This thead was motivated by recent posts in the Nemesis: BS or what? thread, in the ATM section.

What are the (scientific) techniques which can - in principle - be used to search for a 'Nemesis' or a 'Planet X' or another Sedna/Buffy or ...? What are the strengths and weaknesses of such techniques?

In terms of the total parameter space of 'unseen companions', what regions are most certainly empty? What are totally unexplored?

A definition to constrain the scope of this thread: the 'unseen companion' must be gravitationally bound to the solar system/Sun, and have been so for at least 1 billion years; however it may be more massive than the Sun.

The parameter space relevant to this thread is, essentially, the six plus orbital elements needed to specify the orbit of any unseen companion; physical data about any such companion (e.g. mean density, albedo, size, temperature) would also be of interest, but are not the primary parameters.

I'll go first, with a negative. The fossil record of mass extinction, alone, is a very poor technique for constraining regions in the parameter space. Not only is it difficult to get a good signal from such a record, but the link from a well-documented set of periodic mass extinctions (should we have one) and the orbit of any unseen companion is quite indirect.

[Note that there is aleady as separate thread on the status of the Nemesis hypothesis, in terms of mass extinction periodicities in the fossil record, here.]

If we would have a massive (brown dwarf or larger) companion, i.e. if we would be a binary star, then wouldn't the motion of the sun around the common barycenter be obvious with regards to the "background" (the Milky Way and nearby stars in it)? Hence, if the Sun has a fairly fluid motion around the centre of the Milky Way, with only a minor wobble caused by the gravity of Jupiter and so on, then no massive companion for the Sun can exist.
Just some thoughts, I haven't researched this in any way...

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A small segment of a very large ellipse might be indistinguishable from a line segment. If the unseen companion would be at 10,000 Astronomical Units from the Sun, and would have an orbital period of 1,000,000 years, we might need more than a few hundred years of observation to notice the variations caused by it of the Sun's direction of motion.

But it should be possible, from existing observations, to put some upper limit to the companion's mass divided by some function (the cube, I think) of its distance.

This Background and Motivation discusses various aspects of the unseen companion hypothesis as well as proposes some observing techniques.

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It's an interesting DRAFT paper, but I can't see how it relates to Nemesis, Buffy2, Sedna2, Planet X, or whatever (i.e. an 'unseen companion' for our solar system/Sun). I confess that I merely skimmed the 35 pages - would you be so kind as to explain how this paper addresses Nemesis/Planet X/Buffy2/...?

No one's mentioned it yet ... what about a survey, of the trignometric parallaxes of all stars, down to Vmag ~ x?

The advantage of such a technique is that if there is a solar system companion which has a V <~ x during the survey period, it would very, very likely be detected.

Of course, several such surveys have been conducted, the most precise (in terms of measured parallax) is HIPPARCOS.

Anyone want to take a stab at saying what regions of parameter space the results from HIPPARCOS (both the HIP and Tycho catalogues) rule out (re any unseen companion)?

Any offers, re other techniques?

If there are many such objects at random orbits, the effects would cancel out. To simplify, imagine a brown dwarf or super-jup on each side of the sun with the same period. The sun would not wobble from that.

Even if the Sun wobbled due to some massive object >1000 AU, the Earth and the rest of the planets would wobble with it and we would not notice the wobble.

I considered it relevant here, but maybe it isn't.

Sorry, I'll restrict my posts to one thread for now.

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"Where the telescope ends, the microscope begins. Which of the two has the greater view?" - Hugo

"Men occasionally stumble over the truth, but most pick themselves up and hurry off as if nothing had happened." - Churchill

Oh yes, we would, because the background (the stars, galaxies, ...) does not wobble with us.

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Only in some extraordinary cases, like really clouds, rings, of objects, like Oort and Kuiper. But we are talking here about companion stars or huge planets (Neptune size or larger), and the chance that those come in a cloud or belt or so is minimal, I think. In most cases, the effects would not cancel out, and we would have some complicated but detectable movements instead of a wobble.

