Every number here is old news
Radio travels at the speed of light, \(c \approx 299{,}792\) km/s — fast, but space is big. The signal time on each card is
where \(d\) is the spacecraft's distance from Earth. A command sent to Voyager 1 takes most of a day to arrive, and its reply takes as long again. Whatever you see from it has already happened.
Why a distance from Earth wobbles
Each spacecraft's position is measured from the Sun, but we listen from Earth, and Earth is circling the Sun at about 30 km/s. Voyager 1 only moves outward at about 17 km/s, so for a few months each year Earth swings towards it faster than it flies away — and its distance from us shrinks even though it's still leaving the Solar System.
Borrowing speed from planets
Europa Clipper, Juice, Psyche and Lucy all fly past planets — even Earth — on purpose. In a gravity assist the spacecraft falls towards a moving planet and is flung out the other side. In the planet's frame its speed in and out is the same; in the Sun's frame it picks up some of the planet's orbital motion. The planet slows down by an immeasurably tiny amount to pay for it.
How the map is drawn
Positions come from NASA JPL's Horizons system, which holds the navigation teams' latest trajectory for each spacecraft. We fetch one point a day and join them with curves that follow each spacecraft's velocity (cubic Hermite interpolation). The planets come from the same Keplerian orbits used on Tonight's sky. Seen from above, the Solar System is mostly empty — so the Whole fleet view squashes distance with a logarithm to fit Voyager and Mercury on one screen.
Try it yourself: the orbit simulator experiment builds a tiny version of the same idea.