edit: Can you explain this line (from the beginning): "Whenever the date flips, it represents the point of least distance between the departure and destination planets."
I wasn't happy with the way I phrased that line. The dates represent the time at which two planets are at their periapsis (http://en.wikipedia.org/wiki/Apsis). This significantly reduces the time to travel between two planets. For the gas giants, this happens once every 172 years (http://tinyurl.com/d6r3rnn).
This is first shown at 3:15 when the date flips from 2153-02-27 to 2154-06-16, which marks the closest date that Mars and Jupiter approach each other. Voyager spacecraft were launched to take advantage of this relatively short distance.
The video is a small part of a longer video I had envisioned to excite kids about space exploration:
http://www.youtube.com/watch?v=wM0JMaM_tdQ
It uses time to give the viewer a feel for the expansiveness between the planets.