A planetary paran in locational astrology is commonly shown as an east–west latitude band. Its geometric seed is a point where two natal angular lines meet. This guide explains why the band and the seed point answer different questions.
Four angular conditions
| ASC | The planet's center is on the eastern geometric horizon, rising. |
|---|---|
| DSC | The center is on the western geometric horizon, setting. |
| MC | The planet crosses the upper meridian. |
| IC | The planet crosses the lower meridian, possibly below the visible horizon. |
These are physical angular conditions in the sky at the same UTC instant. The planetary coordinates are not changed when the location is moved on Earth. All four conditions are checked for each planet; two different planets produce sixteen angle-pair searches.
From one crossing to a latitude band
An exact crossing solves both conditions at one latitude and longitude. Its dot on the map is simultaneously angular for both planets. Astrological paran practice treats the latitude of that dot as relevant across other longitudes, so the finder draws a horizontal band through it. The rest of the band is a locational interpretation, not another set of simultaneous angular crossings. A selected reference place can be far from the seed longitude yet close to its latitude; the table reports that north–south gap explicitly.
If two selected curves do not cross between 85°S and 85°N, this calculator reports no seed for that angle pair. It does not manufacture a band merely because both planets each have an angular longitude at the same latitude: that looser condition is true across broad latitude ranges and cannot identify a discrete paran. Continuous coincident meridian curves likewise have no single seed latitude.
The numerical geometry
For right ascension α, declination δ, and Greenwich sidereal angle G at birth, the MC longitude is α − G and IC is 180° farther around Earth. At latitude φ, the ideal horizon hour angle H satisfies cos H = −tan φ tan δ. The ASC longitude is α − G − H and DSC is α − G + H. Longitudes are wrapped to −180° through +180°. The solver compares two selected curves across latitude, brackets sign-changing longitude differences, then refines roots by bisection. It also checks local minima for tangent contacts and rejects false roots at the date-line wrap. Horizon roots are omitted where the cosine lies outside −1 to +1.
Displayed seeds stop at ±85° latitude. The reference gap is absolute latitude difference multiplied by approximately 111.195 km per degree on a sphere. It is a north–south comparison, not distance to an angular curve or actual travel distance. The map is an equirectangular projection using Natural Earth coastlines.
Birth details and limits
An incorrect birth time shifts angular lines in longitude. The historical UTC offset must be supplied; a modern city offset may be wrong for a past date. Atmospheric refraction, visible horizon height, topography, and polar regions beyond 85° are outside this geometric map. Apparent geocentric positions use Astronomy Engine 2.1.19 and the true equator of date. A paran is a traditional interpretive relationship and does not establish that living at a latitude causes an outcome.