One birth instant, two observing places
An angular map starts with one instant identified by the recorded local birth time and the historical UTC offset at the original birthplace. That instant is the same in both cities. The map asks where a planet would have met an angular condition from each possible observing place at that instant. It does not recast the birth moment using a destination’s civil time.
The four conditions are rising on the eastern horizon (ASC), setting on the western horizon (DSC), crossing the upper meridian (MC), and crossing the lower meridian (IC). This site calculates ten planets independently from Astronomy Engine, without copying that map or its interpretations. It does not include lunar nodes in this comparison.
What the city number measures
For each planet and angle, the tool traces the angular line across the mapped domain from 85°S to 85°N. It searches that curve for the point with the smallest great-circle distance to each city, using a 6,371.0088 km spherical Earth. A coarse latitude sweep finds candidate minima, and each is refined numerically. The first tables rank these nearest-curve distances, and the detailed table reports the nearest latitude and longitude. They are geometric separations, not road or flight distances.
The detailed table separately finds the line’s longitude at the city’s exact latitude. It wraps the shorter east–west difference across the date line and computes the arc as Earth radius × cos(latitude) × longitude difference in radians. This along-latitude crossing gap can exceed the nearest-curve distance. The search stops at 85° in either hemisphere, matching the visible map; it makes no claim about an unplotted polar extension. The flat equirectangular map is an overview and does not preserve distances.
Why some rising or setting entries are absent
At high latitudes a planet can remain above or below the geometric horizon for a full rotation. The horizon equation then has no rising or setting solution at that latitude. The along-latitude row says “No horizon crossing at this latitude” rather than reporting a fictitious crossing. The nearest-curve distance can still be finite because a horizon curve may terminate at a lower latitude. The form and plotted curves stop at ±85° because near-polar projections become difficult to read.
The calculation uses apparent geocentric right ascension and declination referred to the equator of date. It assumes a geometric sea-level horizon and omits atmospheric refraction, terrain, observer elevation, and parallax corrections to the angular lines. The Moon in particular can shift with topocentric parallax. The distances use a 6,371.0088 km spherical Earth and are rounded to whole kilometers for display. The numerical search and astronomical approximations make them comparison aids, not survey-grade geodesy.
A worked two-city comparison
The form opens with 1 January 2000 at 12:00 with UTC+8, or 04:00 UTC, and coordinates for Manila and New York. For that example the Sun MC curve passes about 22 km from Manila, while the Mercury IC curve passes about 453 km from New York. Those are different planet-angle combinations. The tables identify which line is nearest to each place; they do not imply that one city is more favorable. Select a planet to see how all four of its angular curves relate to both cities at the same instant.
If a city lies near a curve, inspect the nearest point and the along-latitude crossing separately. A difference between them shows the curve bending toward the city from another latitude. For an ASC or DSC entry with no crossing at the city’s parallel, the nearest point may sit near the horizon curve’s latitude endpoint. Confirm the recorded birth time and historical offset before treating any small distance as meaningful.
Line crossings and Local Space
Crossings on a map are places where two different angular conditions coincide or approach one another. This page compares each planet-angle line at each city’s latitude; it does not solve intersections, parans, or simultaneous contacts between two planets. Two small nearest-curve distances do not prove that the curves intersect one another or that either one crosses exactly at the city. The world angular-lines map helps you inspect individual lines visually.
Local Space uses a different coordinate question: the compass bearing of a planet on a horizon at a chosen reference place. A Local Space great-circle direction is not interchangeable with an ASC, DSC, MC, or IC line. Use the Local Space compass to inspect that separate technique; use the relocation chart for changed angles and houses.
Birth record and interpretation
A rounding error of an hour shifts Earth’s rotation by about 15° in longitude, which can move an angular line hundreds of kilometers depending on latitude. Resolve an ambiguous or skipped daylight-saving time before relying on the comparison. A city’s distance to an angular line is a geometric observation. It does not by itself rank cities, promise an experience, or replace the natal chart and personal circumstances.