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Recent results from Institute for Astronomy at the University of Hawaii at Manoa claim that there is a Jupiter-sized gas giant planet that is independent of a star about 80 light-years from Earth.
The press release refers to this planet as "free-floating" but I assume that it must be in some kind of predictable orbital path.
What is the orbital path of this newly discovered planet?
There is no "orbital path" detected, that's why it is a "free-floating planet". There is no radial velocity mesured, but the informations given by its kinematic location show that it belongs to the beta Pictoris group, that is a stellar group.
For more dirty details, have a look at the submitted paper on PSO J318.5-22: http://arxiv.org/abs/1310.0457
Comment: Apart from that (the following reflects my personal opinion) the term "free-floating planet" is ill-chosen; it is clearly a very low-mass object, but since it is not orbiting around another larger object, it seems to me that the term "planet" is not pertinent. I think that it should be consider more than a "very low-mass brown-dwarf". The problem arises from IAU definition of a brown-dwarf and a exoplanet, that is probably not well-fitted for this kind of objects (and that is not really physical). You will notice, by the way, that this object is moving in a stellar group, which kind of reinforce my point.
We don't know the full story about the trajectory of the rogue planet PSO J318.5-22, more observations are needed.
Even though (according to the article you linked in the question) the planet is not orbiting a star, it is moving with a stellar group. The The β Pictoris Moving Group (Zuckerman et al. 2001), which is
17 star systems, each with one or more characteristics indicative of extreme youth, that are moving through space together with β Pic.
This rogue planet orbits the center of the galaxy Milk Way, (or rather, the center of mass of the system PSO J318 - rest of MW, wherever it is localised) just like the Sun and the other stars.
But I think the details of this orbit, that is eccentricity, period, inclination, etc are not well known. If PSO J318.5-22 be confirmed as a Beta Pictoris association member, I guess it will have an orbit similar to the other members of this association/moving group.
I think it is incorrect to call this object a "free floating planet", or at least it is not clear at all that it is.
The mass of the object is based on (a) evolutionary models of the luminosity-mass relationship and (b an assumed age for the beta Pic moving group.
The first point gives at least factors of two uncertainty in the claimed mass. The second point contains (in my view) a systematic error in that the authors have used an outdated age of 12Myr for the beta Pic group. It has been revised (by myself and others) to about 21-24 Myr. This would make the estimated mass about 30-50% higher and so it would be $\geq 10$ times the mass of Jupiter and could easily be at a deuterium burning mass.
As far as an "orbit" goes, as this object is unassociated with another star directly, but is probably part of a co-moving kinematic group (the Beta Pic moving group), it will share the orbit of that group around our Galaxy.
