Astrocartography

History

Maps of where each planet stood on an angle at a birth were sold under Jim Lewis’s service mark Astro*Carto*Graphy; his patent of 1981 (US 4,304,554) describes the lines, claims an overlay of later positions, and takes Jimmy Carter and Gerald Ford as examples. Far older, Ptolemy’s Tetrabiblos II.3 divides the inhabited world into four quarters by the triplicities and gives 72 nations to the signs; here in Ashmand’s English of 1822.

How it works

Each body’s apparent right ascension and declination and the Greenwich sidereal time come from the app’s ephemeris. A body culminates where the longitude is its right ascension less the sidereal time; the IC line lies 180° away. It rises at hour angle −H₀ and sets at +H₀, where cos H₀ = −tan φ tan δ, so the rising and setting lines are curves that meet the meridian lines where the body stops rising and setting. Crossings and distances are computed on the sphere. Ptolemy’s nations are placed at points from the Pleiades gazetteer.

How it was checked

The tests put the MC lines of ten bodies at five moments from 1913 to 2048 within 0.005° of the Swiss Ephemeris, and their rising and setting points at ten latitudes within 0.01°, each of those points confirmed by the Swiss Ephemeris to stand on the true horizon. They reproduce the patent’s examples: Carter’s Sun line through Iceland and just off Africa, and Ford’s Pluto IC line through San Francisco. At Carter’s moment every point of the curves is checked to lie on the horizon, rising in the east and setting in the west; distances from two places at two moments, against a search along each line; at J2000.0, every crossing of two curves, against a fine search. Ptolemy’s 72 nations are checked by name against his text and his table.

Limits

The lines are geocentric, for the centre of each body, without refraction: the patent asks only for “actual rise”, and these are the app’s choices. Four minutes of birth time move every line a degree. The plate carrée widens the far north and south. Lewis’s readings of the lines are not given: his books are in copyright. Crossings are listed at the place’s latitude, after the patent. Ptolemy’s nations are placed at Pleiades’ points, roughly for some regions; two without a usable point are left off, and the dividing lines are drawn only roughly.