Western Astrology uses the time, place, and date of birth to determine what influences are present at the birth time and imprint on the person for the rest of their life.
Through a series of different charts, influences can be determined at different points in life (transits) and with different people and situations. This is by cross referencing the chart of the involved person(s) and/or the chart of the event.
Synastry is a specialized Western Astrology chart comparing the charts of two people based on the time, place, and date of birth. If the time is not known, a chart can still be cast.