# The Missing Planet

As far as we are aware, the first person to contemplate the existence of a planet between Mars and Jupiter was Johannes Kepler. His argument was not a scientific one but rather based on his ideas of harmony, convinced that a creator God would create a universe with pleasing numerical properties. He wrote in the Preface of Mysterium Cosmographicum (1595):-
There were three things in particular about which I persistently sought the reasons why they were such and not otherwise: the number, the size, and the motion of the circles. ...  In the beginning I attacked the business by numbers, and considered whether one circle was twice another, or three times, or four times, or whatever, and how far any one was separated from another according to Copernicus.  I wasted a great deal of time on that toil, as if at a game, since no agreement appeared either in the proportions themselves or in the differences; and I derived nothing of value from that except that I engraved deeply on my memory the distances which were published by Copernicus. ...  If (thought I) God allotted motions to the spheres to correspond with their distances, similarly he made the distances themselves correspond with something. Since, then, this method was not a success, I tried an approach by another way, of remarkable boldness.  Between Jupiter and Mars I placed a new planet, and also another between Venus and Mercury, which were to be invisible perhaps on account of their tiny size, and I assigned periodic times to them.  For I thought that in this way I should produce some agreement between the ratios. ...  Yet the interposition of a single planet was not sufficient for the huge gap between Jupiter and Mars; for the ratio of Jupiter to the new planet remained greater than that of Saturn to Jupiter.
Kepler himself did not continue to work on the idea of a planet between Mars and Jupiter but he put the idea into the arena. It was a long time, however, before anyone else seems to have commented on this. The next we know of is a comment by William Whiston in 1707 where he gave the distances of the planets from the sun, in millions of miles, as follows
Mercury   Venus   Earth   Mars   Jupiter   Saturn
32       59      81     123      424      777
(The actual distances, in millions of miles, are 36, 67, 93, 142, 484, 890 so the 1707 values are too small by about a factor of 0.87).

Whiston comments that the gap between Mars and Jupiter is larger than he would expect. Soon others commented on the gap, one theory being that there had been a world there that had been destroyed by a comet. Colin Maclaurin postulated in around 1739 that there must be an undiscovered planet between Mars and Jupiter. In 1761 Johann Lambert published Cosmologische Briefe über die Einrichtung des Weltbaues in which he writes:-
And who knows whether or not there are missing planets which have moved out of the wide space which exists between Mars and Jupiter.
A more convincing argument for an undiscovered planet between Mars and Jupiter came through Bode's Law. This takes the sequence
44+34+64+124+244+484+96, ...
Divide by 10 to get
0.40.71.01.62.85.210.0, ...
The distances of the planets Mercury, Venus, Earth, Mars, Jupiter, Saturn from the Sun (taking the distance of the Earth as 1) are
0.390.721.01.525.29.5.
Bode's Law, which is not a "law", has a rather complicated history which we will now summarise.

In The Elements of Astronomy (1702), David Gregory writes:-
... supposing the distance of the earth from the Sun to be divided into ten equal parts, of these the distance of Mercury will be about four, of Venus seven, of Mars fifteen, of Jupiter fifty-two, and that of Saturn ninety-five.
Christian Wolff (1679-1754), the professor of mathematics and philosophy at Marburg, wrote a book in 1726 in which he repeated David Gregory's words so closely that he must have read The Elements of Astronomy (1702). Neither David Gregory nor Christian Wolff make any mathematical sequence from the numbers they quote.

