The same chart twice, an arcsecond apart

We computed one chart from the data this app uses, then computed it again from a rival built by different people from a different fit, and compared all 10 positions. The largest disagreement was 0.95 arcseconds. You could fit 114044 of them inside a single zodiac sign. Whatever two astrologers are arguing about, it is not this.

What the word actually means

An ephemeris is a table of where things were and will be. That is the whole idea, and the word carries its history openly: the Greek ephemeris meant a diary or a day-book, something kept daily, from ephemeros, of the day. The astronomical sense is a much later narrowing, from Latin and English in the fifteen fifties.

So the Greeks did not use the word for this, which is worth saying because the etymology gets told the other way round. They had the thing without having the name for it.

The modern version is not a table at all. It is a model of how the Sun, Moon and planets pull on one another, integrated forward and backward step by step, with its starting conditions and the masses adjusted until the whole thing agrees with radar bounced off Venus, radio tracking of spacecraft, lasers reflected off mirrors left on the Moon, and two centuries of telescope measurements. What you look up is the model's answer, checked against those.

How good is it, and how would you know

There is no way to look up the true position of Saturn and compare. What you can do is compute the same instant twice, from two ephemerides that were built separately, and see whether they agree.

An arcsecond is a 3600th of a degree. Held at arm's length it is roughly the width of a hair seen from a hundred metres away. Nothing in a reading is sensitive at that scale, and nothing in a reading ever will be.

But the agreement is not uniform, and where it fails is the interesting part.

Every worst case in that table sits near one end of the range or the other, and the pattern by decade is unmistakable: the two agree to about an arcsecond through the nineteen-seventies to the twenty-twenties, and drift apart towards both edges. That is what a fitted model looks like. It is tightest where the measurements are, and the measurements are recent, because radar and spacecraft and lasers are recent.

The Moon is the worst offender by a wide margin, which is not a surprise: it is the nearest thing in the sky, so an error in its position is spread over the smallest distance and shows up as the largest angle.

It is tightest where the measurements are, and the measurements are recent. An ephemeris is a fit, and a fit sags at the ends.

Where it stops

Ask this app for a chart outside the years its data covers and it does not guess. It stops. We found the two edges by asking for charts on either side of the boundary and narrowing down to the minute.

Someone born before that first instant cannot have a chart computed from this data at all. That is a real limitation and we would rather state it than have you discover it.

Three different meanings of where

Here is something that sounds like pedantry and is not. There are three different answers to where a planet is at a given moment, and they differ by amounts you can measure.

Where it is, right now, which nobody can see. Where it was when the light now reaching us left it. And where it appears, which adds the tilt our own motion puts on that light, the way rain slants when you run through it.

Read the last two columns against each other. The fourth column depends on how fast the body moves and how long the light takes, so it is largest for Mercury at 30.5 arcseconds and falls away with distance. The fifth depends on how fast we are moving, so it never exceeds about twenty arcseconds no matter how far away the target is, and it varies only with the angle between the body and the direction the Earth is travelling in.

The Sun is the case that catches people out. Its own displacement while the light crosses is 0.01 arcseconds, essentially nothing, because the Sun barely moves against the background in eight minutes. The twenty arcseconds by which the Sun appears displaced is entirely our motion, not its own. The familiar line about the Sun you see being eight minutes old is true and the number attached to it usually belongs to the other effect.

None of this changes a reading. All of it is in the numbers anyway, because leaving it out would make the positions wrong by a measurable amount, and being wrong on purpose is a strange thing to build on.

Two thousand years of tables

From here down we are reporting rather than measuring.

One correction to our own copy

This product has described its data as NASA telemetry. That is wrong and we are fixing it. Telemetry is what a spacecraft radios back about itself. An ephemeris is a dynamical model fitted to measurements, of which spacecraft tracking is one input among several.

The distinction matters for exactly one reason: the claim we make about our numbers is the only claim in this product that a specialist can check in a minute, and it is the one we cannot afford to be sloppy about. If we say something an astronomer would wince at, there is no reason to believe us about anything harder.

So, precisely: positions come from JPL's DE421, an integration of the equations of motion fitted to radar ranging, spacecraft tracking, lunar laser ranging and optical astrometry. It is not a measurement of where Saturn is tonight. It is a model whose parameters were measured, and which is checked against measurements continuously.

Sources

• Positions: JPL DE421, compared against Swiss Ephemeris 2.10.03 at 241 instants between 1 Jan 1905 and 1 Jan 2048.
• W. M. Folkner, J. G. Williams and D. H. Boggs, "The Planetary and Lunar Ephemeris DE 421", JPL Interoffice Memorandum 343R-08-003 (2008), published in the IPN Progress Report 42-178 (2009). The method statement quoted above is from the successor paper on DE440 and DE441, Park and colleagues, Astronomical Journal, 2021.
• Otto Neugebauer, Astronomical Cuneiform Texts, 3 volumes, 1955; Mathieu Ossendrijver, Babylonian Mathematical Astronomy: Procedure Texts, 2012; John Steele on the Goal-Year texts.
• Ptolemy, Handy Tables, critical edition by Anne Tihon.
• Alfonsine Tables (Castile, about 1252), Erasmus Reinhold, Prutenic Tables (1551), Johannes Kepler, Rudolphine Tables (1627). The fiftyfold estimate of the improvement is Owen Gingerich's.
• Regiomontanus, Ephemerides (Nuremberg, 1474). For the Jamaica eclipse, Ferdinand Columbus's life of his father; the attribution of the almanac is disputed.
• HM Nautical Almanac Office for the first Nautical Almanac, published for 1767 under Nevil Maskelyne.
• A note on the etymology: the Greek word meant a diary; the astronomical sense is a sixteenth-century narrowing in Latin and English, not an ancient usage.