This was inspired by the Nibiru thread. There are some ways of looking for extra planets, and it's worth taking a look at them.

* Reflected sunlight. This is good for anything that is not too far away from the Sun. The observed luminosity ~ (radius)^2/(distance)^4, meaning that the minimum detectable radius goes up as (distance)^2. The farthest directly-observed objects are the Kuiper-Belt ones, which have Pluto as their largest member. Comets may come from greater distances, but they are not observed at such disances.

So it would be difficult to observe an Earth-sized planet much beyond Pluto; however, such a planet would be very cold, and its inhabitants would have to live in protected environments that are little different from free-flying spacecraft. So why suffer from planetary chauvinism? To use a term coined by Isaac Asimov and Gerard K. O'Neill.

* Thermal emissions. This requires a body with a significant amount of internal heat, which would have to be at least as massive as Jupiter. However, Jupiter is close to the largest "cold" object with its composition, "cold" meaning not hot enough for temperature to contribute a significant amount of pressure. Meaning that a several-Jupiter-mass brown dwarf would be smaller than Jupiter.

* Gravitational effects. Extra Solar-System mass would perturb the orbits of known SS objects, and observed-calculated discrepancies could be used to search for new objects. Alternately, upper limits on such discrepancies could be used to set upper limits on such extra mass. Famous examples:

Mercury's excess perihelion advance. A logical hypothesis was intra-Mercurian planets, but no objects with sufficient size were ever found. However, General Relativity predicts extra gravitational effects with the expected size.

Neptune from Uranus discrepancies. A success.

Pluto from Neptune's discrepancies. Pluto turned out to be too low-mass to cause those discrepancies, and improved outer-planet mass estimates resulting from spacecraft flybys successfully eliminated those discrepancies.

The supposed planet "Clarion", an Earthlike planet which orbits in Earth's orbit on the opposite side of the Sun. It would produce very noticeable perturbations of the nearby planets' orbits in only a century, and it would have a noticeable effect on interplanetary satellites' orbits (something like 1 arcsecond per year). But such effects are not observed.

And this is very likely correct for all of the Solar System inside of Neptune's orbit, meaning that extra Earths could only exist in the very cold outer reaches of the Solar System, in the Kuiper Belt and beyond.

An indirect hint is provided by Milankovitch climate cycles, which are connected to Earth-orbit perturbation oscillations; wandering Earth-like planets would likely disrupt those cycles.

Finally, according to a certain Truman Bethurum, Clarion is the home base of a flying-saucer pilot named Aura Rhanes, who looks like an Earthwoman who is "tops in shapeliness and beauty".

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Why doesn't anyone report UFOnauts that look like big mechanical spiders? [img]/phpBB/images/smiles/icon_razz.gif[/img]

Could you give a cite for this? It's counterintuitive to me. I'd think that any internal heating would cause expansion pressure that would tend to increase the size of a brown dwarf.

In fact, this was an early suggestion for the source of the Sun's energy output: continued gravitational contraction, opposed by internal pressure from heating. Unfortunately, that only kept a star shining for a few millennia; and it required a dense sun (iron) even for that. When the Sun was found to be mostly hydrogen, the gravitational heating theory fell apart.

Anyhow, I'd like to understand how an object with several times Jupiter's mass, and greater internal heating, could be smaller and denser than Jupiter. (Assuming similar compositions, of course.)

Only true if they went there from here. In the unlikely event that life had actually begun there however, it would have evolved to live openly in that environment.

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Actually, Earth would be a piece of cake at Pluto's orbit; it would be very roughly 11th magnitude or so: easy to find in an amateur 'scope. At twice Pluto's distance it would start to get tough, in a small 'scope. However, the big trans-Neptunian object surveys would find it pretty easily.

There is a great webpage discussing hypothetical planets at http://seds.lpl.arizona.edu/nineplan...nets/hypo.html

OK, so what would be hard to detect and still have the mass in question. I know I'm being a pain indy butt, but I didn't get satisfactory answers in my "Space Junque" thread before it was axed. I'm very curious about the missing mass business and this seems to be walking along a parallel branch of the same path.

I'm reluctant to believe in what I call "Magic Matter" and black holes are almost cliche at this point. Help me Obiwan!

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Here's a simple answer to the more-massive-yet-smaller question for "cold" objects:

In ordinary matter, electrons are held to nuclei by their electrostatic attraction, an effect that generates atomic structure. But electrons screen out nearby nuclei, meaning that this effect is non-cumulative for large objects.

But gravity is cumulative over an entire object, and a more massive object has greater gravitational force, enough to make it smaller if gravitational effects are stronger than electrostatic ones. In effect, the atomic structure gets crushed.

Growth, then shrinkage with increasing mass implies that there is a maximum-size mass, and that mass is approximately the mass of Jupiter. And this shrinkage also explains why solar-mass white dwarfs are approximately Earth-sized; white dwarfs are relatively cold.

I can use some simple algebra to get some approximate numbers if anyone desires.

What do you mean by:

"The atomic structure gets crushed"?

As far as I'm aware this only happens under the conditions that produce a neutron star, which is an entirely different beast.

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Up the Imps!

I think lpetrich means "partially crushed" -- the electron orbits get smaller, and the atoms pack closer together, but there's no actual degenerate matter (nuclei with no electron shells at all)... right?

By the way, thanks. I was not aware of that mass/density relationship, and that our solar system contains an example of an object near the peak of the curve.

Sorry to be a bore, Ipetritch, but have you got any references for that effect - it's not one I'm familiar with and I'd like to see the standard work on it.

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Relatively cold? If compared to other stars then white dwarves are extremely hot, with a surface temperature of something like 2-3 times as hot as our Sun IIRC. If they were in fact colder then our sun we would call them orange or red dwarves, becuase that's the way they would look.

First off, degenerate matter can still have free electrons; in that state, it is essentially a squeezed metal. And that's what most of a white dwarf is.

Also, I have used a special definition of "cold" here -- temperature being low to contribute significant internal pressure. By that definition, a white dwarf is cold.

And as to good nontechnical references to how degenerate matter works, I don't know of any offhand.

Maybe we ought to have some sections on stellar structure, both nontechnical and with simple algebra.

In general the minimum brown dwarf mass is about 11 times the mass of Jupiter (according to the models). Above this the core temperature and pressure is enough for a period of deuterium fusion into helium. This period is shorter than the lifetime of full-fledged stars, so older brown dwarfs can get "cold" too. Below the 11-Jupiter-mass cutoff no fusion occurs, so gravitational collapse is the most important source of heat.

Brown dwarfs, if defined as objects than ever fused deuterium, would range from 11 Jupiter masses to 65-85 Jupiter masses. This upper limit is more dependent on composition, and is the lower limit for fusing regular hydrogen into helium, i.e., a real star.

For sub-stellar objects, age is as important a factor as size in determining internal heat.

The fact that objects of several Jupiter masses could be smaller than Jupiter is a matter of phase transitions (transitions of matter under pressure to a more compact state) and is not necessarily related to whether or not fusion occurs.

As far as Jupiter being close to the largest possible "cold" object, bear in mind that it's shy by a factor of ten. That's close in terms of the scale of the universe, but Jupiter has only 9% of the mass needed to "burn" deuterium and only 1% of the mass needed to be a star.

Bob Johnston
http://www.johnstonsarchive.net

When I mentioned Jupiter being the largest relatively-cold object, I had in mind physical size and not mass.

OK, that makes sense. And that really is an interesting point--that in terms of diameter, planets don't get much larger than Jupiter (unless you catch them very young).

Bob Johnston
http://www.johnstonsarchive.net