This video shows the orbital motions in the triple system. The orbits are drawn to scale, showing the actual motions of the two stars (red and yellow) and the pulsar (white). The first ten seconds are played relatively slowly, showing the motion around the inner orbit, then we speed up to see the motion around the outer orbit. For a sense of the time scale, an "MJD" is a modified Julian day, so a single day long. The larger left panel shows all three bodies, with trails marking the motion of the outer companion and the center of mass of the inner system. The inset in the top right zooms in on the inner system, showing the pulsar and the companion, with trails marking their orbits. The dots that appear on the orbits mark moments when we have observations of the system, color-coded by telescope; it should be clear that we have quite thorough coverage of both orbits. Each measurement tells us the distance to the pulsar to within a kilometer, so that we can measure the tiny deviations of these orbits from perfect Keplerian ellipses, allowing us to reconstruct the orbit.
There's a little more to it than that.
More specifically, this video shows the system face-on, but in fact it's tilted about forty degrees, so we're seeing it at an angle. And, so far, we can't actually see anything move on the sky (though we're close! Maybe by the end of next week, preliminarily, but that's a whole other story). So what we actually measure, at each dot, is just how far the pulsar is from us - it's a little like knowing only the height of the white dot, only at the moments of our observations, and still being able to reconstruct the whole orbit. Some things are easy: the orbital periods, for example, you can just read off the pulse arrival times, how long it takes to go from early to late to early again. But you don't, for example, know how much it's tilted, so under normal circumstances you can't tell whether it's a small system seen edge on or a big system seen almost face-on. Here, though, the tiny deviations from elliptical orbits - too small to see in this animation, though I do draw them - are enough to measure, and modelling the measurements has allowed me to determine everything I show here.
The NRAO made a much glitzier video, but I think it's a little confusing. It would be really interesting to work on something like this with someone with the artistic talent that I lack, to try to make a video that was both neat-looking and informative.