Where the numbers come from

Say what an ephemeris is, what a modern one actually contains, and name the four things that make a beautifully precise chart wrong.

Lesson 8 of 10 in Astronomy for Astrologers · free to read · no account, no email

A table of the sky, one row per day

An ephemeris — from the Greek for “daily” — is a table of where everything was. For most of astrology's history it was a printed book: one page per month, one row per day, a column per planet, positions given for midnight or noon at Greenwich. You looked up the day, looked up the next day, and interpolated for the hour you actually wanted.

The lineage is long and unbroken. Babylonian scribes kept tables on clay of where the Moon and the planets would be. Ptolemy published the method for computing them in the second century. The Alfonsine tables carried it through the medieval world; Kepler's Rudolphine tables replaced them with ellipses; and printed ephemerides have come out annually ever since.

The point worth holding is that the table was always the boring half and always the indispensable half. No reading of any kind is possible until somebody has worked out where the planets were, and for two thousand years that was skilled, slow work done by hand.

What a modern ephemeris actually is

It is no longer a table. It is a numerical integration of the whole solar system.

The reference standard is the set of Development Ephemerides published by NASA's Jet Propulsion Laboratory. Radar ranging to planets, laser ranging to the Moon's retroreflectors, and tracking data from spacecraft are fitted into one model of the solar system's gravity, which is then integrated forwards and backwards in time and stored as polynomial coefficients. The inner planets are known to within metres. The Moon's distance is known to centimetres. These are among the best-measured quantities in science.

Astrology software takes one of two roads from there. It can carry a compressed ephemeris file and look positions up, or it can compute them from a fitted analytical series — a long sum of periodic terms that reproduces the integration to some accuracy over some range of dates. Umbriel computes.

Which means Umbriel has to prove it, and does. Positions are checked body by body against JPL's published values, the check is a test rather than an impression, and it runs. That is the only honest basis for the rest of this course: if a lesson ends in the reader's own number, the number has to have been verified against something outside the program that produced it.

Precision is not accuracy

A program can print arcseconds from a wrong model all day long. Four things actually go wrong, and every one of them has bitten real software.

The calendar. The switch from the Julian to the Gregorian calendar happened in 1582 in some countries, 1752 in others, and 1918 in another. A date before the switch is only meaningful once you know which calendar wrote it down, and a program that assumes Gregorian back to the beginning is silently ten days out for centuries of history.

The fitted range. An analytical series is fitted over a span — say 1900 to 2100 — and outside it the error grows without any warning appearing on screen. A chart for 1650 from a formula fitted to the twentieth century is confidently wrong, which is the worst kind.

Earth rotation. Planetary positions are functions of a uniform timescale; the turning of the Earth, which sets your Midheaven and Ascendant, is not uniform. The gap between them is the next lesson's subject, and getting it wrong moves the planets without moving the houses — so planets land in the wrong rooms.

Bodies with no observations. Hypothetical points, and anything whose orbit is reconstructed rather than measured, carry an uncertainty that no amount of decimal places removes. A figure is only as good as what it was fitted to.

Hence the working rule for everything in this course: compute, never quote. If a reading contains a figure, it came from the engine, and the engine was checked against a second path. A number you cannot trace is a number you should not say out loud to somebody.

What that looks like

Ask for a chart dated 4 October 1582 and then 15 October 1582. In the country that made the switch, there was no 5th through the 14th: the days do not exist. A program that does not know this will happily produce ten charts for ten days that never happened, with positions printed to the arcsecond. Nothing about the output looks wrong. That is exactly the problem, and it is why the calendar is the first thing a careful engine settles.

What to take away

• An ephemeris is a table of positions: for most of astrology's history a printed book you interpolated by hand, and always the indispensable first step.
• A modern one is a numerical integration of the solar system fitted to radar, laser and spacecraft data, accurate to metres for the inner planets.
• Umbriel computes rather than looks up, which is why its positions are checked body by body against JPL's published values as a test that runs.
• Precision is not accuracy. The calendar, the fitted date range, Earth-rotation time and unobserved bodies are the four ways a beautifully printed chart is wrong.

The common mistake

Treating decimal places as evidence. Arcseconds tell you what a program computed, not whether the model behind it was right for the date you asked about — and the most dangerous charts are the historical ones, where nothing on screen looks unusual.

Try it on your own chart

Cast a chart for someone born before 1752 in Britain or its colonies, or before 1918 in Russia, and check what your source says about the calendar. Then cast one for a date in the 1600s and ask yourself what the software was fitted over. You are not looking for an error — you are practising the habit of asking where a number came from before you build a sentence on it.

Check yourself

The same questions the lesson asks in the app. Open one to see the answer.

Keep going

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