The local time is read in the chosen place's own time zone, historical daylight saving included, and the place gives the story its Ascendant, Descendant, Midheaven and IC. Nothing you type is stored or sent anywhere except the city name, which goes to a public geocoder to look up its coordinates. Any moment from 1926 to 2126 can be told, the named asteroids included — a few of the near-Earth ones stand down at the far ends of that range, where their orbits stop being predictable, and the story says so when they do.