  Cosmological simulations have been used to study interacting galaxies as a
function of galaxy pair separation, enabling comparisons with observational
studies of galaxy pairs. The study of interacting galaxies as a function of
time (i.e. merger stage) has mostly been limited to high resolution merger
simulations, due to the poor time sampling available in cosmological
simulations. Building on an earlier study of galaxy pairs in the IllustrisTNG
cosmological simulations, we reconstruct the orbits of galaxy pairs involving
massive galaxies ($M_* > 10^{10}M_{\odot}$) at redshifts of $0 \leq z < 1$,
using a novel kinematic interpolation scheme to model the orbits in between the
IllustrisTNG snapshots (which are separated by 162 Myr on average). We assess
the accuracy of these interpolations using a pre-existing suite of merger
simulations, and find that kinematic interpolations provide a remarkable
improvement in accuracy compared with interpolations that use only radial
separations or 3D positions. We find that nearly 90 per cent of the closest
pairs ($r < 25$ kpc) have had a pericentre encounter within the past Gyr. Many
of these close pairs are found on rapidly shrinking orbits, and roughly 85 per
cent of these pairs will merge within 1 Gyr. However, approximately 3 per cent
of these close pairs appear to be flyby systems that will never merge. These
reconstructed orbits will be used in future studies to investigate how and when
galaxy properties change during close encounters and mergers between galaxies
in IllustrisTNG.
