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A star and planet can share a tropical zodiac longitude while sitting far apart in the visible sky. A paran asks a different question: at a given observing place, do their daily angular events happen at nearly the same clock time? One can be rising while the other culminates, or both can be setting. Latitude changes whether a star rises at all; longitude and local time rules determine when an event falls on the selected calendar day.
| Rising | The object's center crosses the eastern ideal horizon. |
|---|---|
| Setting | The center crosses the western ideal horizon. |
| Upper culmination | The object crosses the upper local meridian, reaching its highest daily altitude. |
| Lower culmination | The object crosses the opposite meridian; this event may be invisible below the horizon. |
Why a birth date is not a birth instant
A whole-day paran table finds event pairs sometime during that civil date. A star shown in a pair is not necessarily angular at the exact recorded birth minute. Our calculator gives the event time and the separation between star and planet events so a reader can distinguish those claims. It uses a selectable clock-time window rather than silently converting minutes into degrees.
Why place changes the list
The horizon depends on geographic latitude. Far-northern or far-southern stars can stay above or below a given observer's horizon. Rising and setting times therefore differ across places even when the two objects have the same equatorial coordinates. Meridian events use the observer's local hour angle, which the US Naval Observatory relates to sidereal time. An accurate recorded civil date also needs the historical UTC offset, including daylight saving when applicable.
What the table does not claim
The 20 selected stars come from the IAU name table. Their J2000 directions are treated as fixed for this modern 1900–2100 calculator; individual proper motions are not propagated. The rise and set criterion is geometric altitude zero, without refraction, terrain, or visibility testing. This is not a heliacal rising finder, a full sky catalogue, or a reproduction of a proprietary paran report. It offers a transparent astronomical comparison, not evidence that a star determines a person's life.
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.