What counts as a crossing?
A natal angular line connects all mapped observing places where one planet met one angular condition at the same birth instant. The Sun MC line, for example, is the meridian longitude where the Sun was on the upper meridian. A second planet’s rising or setting curve can meet that line at a particular latitude. At a mapped intersection, both selected angular conditions hold at one latitude and one longitude. The finder reports that coordinate, not a country ranking or an influence radius.
This independent calculator focuses on a selected pair so the geometry and result stay legible. It includes the Sun, Moon, and eight planets used by this site’s planetary-line engine. It does not include lunar nodes, asteroids, fixed stars, or a complete all-pairs crossing atlas.
How the intersections are solved
Enter the recorded local birth date, time, and historical offset at the original birthplace. The tool converts those fields to UTC and obtains apparent geocentric right ascension and declination and Greenwich sidereal time through Astronomy Engine. At any latitude, an MC curve has longitude right ascension minus sidereal angle; an IC curve is 180° opposite. Rising and setting longitudes come from the geometric horizon equation, with the two hour-angle signs selecting eastern and western horizon branches.
For a selected pair, the calculator samples the longitudes every quarter degree of latitude from 85°S to 85°N, restricted further where either horizon condition is impossible. It searches for a zero of the wrapped longitude difference, refines sign-changing roots by bisection, and searches local near-zero minima for touching curves. Longitude wrap at the date line is handled as a 360° coordinate seam, not counted as a crossing. Coincident meridian curves are reported as an overlap rather than an arbitrary point. The results are sorted south to north and displayed to 0.001°; their precision is a display convention, not a claim of survey accuracy.
Why a line may stop
Near a pole, a planet may remain above or below the horizon for the entire rotation. It then has no ASC or DSC solution at that latitude. A selected pair can have no mapped intersection, even when both lines are visible elsewhere. This finder stops at ±85° to match the line map and does not claim a result in the unplotted polar caps. The coastlines and rectangular projection are visual context; the crossing computation works in longitude and latitude before projection.
Crossing versus paran
Astrocartography readers also discuss parans: two planets are simultaneously angular along a latitude, potentially at different longitudes. A paran can therefore describe a latitude band without a single point where two map curves intersect. This finder asks for the stricter same-place intersection. It does not calculate paran bands or their separate timing conventions. Likewise, two curves passing close to the same city do not necessarily cross at that city; use the two-city distance comparison to inspect proximity separately.
Limits of a natal map
The model treats the horizon as geometric and sea-level. It omits refraction, terrain, elevation, and topocentric parallax, which can matter especially for the Moon. The apparent positions are referred to the equator of date. A reported crossing moves if the recorded time or original UTC offset changes: Earth turns about 15° in an hour. Historical civil-time ambiguities, unknown birth hours, and rounded records should be resolved before interpreting a small location difference.
These angular conditions describe one instant from different observing places. They do not show a current transit, assess relocation houses, or rank destinations. Read any map feature with the natal chart and the practical circumstances of a place. Open the crossing finder →
About the calculation
- Planetary positions and Greenwich sidereal time: Astronomy Engine 2.1.19. Coastline: Natural Earth 1:110m, public domain.