Astrocartography Crossings & Parans
A crossing is a point where two planets' lines meet on the map. A paran is the latitude of that point, taken all the way around the globe: along it, at some moment every day, the same two planets are on angles together. This page sets out exactly how the site's map finds both, and works through Steve Jobs's map, which has 78 crossings between 66°S and 66°N grouped into 53 one-degree paran bands.
How the map finds crossings and parans
- The lines are zodiacal. Each planet's line marks where its degree of the ecliptic, its zodiac longitude, is on an angle. The planet's latitude north or south of the ecliptic is ignored. The other convention, in mundo, uses the body itself: its right ascension for the MC and IC lines, its real rising and setting for the ASC and DSC lines. Both are in use; this site's map and every figure on this page are zodiacal unless labeled in mundo.
- Only two kinds of line can meet. MC and IC lines are meridians at fixed longitudes, so they are parallel and never cross each other. Two horizon lines never cross on a zodiacal map either, because at any place the Ascendant is a single degree. Every crossing is therefore one planet's ASC or DSC line meeting another planet's MC or IC line, and any such pair meets at most once.
- Crossings are solved exactly. The meridian line fixes the local sidereal time; the crossing is the latitude where, at that sidereal time, the other planet's degree is on the horizon. That has a closed-form answer from the degree's right ascension and declination, so nothing is interpolated. The map keeps crossings between 66°S and 66°N, inside the polar circles where every line is continuous. An earlier version compared the lines row by row, half a degree apart; on this chart it missed one crossing and listed two twice.
- A crossing's latitude is a paran. At that latitude the sky turns the same way at every longitude, so once a sidereal day the two degrees are angular together there too, with the planets' positions held as they were at birth. The crossing point is simply where this was happening at the birth moment.
- Parans are grouped into one-degree bands. Each crossing goes into the band of its nearest whole degree of latitude, rounding halves up (36.5° goes to 37°), so a band spans half a degree either side, about 111 km in all. A band can hold unrelated crossings, and its list of planets is everything in it, not one combined paran.
- What the map leaves out. Parans between two horizon events (two planets rising together, or one rising as another sets) exist only in mundo and are not drawn; nor are parans with fixed stars, of the kind Bernadette Brady's Brady's Book of Fixed Stars (1998) maps, or anything beyond 66°.
One crossing, one parallel: the Denver example
On Steve Jobs's map, Uranus's ASC line meets the Moon's MC line at 39°45′N, 164°08′E, in the open Pacific: at the birth moment, Uranus's degree (24°08′ Cancer) was rising there while the Moon's (7°44′ Aries) culminated. Denver lies on almost the same parallel, 2.3 km from it. The birth was at 8:15 PM on February 24 by Denver's clock. At 2:08 PM the next day, 17.9 hours later, Denver's sidereal time reached the Moon's degree, and on that parallel at Denver's longitude the Moon's birth degree culminated while Uranus's rose: the same paran, half a world from the crossing.
The paran belongs to the birth positions, not to the sky of the following day. By that afternoon the real Moon had moved 10.6 degrees along the zodiac, while Uranus had moved 0.02. Astrologers who read parans read them as properties of a latitude in the natal chart.
Steve Jobs's 78 crossings
His birth certificate gives 7:15 PM, February 24, 1955, in San Francisco. Load that map to compare. His crossings split almost evenly between the four possible kinds: 20 rising-line crossings with an MC line, 19 with an IC line, 19 setting-line crossings with an MC line and 20 with an IC line.
They also come in exact pairs. If planet A rises at latitude φ while B culminates, then at −φ, on the opposite meridian, A sets while B is at the lowest point. Each of his 39 northern crossings has a southern twin, so the table lists the northern half; flip the latitude, swap rising for setting and MC for IC, and add 180 degrees of longitude for the other 39.
