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realDonaldTrump suggested the following story:

https://iopscience.iop.org/article/10.3847/2515-5172/ab158e

Following their encounters with the outer planets in the 1970s and 1980s, Pioneers 10 and 11 and Voyagers 1 and 2 are now on escape trajectories out of the solar system. Although they will cease to operate long before encountering any stars (the Pioneers already have), it is nonetheless interesting to ask which stars they will pass closest to in the next few million years. We answer this here using the accurate 3D positions and 3D velocities of 7.2 million stars in the second Gaia data release (GDR2, Gaia Collaboration 2018), supplemented with radial velocities for 222,000 additional stars obtained from Simbad.3

We adopt the same method we used for tracing the possible origin (and future encounters) of the interstellar object 'Oumuamua (Bailer-Jones et al. 2018a). We determine the asymptotic trajectories of the four spacecraft by starting from their ephemerides from JPL's Horizons system,4 propagating them numerically to the year 2900, and then extrapolating to the asymptote. Using a linear motion approximation we then identify those stars which approach within 15 pc of each spacecraft (~4500 stars in each case). Finally, we integrate the orbits of these stars and the spacecraft through a Galactic potential and identify close encounters. Statistics of the encounter time, separation, and velocity are obtained by resampling the covariance of the stellar data and integrating the orbits of the resulting samples. The uncertainties on the asymptotic spacecraft trajectories are negligible compared to those of the stars, and are therefore neglected.

Meanwhile, Fox gives us the following:

....the next star that Voyager 1 will pass will be Earth's nearest stellar neighbor, Proxima Centauri, in 16,700 years. However, this encounter will be unremarkable, as the craft's closest approach will be 1.1 parsecs (pc) from the star, which equates to 3.59 light-years — very, very far away. In fact, Voyager 1 is currently 1.3 pc (4.24 light-years) from the star, so this encounter won't be much closer than the craft's current location is. (Earth's sun is 1.29 pc, or 4.24 light-years, away from Proxima Centauri.)

Voyager 2 and Pioneer 11's next close encounters will also be with Proxima Centauri, while Pioneer 10's next flyby will be with the star Ross 248, a small star 10.3 light-years from Earth in the constellation Andromeda.

Original Submission