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I don't think anyone has mentioned that for the larger objects (Neptune sized or larger) we might see an impact on the orbit of Neptune or Pluto or Sedna or the new "planet".

This wouldn't be the case with more Pluto sized objects.

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They're too far away. When you drive down the freeway and the Moon is on the horizon, it appears to follow your car. If you drove forward 1 block, reversed 1 block, etc, the Moon would "follow" you. If you considered the Moon's position with respect to another stationary passenger in the car, it would appear not to move. You would not be able to discern the car's "wobbling" motion by looking at something "wobbling" with you against a background at infinity.

But if another person in the car were jumping between the front and back seat, you'd notice their movement relative to the Moon. They would be "wobbling" independent of you and you would notice them wobble against a background at infinity.

So if the Earth wobbled independent of the Sun, we could notice the Sun wobbling against the background stars. But if the Earth wobbled with the Sun, we would not notice the wobble.

No. To take your Moon example: you don't see the Moon move, but you see the foreground move wrt to the Moon. The moon is behind some trees, you drive 100 metres, and now the moon is above those trees. The trees may look just as big as they did before to the naked eye, and the Moon is certainly just as big to the naked eye, but their relative positions have changed.
In the same way, we would see the Sun, the Moon, and the other planets move with regards to the background.
Plus, our measurements are precise enough to notice such a wobble anyway, even without comparing to foreground objects.

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Knowledge is a curse, but ignorance is worse

That's because the trees didn't "wobble" with you. If you drove 100 meters, and the trees shifted 100 meters in the same direction, you wouldn't notice them move against the background moon. Just as if the Sun wobbled 1 AU and the Earth wobbled 1AU with it, you would see no change relative to the background.

With current techinques, the parallax of close stars would be hard to measure simply because of the period of the wobble. The parallax of distant stars and galaxies would not be detectable at all.

My background idea with the trees wasn't to clear, but apart from that: we can't all wobble the same distance. That's no wobble, that's a shift.
Let's say the Sun has a slight wobble, from O to O. To keep the ecliptic looking as if nothing has changed, Mercury would have to rise a short distance, Venus a bit more, etcetera. Of course, they would all change by the same degree, but the distance would be different. So the Sun and the Earth both wobbling 1 AU is not really realistic.
Now, if that wobble was e.g. 1 arcsecond, then the position of the stars would be of by 1 arcsecond at the most, and the circle they described at night (visually, I mean) would be different. We wouldn't notice that with the naked eye, but astronomers would know.
It's like driving from the flat up a hill, with Sirius right in front of you. You have only to drive a few metres to see the position of Sirius change drastically, as you are tilted. It looks like Sirius suddenly drops a lot. This is the effect I try to describe and I except you would get when the Earth would wobble. Of course thiswould happen much slower and less dramatic, but it would be noticeable and noticed.

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I'm not quite sure I follow your last explanation. But if you saying that the Sun and Earth wouldn't wobble at the exact same rate, I can agree with that. But I think it would be close enough to escape detection.

What I mean (and I'm not very good at explaining it) is that if the whole solar system wobbles, then you have a central point that doesn't move (an axis for the wobble), and everything around it moves "up" and "down", and the further you are of that axis point, the more distance you move. The position of all planets and the Sun relative to one another stays the same.
Now, if you are on the Earth, and you look at a star that is more or less straight towards (well, beyond) the axis point, then even a very slight wobble will be immediately clear, as that star will move "up" or "down" in your view as well, just like when you go from a flat to a slope while looking at the Moon in front of you.

I don't think my view that the movement would be quite clear for every astronomer (depending on how large a wobble it is of course) is wrong, but perhaps my idea of what a wobble is, is wrong. If e.g. it is not the tilt of the axis that changes, but the height position of the system (both seen with e.g. the galactic plane as a baseline), then the result may be quite different.

I hope I'm a bit clearer now...

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