Charles Bonnet was a naturalist who wrote the book Contemplation de la nature (1764) in an attempt to show nature had structure and purpose designed by its Creator. The book contains little relevant to Bode's Law but there is a sentence:-
Not only has it been reserved for modern astronomers to enrich our sky with new planets, but also to push back the frontiers of our planetary system.
Charles Bonnet's book was translated into Italian, German, English and Dutch. The German translation was made by Johann Daniel Titius (1729-1976) who was the professor of astronomy at Wittenburg. He added the following footnote in his translation referring to the sentence we have quoted above:-
Take notice of the distance of the planets from one another, and recognise that almost all are separated from one another in a proportion which matches their bodily magnitudes. Divide the distance of the Sun to Saturn into 100 parts: then Mercury is separated by 4 such parts from the Sun, Venus by 4 + 3 = 7 such parts, the Earth by 4 + 6 = 10, Mars 4 + 12 = 16. But notice that from Mars to Jupiter there comes a deviation from this so-exact progression. From Mars there follows a space of 4 + 24 = 28 such parts, but so far no planet or satellite was sighted there. But should the Lord Architect have left that space empty? Not at all. Let us therefore assume that this space without doubt belongs to the still-undiscovered satellites of Mars; let us also add that perhaps Jupiter still has around itself some smaller ones which have not been sighted yet by any telescope. Next to this still-unexplored space there rises Jupiter's sphere of influence at 4 + 48 = 52 parts; and that of Saturn at 4 + 96 = 100 parts. What a wonderful relation!
Johann Elert Bode (1747-1826) had published the elementary treatise on astronomy Anleitung zur Kenntnis des gestirten Himmels in 1768. The book was very popular and ran to ten editions. In the second edition, published in 1772, Bode added a footnote, essentially copying Titius's footnote in Charles Bonnet's book:-
This latter point seems in particular to follow from the astonishing relation which the known six planets observe in their distances from the Sun. Let the distance from the Sun to Saturn be taken as 100, then Mercury is separated by 4 such parts from the Sun. Venus is 4 + 3 = 7. The Earth 4 + 6 = 10. Mars 4 + 12 = 16. Now comes a gap in this so orderly progression. After Mars there follows a space of 4 + 24 = 28 parts, in which no planet has yet been seen. Can one believe that the Founder of the universe had left this space empty? Certainly not. From here we come to the distance of Jupiter by 4 + 48 = 52 parts, and finally to that of Saturn by 4 + 96 = 100 parts.
On reading this, Johann Lambert wrote to Bode in a letter dated 3 February 1772:-
Your noticing on page 462 of your book of the distances of the planets would have pleased Kepler, who wrote an entire book on this question; it could lend a reason as to why the planets are distant from the Sun according to a particular and simple law unrelated to their mass.
In the 1777 third edition of his book, Bode added the sentence:-
That this chief planet between Mars and Jupiter must complete its revolution around the Sun in $4\large\frac{1}{2}\normalsize$ years can be computed from a law discovered by Kepler, namely that the squares of the orbital periods of two planets are to one another as are the cubes of their distances from the Sun.
One might reasonably ask why we speak today of "Bode's Law" since he seems to have done nothing more than quoted Titius. Well, today many prefer to call it the "Titius-Bode Law" in recognition of the fact that Titius seems to be the first to enunciate it as a mathematical progression. Bode never claimed originality, always saying that he copied Titius's footnote in Charles Bonnet's book. Perhaps the fact that Titius himself claimed that he had done nothing original, saying he simply followed Christian Wolff, might be a factor in the naming of the Law. Of course Titius was being over modest here since Wolff never mentions the mathematical progression.

On 13 March 1781 William Herschel discovered the planet Uranus, the first planet to be discovered in historic times, observing from 19 New King Street, Bath, England. Let us explain briefly the circumstances. Herschel had been examining double stars, that is two stars appearing close together in the sky. His hope was that the fainter one was much further away and he would be able to determine the relative distances using parallax with the diameter of the Earth's orbit as the base line. He was observing the double star Eta Geminorum (also known as Propus) which consists of a 3.3 magnitude star and a 6.5 magnitude star 1.5" apart. He noticed an object so close to the pair as to almost make it look like a triple system, but this third object showed a disk. Three days later he observed that it had moved but he was unsure whether it was a planet of a comet.

Remarkably, when its orbit was computed, it was seen to come close to satisfying Bode's Law. Continuing the progression, the next planet to Saturn, according to Bode's Law, should at distance 196 from the Sun, so 19.6 times further away than the Earth. In fact, on average, Uranus is 19.2 times further from the Sun than the Earth. Many who had thought (probably correctly!) that Bode's Law was a coincidence, now came to believe it must have a scientific basis. Is this not just how science works? Propose a theory to explain the current data, make a prediction and, if the prediction is true, then the theory is confirmed! Once Uranus was confirmed as a planet, in 1783, then astronomers began to search for the 'missing planet' at distance 2.8 times further from the Sun than the Earth.

Franz Xaver von Zach (1754-1832) was tutor to the Saxon ambassador, Hans Moritz von Brühl. Von Zach was based in Paris during 1780-83 when he frequently met Jérôme Lalande and Pierre-Simon Laplace. In 1883 his work took him to London where he discussed Bode's Law with William Herschel. He became passionate about finding a "missing planet" between Mars and Jupiter and, by 1785 he had computed what he supposed to be its orbit giving confidently its distance from the Sun as 2.82 times the distance of the Earth from the Sun, its orbital period as 4.74 years, its inclination 1º 36', etc. He deposited this information in sealed envelopes with various astronomers including Johann Bode and Johann Gottfried Köhler (1745-1801), the director of the Mathematisch-Physikalischer Salon, a museum of scientific instruments in Dresden. Bode was appointed director of the Berlin Observatory in 1786 and von Zach was appointed director of the new observatory on Seeberg hill at Gotha in 1786.

