Two Questions:
1) Are rogue planets in motion, i.e. are they just wandering freely in space or stationary?
1) Do rogue planets have defined path or a one which can be anticipated? I understand that there cannot be at absolute rest as they are moving along with the galaxy.
2) Do rogue planets rotate around their axes?
If they are in motion, and they outnumber the stars in our galaxy, why our solar system never had a guest?
On the numbers
Rogue planets are thought to be more abundant than stars in the milky-way and depending on where you make the cut-off, rogue dwarf-planets for example, are expected to enormously outnumber the number of stars. older article quoting the MOA survey.
This article - OGLE survey, or, Portland's Optical Gravitational Lensing Experiment estimates:
Based on a statistical analysis of more than 2,600 microlensing events, drawn from six years of observations on about 50 million stars, the OGLE team estimates that there is perhaps one Jupiter-mass rogue planet for every four stars in the galaxy.
It's not an experiment it's a survey, but I guess they couldn't resist the name OGLE, so they went with that, so, props on the name, but I digress.
There's still some disagreement between MOA and OGLE, though I think the consensus is that OGLE gives a slightly better estimate of 1 Jupiter-mass rogue for every 4 stars.
Due to the nature solar-system formation, we expect that a number of planets get cast out during the early period and larger orbiting objects are good at casting out smaller ones when they pass to close, but it's almost impossible for smaller objects to cast out a larger one. We expect that the number of smaller rogue planets should increase significantly, perhaps even exponentially. But the OGLE survey had difficulty locating smaller planets, 1-10 Earth masses. That may be because they are more difficult to see, or they might be less common than expected.
Binary star systems, for example, with two or more much more massive than Jupiter objects could cast out larger objects like Jupiter-mass planets fairly easily, so there are significant unknowns on the number of smaller than Jupiter rogue planets. Estimates are high, observations are low. NASA's WFIRST might be powerful enough to resolve this after it's launch in 2020.
This article a study by the Kavli institute, suggests an aggressive estimate of 100,000 rogue-planets (or Nomad planets) for every star in the Milky-way, based on the 2011 MOA estimate of two Jupiter-Mass objects for every star and extrapolating based on how common Pluto sized objects are thought to be relative to Jupiter sized (about 50,000 to 1). If we adjust for the 1 to 4 instead of 2 to 1, that estimate is shaved down to about 12,000 pluto or larger rogue planets per star.
Whatever the real numbers are, if we count all the way down to dwarf planet size, Rogue planets should significantly outnumber stars and an estimate of 3-4 magnitudes isn't unreasonable. For planet sized, say Mercury to Neptune, better observations would help with this estimate a great deal, but a bad estimate of Mercury and up Rogue planets outnumbering stars 10 or 20 to 1 isn't crazy.
I'm fussing on the numbers because it's relevant to how many pass through the solar system. Using this question/answer as an approximation and because the escape velocity from a solar system is usually tiny compared to the escape velocity from a galaxy or the orbital speed around the galaxy, generally speaking, rogue planets should have star-like orbits around the Milky-way. If a star passes within one light-year of our sun about once every million years, even if you set a relatively high estimate of 100,000 rogue planets (pluto size and up), that's still one every 10 years, and that's within 1 light year. If you want to estimate within the Kuiper Belt - where we might expect to observe a pluto sized rogue planet passing through. The target area of the Kuiper belt is about a million times smaller than the 1 lightyear radius, so a rogue planet passing through the Kuiper belt - by this math, once every 10 million years.
The reason why it's never been observed is that they are usually very far away and too small to be noticed. Even with today's best equipment, it's nearly impossible to see a Pluto sized rogue planet passing through a lightyear or half a light year away and if they only pass through every 10 or 100 or more years, well, that's why we've never seen one.
It's possible, in our lifetime, someone might see one or two rogue planets pass within 1 light year of us, or inside the Oort cloud just past 1 light year, but we'll almost certainly need an upgrade in telescopes first.
on capture
In a two body system, gravitational capture is impossible and a rogue planet to our solar system is very much like a two body system. The problem is the rogue object accelerates towards the larger object (the star) and it adds velocity. That added velocity means it flies away just as fast. In a two body system, objects are either already in orbit or they fly past.
In a loose sense, all the stars in the galaxy create an N-body system where capture becomes possible, but the problem is that the stars are so far apart that any secondary body gravitational effects from other stars is close to negligible. The chance of Alpha Centauri (for example) slowing down an object so our Sun can catch it, is close to zero. If it happened at all, it would be a very distant and very tenuous capture. That's not to say it never happens. Over 4 billion years of our solar system, capture may have happened several times, but I wanted to point out why capture is difficult and likely rare. Most Rogue planets that got close enough would likely just pass through.
Capture becomes statistically more likely when a massive 3rd body is close.
If a Pluto-sized rogue planet passed close enough to one of our 4 large planets, or, the theoretical planet X, then it's direction and velocity could be significantly changed, and the odds of capture way up. Needless to say, those 4 planets and the theoretical "Planet Nine" make very tiny targets in the vastness of space, but that's one way capture could happen and over the 4 plus billion years the solar system's been around, capture probably has happened from time to time. The trick is getting a close enough look at distant orbiting objects to see if their chemistry indicates they aren't from our solar-system.
In addition to Rogue planet capture, when two stars pass close enough to each other, two stars exchanging Oort cloud objects probably happens too and might be the more common method of object exchange. Oort cloud objects already have a relatively slow orbital speed around their star which makes striping them away from one star and being captured by another, somewhat more likely. It would also depend on the relative velocity of the two stars also and how close they passed. But this method of exo-object capture might be quite a bit more common than rogue object capture.
If an object like Sedna is eventually identified as not being from our solar-system, it would be hard to know if it had been a rogue planet or a "stolen" object from the Oort or Kuiper belt from a close passing star from long ago.
1) this question has no real answer as it depends on the reference frame being used. It is very unlikely that they will be stationary except in their own reference frame.
rephrased 1) In theory their paths can be calculated precisely if you know their speed and the positions and motions of all other bodies (also gas and dust clouds) that might influence their motion. Practically, you will not have that knowledge, as most non-stellar bodies that the rogue planet may encounter will be very dim and you will not be able to detect them. On the other hand space is for the most part empty, so you might reasonably expect their paths to be quite predictable (within a limited time frame). They'll probably be in orbit (either an elliptical, parabolic, or hyperbolic) around the centre of the milky way.
2) yes, they will probably have some angular momentum left from where they formed.
Space is very large so it is not very likely that one will appear in our solar system in our lifetime. And of course we do not know if none ever moved through the solar system.
Relative to Earth, based on the movement of the Solar System through space, and the rotation of the Milky Way itself, 60 km/s or above is probably a good cutoff. While it's probably nearer 45 km/s, it doesn't really matter. Since one arrived, there is an "astronomically small" chance that another might. (pun intended)
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