| Latitude | Crossing | Longitude | Paran band | Large city within 300 km |
|---|---|---|---|---|
| 65°25′N | Pluto ASC × Mars MC | 175°55′W | 65° | |
| 65°25′N | Uranus ASC × Pluto IC | 124°37′E | 65° | |
| 65°05′N | Mercury DSC × Moon MC | 164°08′E | 65° | |
| 64°04′N | Venus DSC × Pluto IC | 124°37′E | 64° | |
| 63°46′N | Jupiter ASC × Pluto IC | 124°37′E | 64° | |
| 62°48′N | Sun DSC × Saturn IC | 154°14′W | 63° | |
| 62°30′N | Uranus ASC × Sun MC | 134°34′E | 63° | |
| 61°46′N | Neptune ASC × Mercury IC | 66°08′W | 62° | |
| 60°40′N | Venus DSC × Sun MC | 134°34′E | 61° | |
| 60°15′N | Jupiter ASC × Sun MC | 134°34′E | 60° | |
| 59°46′N | Mars DSC × Mercury IC | 66°08′W | 60° | |
| 53°54′N | Saturn DSC × Jupiter IC | 89°12′E | 54° | |
| 53°12′N | Saturn DSC × Venus MC | 89°55′E | 53° | |
| 50°05′N | Mercury DSC × Neptune IC | 176°54′W | 50° | |
| 49°49′N | Saturn DSC × Uranus IC | 93°03′E | 50° | |
| 48°46′N | Mercury DSC × Mars MC | 175°55′W | 49° | |
| 48°03′N | Jupiter DSC × Saturn MC | 25°45′E | 48° | |
| 47°29′N | Venus ASC × Saturn MC | 25°45′E | 47° | |
| 44°43′N | Uranus DSC × Saturn MC | 25°45′E | 45° | Bucharest (42 km) |
| 44°41′N | Saturn ASC × Sun IC | 45°25′W | 45° | |
| 39°45′N | Uranus ASC × Moon MC | 164°08′E | 40° | |
| 34°13′N | Venus DSC × Moon MC | 164°08′E | 34° | |
| 33°32′N | Pluto ASC × Saturn IC | 154°14′W | 34° | |
| 32°54′N | Jupiter ASC × Moon MC | 164°08′E | 33° | |
| 25°18′N | Saturn ASC × Pluto MC | 55°22′W | 25° | |
| 23°15′N | Mars ASC × Jupiter IC | 89°12′E | 23° | Khulna (62 km) |
| 20°10′N | Mars ASC × Venus MC | 89°55′E | 20° | Khulna (296 km) |
| 19°31′N | Neptune DSC × Jupiter IC | 89°12′E | 20° | |
| 16°09′N | Neptune DSC × Venus MC | 89°55′E | 16° | |
| 11°54′N | Jupiter DSC × Mars IC | 4°04′E | 12° | Sokoto (180 km) |
| 10°16′N | Venus ASC × Mars IC | 4°04′E | 10° | Ilorin (205 km) |
| 9°32′N | Jupiter DSC × Neptune MC | 3°05′E | 10° | Ilorin (198 km) |
| 7°52′N | Venus ASC × Neptune MC | 3°05′E | 8° | Ibadan (106 km) |
| 6°22′N | Mercury ASC × Saturn MC | 25°45′E | 6° | |
| 5°49′N | Saturn DSC × Mercury MC | 113°51′E | 6° | |
| 5°07′N | Mars ASC × Uranus IC | 93°03′E | 5° | |
| 2°35′N | Uranus DSC × Mars IC | 4°04′E | 3° | |
| 0°07′N | Neptune DSC × Uranus IC | 93°03′E | 0° | |
| 0°03′N | Uranus DSC × Neptune MC | 3°05′E | 0° |
Most of his crossings are far from big cities. Four lie within about 110 km of a city of a million or more: Uranus DSC × Saturn MC, 42 km from Bucharest; Pluto DSC × Saturn MC, 49 km from Port Elizabeth; Mars ASC × Jupiter IC, 62 km from Khulna; and Venus ASC × Neptune MC, 106 km from Ibadan. Of the 53 bands, 32 hold a single crossing; the busiest is the equator band, with 4.
A birth-time error moves every crossing east or west with the lines, 3°45′ of longitude per 15 minutes, but barely moves it north or south, because the latitude depends only on where the two planets were. On this chart, 15 minutes either way changes no crossing's latitude by more than 0.23°, and only those involving the Moon by more than 0.07°. Paran latitudes hold up better under an uncertain birth time than anything else on the map.
Lines that run side by side and never meet
Lists of "notable crossings" sometimes pair two MC lines, or a rising line with a setting line. The first kind cannot happen on any astrocartography map, and the second cannot happen on a zodiacal one. Steve Jobs's chart shows what such pairs look like instead. Venus at 21°10′ Capricorn and Jupiter at 20°30′ Cancer are 0°39′ from an exact opposition, so his Venus IC and Jupiter MC meridians run 0°42′ apart through Yucatán, and his Venus DSC and Jupiter ASC curves run 79 km apart at the equator and 55 km apart at 60°N, side by side across the map without crossing.
Zodiacal crossings against in-mundo parans
Computing the same 78 pairs in mundo, from each body's own right ascension and declination with the Swiss Ephemeris, moves their latitudes by a median of 2.1°. The largest change involves Pluto, which was 10°32′ north of the ecliptic: its Pluto ASC × Mars MC crossing moves from 65°25′N to 53°10′N, about 1,363 km south. Two crossings leave the map's latitude range in mundo, and 16 in-mundo crossings have no zodiacal counterpart inside it, mostly near the edges and mostly involving Pluto or the Moon.