By 1800, von Zach's efforts to observe the "new planet" had continued to be unsuccessful. He therefore decided the best step forward was to set up a society of 24 astronomers and divide the zodiac into 24 zones, one astronomer to be assigned to each zone. The Society, the Himmels Polizei or Celestial Police, was set up on 20 September 1800 with 24 astronomers including von Zach, Bode, Johann Karl Burckhardt, Pierre François-André Méchain, Charles Messier, Nevil Maskelyne, William Herschel, Barnaba Oriani, and Giuseppe Piazzi. It is unclear which of these received invitations before Ceres was actually discovered. Some who received the invitation, such as Lalande, turned it down and von Zach replaced them with another. In fact although Piazzi was on the list to receive an invitation, he found Ceres before von Zach got round to sending out his invitation! Let us now look at how Piazzi made his discovery.

On 1 January 1801, Piazzi was working with his assistant Niccolò Cacciatore (1770-1841). Cacciatore had studied mathematics and physics at Palermo and began to assist Piazzi in 1798, officially becoming his assistant in 1800. It was on this first day of 1801 that Ceres was first seen by Piazzi and we give below the account by Captain Basil Hall in 1841, relating the story as told to him by Niccolò Cacciatore, Piazzi's assistant in 1801 but the Director of the Palermo Observatory by the time the meeting with Basil Hall took place (see, for example, [9]):-
Most people are aware that the celebrated astronomer Piazzi discovered the small planet Ceres at Palermo in this very observatory, with an instrument of Ramsden's which we had the satisfaction of seeing. It was made on the 1st of January, 1801, at which period the present astronomer, Cacciatore, was Piazzi's assistant in the observatory of which he is now the chief. As Piazzi was at that time engaged in making the noble catalogue of the stars, which has since become so well known, he placed himself at the telescope, and observed the stars as they passed the meridian, while Cacciatore wrote down the times, and the polar distances, as they were read off by his chief. Certain stars passed the wires, and were recorded as usual on the 1st of January, 1801. On the next night, when the same part of the heavens came under review, several of the stars observed the evening before were again looked at, and their places recorded. Of these, however, there was one which did not fit the position assigned to it on the previous night, either in right ascension, or in declination. "I think," said Piazzi to his companion, "you must, accidentally, have written down the time of that star's passage, and its distance from the pole, incorrectly." "To this," said Cacciatore, who told me the story, "I made no reply, but took especial pains to set down the next evening's observations with great care. On the third night there again occurred a discordance, and again a remark from Piazzi that an erroneous entry had probably been made by me of the place of the star. I was rather piqued at this," said Cacciatore, "and respectfully suggested that possibly the error lay in the observation, not in the record. Under these circumstances, and both parties being fully awakened as to the importance of the result, we watched for the transit of the disputed star with great anxiety on the fourth night. When lo, and behold! it was again wide of the place it had occupied in the heavens on the preceding and all the other nights on which it had been observed. 'Oh, oh!' cried the delighted Piazzi, 'we have found a planet while we thought we were observing a fixed star; let us watch it more attentively?'" The result soon confirmed this conjecture, and thus was made one of the most interesting, and I may say useful, astronomical discoveries of modern times.
Piazzi made nineteen observations of Ceres over 42 days but on 12 February it moved too close to the sun to be visible.

The way that Piazzi announced his discovery was a little strange. The following notice, dated 15 January 1801, appeared in the Journal de Paris in February 1801:-
Sicily - Palermo, January 15. On the 1st of this month, a new comet in the shoulder of Taurus, near the 19th star of Mayer, was discovered from our observatory. It was observed on 1st, 2nd, 3rd and 4th, as it passed the meridian. Although it is not covered with any kind of nebulous spot, it still cannot be seen with the naked eye. Its movement is retrograde; it goes forward towards the north.
Confusion arose from this announcement since it contains a misprint. Instead of the "19th star of Mayer," it should have read the "109th star of Mayer." This refers to the catalogue of Tobias Mayer.

