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Obviously, it's now an essentially inert artifact not going anywhere under its own thrust. The perihelion of 67P is about 20% larger than Earth's aphelion. Assuming its orbit is stable, neither the comet nor any debris or human artifact it may shed could be expected to come anywhere near Earth. But, is its orbit stable? If not, in what way is it changing? Would it get closer to Earth in the future - perhaps centuries or millenia from now?

Anthony X
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I used the JPL Horizons database and downloaded the predicted positions (state vectors) of Earth and Comet 67P at 10 day intervals from 1600-Jan-01 to 2500-Dec-01.

edit: As @pericynthion pointed out in comments, since comets are subject to various non-gravitational forces, including "propulsion" by gasses vented unevenly and unpredictably by the rotating (and potentially wobbly) comet, long term predictions are not necessarily as reliable as they would be for far more massive planets. I'll see what I can to do find out more about this particular ephemeris for this particularly well-characterized comet that never gets closer than 1.2 AU from the sun (within this prediction).

In the case of the ephemeris I've used here, the three Marsden non-gravitational force parameters $A_1, A_2, A_3$ are shown and presumably are active. This is an empirical way to try to parameterize and approximate all of the forces besides gravity that affect a comet's orbit.

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Here are the results. I'm not sure this answers your question yet. It's a good question - why there are a series of closer approaches between the years 1950 and 2200, and the answer is what it usually is - Jupiter! A close approach around 1959 bumps it into an orbit that occasionally gets ear earth, and later another close approach around 2209 bumps it out again. That darn Jupiter, always keeping things interesting!

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uhoh
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    Orbit perturbations from cometary activity is not modeled by the kernels used in HORIZONS (indeed, it's virtually impossible to predict with any accuracy) and will make the current ephemeris progressively less valid over time. I would guess (and it's just a guess) that 2209 is far enough in the future as to make the prediction of the Jupiter encounter completely unreliable. – pericynthion Oct 01 '16 at 07:49
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    @pericynthion can you support this with a citation about 67P rather than generalizations, speculation and prose? I think you are just muddying the water here for other readers. This question is about 67P. I mention Philae and Rosetta because they provided high precision distance and velocity measurements of the comet for two years, including a pass through one perihelion. Combined with 47 years astrometry of 67P starting in 1969, and the fact that perihelion is always beyond 1.2 AU, this comet has a better-than-typical ephemeris. – uhoh Oct 01 '16 at 22:38
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    This is basic dynamics, applicable to all comets as well as many other dynamical systems. It's a little hard to find references that are both specific to 67P and spell out such basic concepts, but here are some starting points: https://arxiv.org/pdf/1412.1983.pdf (note this paper shows that 67P's trajectory is chaotic) http://www.ifa.hawaii.edu/UHNAI/ws/readings/7029_duncan.pdf http://www.lpi.usra.edu/books/CometsII/7009.pdf https://arxiv.org/abs/1606.07037 http://ftp.astro.umd.edu/pub/groussin/groussin14Aug06.pdf – pericynthion Oct 01 '16 at 22:54
  • Let us continue this discussion in chat. – pericynthion Oct 02 '16 at 00:05
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    @pericynthion apparently orbit perturbations from cometary activity IS in fact modeled here - in this ephemeris for this comet - via the standard Marsden parameters - please see edit. The data arc: 1995-07-03 to 2016-05-30 used to generate this solution includes 6311 separate measurements that span three sequential passes through perihelion. Read more here - search for "A3" for example. – uhoh Oct 04 '16 at 02:31
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    @pericynthion While of course it is an approximation, is your first sentence "Orbit perturbations from cometary activity is not modeled by the kernels used in HORIZONS" really accurate? – uhoh Oct 04 '16 at 02:36
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    I've asked a related question about 67P's Marsden parameters post-Rosetta. – uhoh Oct 04 '16 at 03:49