Where Will Jupiter Be on Tuesday? Somebody Has Already Worked It Out

The publication lists, for each day or hour over a period, the computed position of the Sun, Moon, planets or other bodies against the background of the sky, together with related quantities such as distance, brightness and the times of rising and setting. The positions are calculated from a model of the motions involved rather than observed, so the table extends into the future as readily as into the past. Its accuracy depends entirely on the quality of that model and on how far ahead the calculation is pushed.

A table of predicted positions answers several practical questions:

• •Finding longitude at sea by comparing the Moon against a star
• •Setting a clock by observing a known transit
• •Predicting eclipses, occultations and conjunctions
• •Knowing where to point a telescope for a faint object
• •Planning a spacecraft trajectory to arrive where a planet will be
• •Dating historical events from recorded celestial observations

The most consequential historical use was determining position at sea. Latitude is easy from the height of the Sun or pole star, and longitude requires knowing the time at a reference place, which before reliable chronometers was extremely difficult. The lunar distance method solved it by using the Moon as a clock, since it moves measurably against the stars, so measuring the angle between the Moon and a chosen star and comparing against a published table gives the reference time. The British publication began in 1767 specifically for this purpose and required enormous quantities of hand computation.

The limit on how far such a table extends is set by the physics rather than by computing power, which is the interesting part. Positions of the planets can be computed accurately for thousands of years in either direction, because the bodies are large and their interactions are well characterised. Small bodies are much worse, since a close pass by a planet amplifies any uncertainty in the starting position, and predictions for some asteroids and comets become useless within a century. Beyond a few tens of millions of years the solar system is chaotic, meaning tiny differences grow without limit and no table can reach further.

The tables were produced by teams of human calculators working on shares of the problem, and the arrangement is the direct ancestor of modern computing practice. Contributors worked from their own homes across the country, each handling assigned months, with results checked against an independent second calculation of the same figures. The word computer meant a person doing this work, and many were women, particularly in the nineteenth and twentieth centuries. Frustration with errors in such tables was among the stated motivations for Charles Babbage's attempts to build a calculating engine.

A table of computed positions at regular intervals extends into the future because it comes from a model rather than from observation. Its greatest use was finding longitude at sea by treating the Moon as a clock and comparing measured angles against published values. The tables were produced by teams of human calculators working from home with independent checking.