The Sun Line in Astrocartography

The site draws each planet's lines from its position along the zodiac, the ecliptic, and leaves out how far the planet sits above or below that circle (its ecliptic latitude). For most planets that shortcut moves the rising and setting lines a little. For the Sun it moves nothing, because the ecliptic is by definition the Sun's own path: in our day-by-day check of every date from 1900 to 2050, the Sun's ecliptic latitude never reached a hundredth of a degree. So the Sun lines here are the same lines Jim Lewis drew when he began mailing out hand-drawn Astro*Carto*Graphy maps in 1976, which follow the body itself rather than its zodiac degree.

Two of the four are straight. The MC line is a meridian, a north-to-south line of constant longitude, because apparent noon arrives at the same instant all along a meridian. The IC line is the meridian on the far side of the globe, 180° away. The other two bend. Taken together, the ASC and DSC lines are the boundary between day and night at the moment of birth, the edge of the Earth's shadow that a satellite photograph shows. In a northern summer that boundary leans so that more of the north is in daylight: the two curves swing away from the noon meridian as you go north and close in on it as you go south.

That geometry gives Sun lines a property no other planet's lines have. The east-west gap between the Sun ASC line and the Sun MC line, at any latitude, is half the length of that day's daylight there, measured in the Sun's hour angle. On Obama's birthday the Sun's declination was 17°02′ north, so his rising and setting lines sit far from the noon meridian in the north and close to it in the south:

These are hours from the Sun's center rising to its center setting, with no allowance for the air. A sunrise table adds a few minutes at each end, because it times the top edge of the disk and the atmosphere bends its light over the horizon. At the equator the figure is exactly 12 hours, which is how you can tell the table is geometric: real equatorial days run a few minutes over twelve hours all year.

All ten planet pages use the same chart: Barack Obama, born 7:24 PM on August 4, 1961, in Honolulu, by his birth certificate. That is 05:24 UTC on August 5, 1961. His Sun was at 12°32′ Leo. The lines below are the ones the site's API returns for that moment, the same call the astrocartography map makes for his chart, and our generating script checked every point against the Swiss Ephemeris before listing the cities near each one.

Every line on the map shifts by the same amount when the birth time changes. A birth four minutes later moves all of them 1°00′ of longitude to the west, because that is how far the Earth turns in four minutes; on the ground that is about 111 km at the equator and 79 km at 45° latitude. Some guides claim the MC and IC lines are less sensitive to a wrong birth time than the rising and setting lines. They are not. An error carries the curved lines exactly as far east or west as the straight ones; the only thing that differs is how far your city sat from each line to begin with.

The date matters far less for the Sun than for any other body on the map. Move Obama's birth to the same clock time one day later and his Sun MC line moves only 0°01′, because the clock day is the Sun's day: in 24 hours the Earth turns about 361°, enough to bring the Sun back to the meridian. What remains is the equation of time, the few minutes by which sundial time runs ahead of or behind clock time over the year. On his birthday it was 5.95 minutes, with the sundial behind the clock. The Moon's MC line, by contrast, moves 12°22′ east in the same day.

No line on the map has an edge, so every practitioner works with an orb, a distance within which a line is taken to count. Jim Lewis gave two figures. His first A*C*G handbook (1976) said that near meant about a quarter of an inch either side of the line on his printed map, which works out to roughly 300 to 400 miles. His Cyclo*Carto*Graphy handbook (1982) called that conservative and allowed up to 700 miles each side.

Applied to Obama's Sun lines, the wider orb takes in a great deal of the world: 779 of the 2,292 cities in the site's list lie within 700 miles (1,127 km) of at least one of the four. A rule that takes in 34% of the list cannot single out many places, which is why it helps to treat 700 miles as the outer edge of a fading effect and to give a city 100 km from a line far more weight than one 1,000 km away. The city tables on this page stop at 200 km for the same reason.

Of all forty lines, the Sun MC line is the one you can work out with a pencil, because it needs only the Sun's hour angle at the moment of birth. Take Obama's chart. Honolulu lies at 157°51′ W, so its local mean time runs 10 hours 31 minutes behind UTC, and the birth at 05:24 UTC was 6:52 PM local mean time. The equation of time that day was −5.95 minutes, which puts sundial time at 6:46 PM: 6 hours 46 minutes after noon. In that time the Earth had carried the Sun 101°39′ west of Honolulu's meridian, so noon was falling 101°39′ farther west, at 100°29′ E. The API's line is at 100°29′ E, the same to the arc-minute.

Two things trip people up when they try this. The first is the time zone: you need the UTC offset that was legal at the place on that date, daylight saving included, not the one in force today. The second is the equation of time, which reaches about a quarter of an hour in February and November; leave it out and the line lands up to four degrees off. For the other thirty-nine lines, and to check your arithmetic, the map does it all: turn off every planet except the Sun to see its four lines on their own, and search a city to see how far each line runs from it.