In mundo there is also a whole family the zodiacal map cannot draw: two horizon events at once. Within 66° of the equator, Steve Jobs's chart has 38 of them, again in mirrored pairs. The Sun and Moon rise together along 57°42′N (and set together along 57°42′S), which their zodiac degrees, 31°59′ apart, could never do; it is the Moon's 5°02′ of ecliptic latitude that lets the bodies share a horizon there.
| In-mundo paran (northern half) | Latitude |
|---|---|
| Mars rising as Uranus sets | 65°57′N |
| Sun rising as Jupiter sets | 65°56′N |
| Moon rising as Venus also rises | 65°55′N |
| Sun rising as Uranus sets | 65°48′N |
| Moon rising as Mercury also rises | 64°19′N |
| Moon rising as Jupiter sets | 63°51′N |
| Moon rising as Uranus sets | 63°27′N |
| Mercury rising as Jupiter sets | 63°20′N |
| Mercury rising as Uranus sets | 62°13′N |
| Saturn setting as Pluto also sets | 60°22′N |
| Sun rising as Moon also rises | 57°42′N |
| Neptune setting as Pluto also sets | 57°03′N |
| Venus setting as Uranus rises | 55°37′N |
| Mars rising as Pluto sets | 55°37′N |
| Mercury setting as Pluto rises | 54°31′N |
| Moon rising as Pluto sets | 45°39′N |
| Sun rising as Pluto sets | 22°18′N |
| Venus rising as Jupiter sets | 7°33′N |
| Mars rising as Neptune sets | 5°54′N |
Each row has a southern twin with rising and setting swapped. Every listed latitude was checked by computing both bodies' altitudes, zero at the same sidereal time.
Reading the four kinds of crossing
Astrocartographers read a crossing by combining the two lines' readings, weighted by the planets involved: Ptolemy's benefics (Jupiter and Venus) read as easing, his malefics (Saturn and Mars) as testing, and the modern planets by modern convention. These are interpretive conventions, not tested effects.
Rising line meets MC line
One planet's degree is coming up in the east while the other's stands at the top of the meridian.
Readers pair the rising planet's first-house themes (manner, body, first impressions) with the culminating planet's tenth-house ones (work and reputation).
Steve Jobs: 20 of these.
Setting line meets MC line
One planet's degree is going down in the west while the other's culminates.
Partners, clients and rivals (the setting planet) are read alongside public standing (the culminating one): work done with, for or against other people.
Steve Jobs: 19 of these.
Rising line meets IC line
One planet's degree rises while the other's is at the lowest point, below the horizon on the meridian.
The person (rising) is read with home, family and property (the planet at the IC).
Steve Jobs: 19 of these.
Setting line meets IC line
One planet's degree sets while the other's is at the lowest point.
Partnership (setting) is read with the household (IC), the pairing that bears on sharing a home.
Steve Jobs: 20 of these.
The twin rule above means every rising-with-MC crossing has a setting-with-IC partner in the other hemisphere, and the map's latitude range is the same north and south, so those two kinds always come in equal numbers, as do rising-with-IC and setting-with-MC crossings.
List your own crossings
Enter a birth date, time and place. The map shows your crossings with their latitude and longitude, and the latitude is the figure that survives an uncertain birth time.
Draw your mapCrossings and parans: questions
What is a crossing in astrocartography?
A place where two different planets' lines meet. On this site's map, which draws zodiacal lines, every crossing is one planet's ASC or DSC line meeting another planet's MC or IC line, at the latitude where the first planet's degree is on the horizon while the second's is on the meridian. Steve Jobs's map has 78 of them between 66°S and 66°N.
What is a paran, and how does the map group them?
A paran (from the Greek paranatellonta, "rising alongside") is a pair of planets on angles at the same moment. Each crossing's latitude is one: everywhere along that parallel, once a day, the same two degrees are angular together. The map groups crossings into one-degree bands of latitude, each centered on a whole degree and about 111 km tall; Steve Jobs's 78 crossings fall into 53 bands.
Why are there no MC and MC crossings?
MC and IC lines are meridians, straight north–south lines at fixed longitudes, so two of them are parallel and never meet. Lists that pair two planets' MC lines describe something no astrocartography map can show.
Why doesn't the map show a Venus DSC line crossing a Sun ASC line?
On a zodiacal map two horizon lines cannot cross: at any place the Ascendant is a single degree, so two planets' degrees can share a horizon only if they are the same or exactly opposite. Measured in mundo, with the planets' real declinations, such pairs do meet at particular latitudes: on Steve Jobs's chart, Venus rises as Jupiter sets along 7°33′N.
Does an inexact birth time move crossings?
East or west, yes, with the lines: about 3°45′ of longitude per 15 minutes. North or south, hardly at all, because a crossing's latitude depends only on the two planets' positions. On Steve Jobs's map a 15-minute change moves no crossing more than 0.23° of latitude, and only those involving the fast Moon by more than 0.07°.
How close to a crossing does a city have to be?
There is no measured answer. The map's paran bands run half a degree, about 55 km, either side of a whole degree of latitude, and astrologers use different allowances for a crossing point. These are conventions for reading the map, not tested distances.