidden planet in a lagrange point

[DJEN]

Oh come on. 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.

Your comment doesn't make sense that much.

[DJEN]

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?

...You don't understand...

[tntristan12]

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

For the restricted three body problem, sure. But the case of three bodies in an equilateral triangle is stable in the general three body problem too. This was one of Newton's solutions to the three body problem, and he came up with two - three in a straight line, and three in an equilateral triangle. The only assumptions made are constant angular velocity of the system (which would hold in this case), and fixed distances between each body (which, since it's an equilateral triangle, would also hold). It works for the restricted three body problem because that is a subset of the general three body problem.

That or my advanced astrodynamics professor last semester was lying to us.

[MC.STEEL]

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?

I want it close to earth so you can reach it easily with 2040s technology and i forgot to say that it has a breathable atmosphere of 40% oxygen, 45%nitrogen and 15% innert gasses and CO2 and has a small ecosistem witch makes it even more easy to spot i bet.

So as such a planet is allready imposible what about making it even smaller like our moon with a solid core of ununpentium:P(yes i know it would decay fast),would that make it harder to spot?

[DaveofDefeat]

I'll leave you with a wonderful Scott Manley video to show an example of how hard it would be to hide such a large object.

All of those are teeny tiny rocks, and we still find thousands of them.

[Ralathon]

I want it close to earth so you can reach it easily with 2040s technology and i forgot to say that it has a breathable atmosphere of 40% oxygen, 45%nitrogen and 15% innert gasses and CO2 and has a small ecosistem witch makes it even more easy to spot i bet.

So as such a planet is allready imposible what about making it even smaller like our moon with a solid core of ununpentium:P(yes i know it would decay fast),would that make it harder to spot?

Can't you just dump the new planet and make Venus the setting? Just say that beneath the clouds of acid the atmosphere calms down and there is life. This would be so much harder to spot from earth that you could probably keep it a secret.

The first sovjet probe that went down to venus's surface had a lock made of sugar in case it fell into water for example. They really didn't know what was below the cloud cover until a few decades ago. This requires a lot less physical impossibilities than a moon sized object with earth's surface gravity in a unstable orbit with life on the surface that was somehow missed by the entire world for 10k years.

[Scotius]

Just say that Aliens did it . Make this obiect an artificial planet/station with gravity generators and stealth cloak. You will have your McGuffin without gutting laws of physics as we know them.

[MC.STEEL]

Just say that Aliens did it . Make this obiect an artificial planet/station with gravity generators and stealth cloak. You will have your McGuffin without gutting laws of physics as we know them.

I was seriously thinking about that at a time

but hiding a planet isnt such a hard task,not everyone looks at the speck in the sky and wonders what is that, professional and backyard astronomers who do try so disclose this secret find themselfes in a corporate ****storm

[Kryten]

If we're still talking something big enough to have a breathable atmosphere, at that distance it'd be one of the brightest objects in the entire sky.

[Awaras]

I was seriously thinking about that at a time

but hiding a planet isnt such a hard task,not everyone looks at the speck in the sky and wonders what is that, professional and backyard astronomers who do try so disclose this secret find themselfes in a corporate ****storm

It would be spotted and well known since ancient times. Anybody with a telescope or larger binoculars would be able to see it. The conspiracy to keep it secret would have to be orders of magnitude more elaborate than the one needed to supposedly fake a moon landing and keep it a secret all this time, and that is ridiculously implausible already...

Edited January 25, 2014 by Awaras

[Ralathon]

It would be spotted and well known since ancient times. Anybody with a telescope or larger binoculars would be able to see it. The conspiracy to keep it secret would have to be orders of magnitude more elaborate than the one needed to supposedly fake a moon landing and keep it a secret all this time, and that is ridiculously implausible already...

Trying to hide a planet like that is equivalent to trying to hide that the earth is round. Anyone with common sense and basic equipment can figure it out. There are waaaay too many people who could expose the secret.

[Awaras]

Trying to hide a planet like that is equivalent to trying to hide that the earth is round. Anyone with common sense and basic equipment can figure it out. There are waaaay too many people who could expose the secret.

And yet there are people like this:

http://en.wikipedia.org/wiki/Flat_Earth_Society

No conspiracy is too large to be unbelievable to some people...

[MC.STEEL]

So its apparently going to be around the brightness of Venus by your description.

there it goes out the window

And whe allready broke the plausibility of gravity but what if it is hidden by a forming moon (a larger boulder and a smog of dust thats not in an orderly ring) so it obscures the planet.

I know the ring has to be very VERY dense but it would make for some great planetary views.

and btw it would probably still be visible by radio telescopes.

Edited January 25, 2014 by MC.STEEL

[K^2]

For the restricted three body problem, sure. But the case of three bodies in an equilateral triangle is stable in the general three body problem too. This was one of Newton's solutions to the three body problem, and he came up with two - three in a straight line, and three in an equilateral triangle. The only assumptions made are constant angular velocity of the system (which would hold in this case), and fixed distances between each body (which, since it's an equilateral triangle, would also hold). It works for the restricted three body problem because that is a subset of the general three body problem.

Three in a line definitely is not stable. These are equilibria, certainly, but are you sure you recall correctly about stability? Three bodies arranged in equilateral triangle are not stable in general. Somewhat stable arrangements obviously exist, but it isn't true in general. For example, if all 3 bodies are of equal mass, the arrangement is unstable. (Take a look at article on Klemperer Rosette.)

[ZetaX]

This reminds me of "gravity juggling", which generalizes the above: you want a set of n (punctual) moving masses in space and such that gravity makes this arrangement periodic, i.e. being the same after a finite amount of time. Some examples are given in the book "The Mathematics of Juggling", but you can probably also find some papers on that. Obviously, such systems are almost always inherently unstable.

[Nibb31]

A Counter Earth at L3 is a pretty classic sci-fi plot device. It's not entirely plausible, but as science-fiction goes, suspension of disbelief works as long as the story is good enough.

[tntristan12]

Three in a line definitely is not stable. These are equilibria, certainly, but are you sure you recall correctly about stability? Three bodies arranged in equilateral triangle are not stable in general. Somewhat stable arrangements obviously exist, but it isn't true in general. For example, if all 3 bodies are of equal mass, the arrangement is unstable. (Take a look at article on Klemperer Rosette.)

I'd need to bust out my notes from last semester to get the actual mass ratios, but in general three bodies in line can be stable if the mass ratios between the three is within a certain range. However, it is definitely true that three in an equilateral triangle is stable for any range of masses. However, in the solar system there is also the fact to consider that other planets will be exerting non-negligible forces on the small third body, which could cause destabilization of a body at that point on an astronomical time scale (hundreds of millions to billions of years). I'll admit that taking one class on the subject doesn't make me an expert, but I'm pretty sure that if the body was small enough (mercury sized as the OP claims) it wouldn't destabilize the system.

[K^2]

However, it is definitely true that three in an equilateral triangle is stable for any range of masses.

That is absolutely wrong. I think you might be confusing stability with equilibrium. I've given you an example where three masses arranged in equilateral triangle are unstable, which can be shown with the most basic perturbation analysis of the effective potential. Three bodies in a line are never stable, as far as I know. They do have an equilibrium if certain conditions are met, and three bodies in an equilateral triangle arrangement are always in equilibrium. Finally, equilibrium is the only thing that Newton looked at. So check your notes, but if I had to bet, I'd say you just mixed these two up.

I'm more and more puzzled that I can't find any papers on resonance stability of L3 specifically. It's not a trivial matter, but it's not exactly a problem of the century, either. If I can't find anything, I might have to write it.