Piazzi and the missing planet

By Frederic Friedel

Recently, during the Christmas season, we took our two grandsons to their first ballet — The Nutcracker, what else? We arrived early and there was a fairly long wait for things to get going. This naturally leads to restlessness and unruly when-will-it-start behaviour, and this was especially the case with five-year-old Enders. There is one sure way to calm him down, to get him to sit still and behave impeccably: tell him a story.

So that is what I did — told him a tale my part-time astronomer father had told me when I was not much older than Enders today. It is a story I will now share with you, fleshing out the somewhat simpler version that had the young boy spellbound in his seat, drinking in every word.

In 1766 the German astronomer Johann Daniel Titius noticed something odd about the distance of the planets from the sun. A few years later he and his colleague Johann Elert Bode published a simple numerical sequence which correlated to those distances. They and soon a lot of other astronomers believed that it had something to do with the formation of the solar system. Here is the sequence:

• Take the numbers 0, 3, 6, 12, 24, 48, 96, etc. (each number is double the one that comes before it).

The final numbers are almost exactly the distance of the planets from the sun, measured in astronomical units (AU, the distance between the sun and the earth, which is set as 1.0). Thus Mercury is 0.4 AU, Venus 0.7 and Mars 1.6 AU away from the sun.

It was all quite neat, but it contained a serious problem: there was no planet at 2.8 AU. Beyond that the rest of the known planets dropped nicely into place: Jupiter was 5.2 and Saturn 9.55 AU. The next number on the Titus-Bode sequence was (96 * 2 + 4)/10 or 19.6, and a decade later, in 1781, William Herschel duly discovered the seventh planet, Uranus, at a distance of 19.22 AU — almost exactly where the sequence predicted it should be!

So what to do about the gap between planets 4 and 5, Mars and Jupiter? The Titus-Bode sequence was so compelling that astronomers actually started to search for a planet at 2.8 AU from the sun. That was quite bizarre, because any planet at this distance would be easily visible to the naked eye and would have been known to mankind for millennia. It was as though reason told you there was a rhinoceros living in your bathroom, and the logic of the arguments is so compelling that you actually start looking for it.

Nobody found anything, for twenty years. Then came Giuseppe Piazzi (1746–1826, image on the left by F. Bordiga for the Smithsonian Institute Library). He was an Italian Catholic priest, mathematician and astronomer, who had compiled the Palermo Catalogue of stars with over 7,600 entries, all documented with unprecedented precision.

In the night of January 1st 1801, at about 8:00 p.m., while working on his star catalogue, Piazzi noticed an unknown eighth magnitude “stellar object” in the constellation of Taurus. During the following nights he discovered that it had moved against the background of stars. After four nights of observations he told his colleagues about his discovery — and a suspicion he entertained:

I have announced this star as a comet, but since it is not accompanied by any nebulosity and, further, since its movement is so slow and rather uniform, it has occurred to me several times that it might be something better than a comet. But I have been careful not to advance this supposition to the public.

What Piazzi was saying was that this just might be the missing planet. He tracked the motion of the object as it moved through the background of stars for 41 days, during which time it covered only a tiny 3° arc of the night sky. After that he took ill, and the area of the sky soon moved into the glare of the sun. No further observations were possible until much later in the year. He published his observations in September 1801, and had all of astronomical Europe discussing the new planet Piazzi may have found.

Once the area of the sky reappeared in the morning sky astronomers got to work searching for Piazzi’s object. But they failed to find anything. The contemporary mathematical tools at their disposal were inadequate — and the sky too vast. Pierre-Simon Laplace, the dean of the French astrophysical establishment, declared that tracking the object from the available data simply could not be done. Astronomers began criticizing the whole story, its accuracy and veracity. “Peoples are starting to doubt,” one of them wrote, “Already sceptics are making jokes about it. What is Devil Piazzi doing?”

But there was one young man who saw things differently. The 24-year-old German mathematician considered it “a mathematical challenge that commends itself by its difficulty and elegance.” All hopes of discovering in the heavens “this planetary atom, among innumerable small stars, after the lapse of nearly a year, rest solely upon very few observations,” he wrote. He went to work and in a little more than a month had devised a method for computing the object’s orbit using only three of Piazzi’s original observations. He produced a perfect ellipse which provided positions that were quite different to those proposed by the astronomers.

The youthful mathematician was Carl Friedrich Gauss. When astronomers trained their telescopes to the area defined by him they were immediately able to locate the new planet. If you want to know more about the subject I recommend you read this section of Giorgia Foderà Serio’s history of the Palermo Astronomical Observatory.

Piazzi called the new planet Ceres. It was later discovered to be 950 km in diameter and located 415 million kilometres from the sun.

Ceres was well within the 2.8 AU gap in the Titus-Bode sequence, but was very small compared to the other planets (the smallest, Pluto, is 2300 km in diameter). So astronomers called it a “minor planet” and continued searching for the big one. By 1808 they had observed three more objects within the same orbital slot: Pallas, Juno and Vesta, all slightly smaller than Ceres. Then came Astraea, discovered in 1845, and after that more and more and more. Soon it became clear that there was no real planet at position five in the Titus-Bode scale. (Here Enders burst out: “It was a planet that had exploded!” Not quite, the rocks had for some reason not been able to coagulate to form a full planet — but nice try, Endy). Today we know that there are billions of objects circling in the Mars-Jupiter slot. They range from pebbles, piles of rubble, massive rocks (80,000 of which have a diameter of a kilometer or more) to minor planets — just four of which make up more than half of the total mass. The rest are called asteroids.

This is a typical depiction of the Asteroid Belt:

But don’t be misled, that is not at all what it looks like. My article True dimensions of Space puts it into somewhat shocking perspective and describes what it is like to traverse the Asteroid Belt.

A nice tale, and Enders could not take is eyes off me while I was narrating. A week later I asked him to retell the story, to reinforce it in his mind. Before he could start his mother called out from the other room: “He has been telling it to everybody, here at home and at daycare.” Clearly it impressed him no end.

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