What the calculation means
A paran is a coincidence in time: a named star and a planet each cross a local horizon or meridian within the chosen window. This table checks the whole selected local civil day, using the latitude, longitude, and historical UTC offset supplied above. It is different from comparing zodiac longitudes. It also differs from a birth-time angular check: a listed pair may occur hours away from any particular recorded birth time.
Rising and setting mean the centers cross the ideal geometric horizon at altitude 0°. Upper culmination means the upper meridian crossing; lower culmination means the opposite crossing and can be below the horizon. The sample is 20 named IAU stars and ten solar-system bodies. Atmospheric refraction, hills, buildings, visibility, stellar proper motion, and heliacal phases are omitted. Events within a few minutes of the cutoff should be treated as approximate.
The calculator applies one UTC offset to a 24-hour local day. A day on which daylight saving time starts or ends can be 23 or 25 hours long; this simple table does not model that clock change. For those dates, check an authoritative local time-zone record before using the first or last hour of the result.
The method uses the IAU published star coordinates and Astronomy Engine event searches. The US Naval Observatory explains the relation between sidereal time and meridian transit.