Ephemeris
A table of where celestial bodies are at each moment — or the code that computes one.
Every chart rests on an ephemeris. Once printed as thick books of tables, now an algorithm: give it an instant, get each body's longitude.
It has a precision limit. The one behind this site resolves to 1e-4°, ample for nearly everything, but not around a slow planet's station: Neptune moves about one arcsecond across that entire day, which falls inside the limit, so no minute-accurate time can be derived. Those events show "all day" on the calendar.
Dates here are computed at build time, not when you open the page. The ephemeris library is a few hundred kilobytes; there's no reason to ship it to every visitor, and no reason to compute the same date ten thousand times.