One has to assume this was sent by Piazzi (although it is just possible, but unlikely, it was sent by Cacciatore) but no name is attached. Lalande, the leading astronomer of the day, learnt of the discovery by reading this notice; Piazzi did not inform him personally. In fact initially Piazzi only sent letters reporting his discovery to two people, Johann Elert Bode and Barnaba Oriani, on 24 January. Bode, the director of the Berlin Observatory, received his letter on 20 March, but Oriani, who worked at the Observatory of Brera in Milan, only received it on 5 April. The delay in the letter reaching Oriani in Milan was due to the occupation by Napoleon. We should note that Oriani was a natural person for Piazzi to write to since the two were long term friends and collaborators. Let us note a rather telling difference in the two letters. To Bode he states that he had discovered a comet but to his friend Oriani he says:-
I have announced this star as a comet, but since it shows no nebulosity, and moreover, since it had a slow and rather uniform motion, I surmise that it could be something better than a comet. However, I would not by any means advance publicly this conjecture. As soon as I shall have a larger number of observations, I will try to compute its elements.
Bode, after receiving Piazzi's letter contacted von Zach, giving him the details he had been sent and details of his attempt to calculate an orbit. Von Zach then wrote an article for the Monthly Correspondence in which he essentially accused Piazzi of deliberately failing to give full information so that he could have the honour of computing the orbit himself. There were errors in Piazzi's information but they were almost certainly misprints and not deliberate attempts to confuse other astronomers. In fact data he gave was sufficient to compute an orbit although nobody who attempted it at this time had the mathematical expertise.

After Piazzi discovery, Ceres moved too close to the Sun to be visible and by the time it reached a position where it could have been seen again, its position was not known accurately enough and it was lost. Bode decided to call the "planet" that Piazzi had discovered 'Juno' while von Zach started to call it 'Hera', the Greek form of Juno. In fact they had used this name from 1785 since von Zach's search for it at this time so impressed his patron, the Duke of Gotha, that the Duke gave the name Hera to the undiscovered "planet". Oriani wrote to Piazzi on 25 July 1801 telling him that these names were universally accepted by the Germans. Piazzi replied to Oriani on 25 August 1801:-
If the Germans think they have the right to name somebody else's discoveries they can call my new star the way they want: as for me I will always call it Ceres and I will be very obliged if you and your colleagues will do the same.
Piazzi had originally wanted to name the "planet" Cerere Ferdinandea, Cerere or Ceres being a goddess whose earthly home was supposed to be Sicily and Ferdinandea for King Ferdinand. The Duke of Gotha did not give up easily, however, and wrote in the Monthly Correspondence:-
The Greek name Hera is preferred to the Latin name Juno, because 1) the latter has already been ascribed to the planet Venus; 2) Hera is the name of a city in Sicily, through which the memory of the discoveries made on this island and the glorious name of the discoverer of this eighth primary planet will be contained and immortalised.
Other suggestions such as Vulkan and Cupido were made while Lalande wanted it called "La planete Piazzi" saying it deserved to be named for his pupil Piazzi. Laplace agreed with the Germans, writing that Napoleon would have preferred the name Juno and he thought it was right to put Juno next to Jupiter. Piazzi then asserted himself and wrote in the Monthly Correspondence:-
I have noted in your journal the desire of a few to give this new planet the name Juno rather than Ceres. I trust that these astronomers, who are peaceful people, will never consent to having their deities called the name of a goddess as anxious, jealous and vindictive as Juno. Jupiter finally chased her from the sky; in her place he had Ceres appear, who has so much more right to the homage of mankind.
Piazzi's attack on Juno won the day. Von Zach then agreed to call the "planet" Ceres but asked Piazzi to drop the name Ferdinandea since it made the name too long.

Johann Karl Burckhardt attempted to compute a possible orbit for Ceres from Piazzi's observations but attempts to find it where his orbit calculations showed that it should be failed. By August 1801 Ceres had not been found again and several astronomers began to think that it did not exist. For example, in December 1801 Barnaba Oriani wrote:-
What is going on with the Ceres Ferdinandea? Nothing has been found as yet either in France or in Germany. Peoples are starting to doubt: Already sceptics are making jokes about it. What is Devil Piazzi doing? Lalande wrote me that Piazzi has changed again his observations and that he has made a new Edition of them! What does that mean? Lalande in his letter adds: "This is why I do not believe in the planet."
By the time Oriani wrote this, an accurate position for Ceres had been predicted by Carl Friedrich Gauss. In fact Piazzi had published his complete set of 19 observations of Ceres in the September 1801 issue of the Monthly Correspondence. Gauss used just three of Piazzi's observations and, developing new mathematical methods, was able to predict the position of Ceres very accurately. Using Gauss's prediction, von Zach found Ceres on 7 December 1801 very close to the estimated position. Gauss refined his methods and published them in the book Theoria motus (1809). Here is an extract from the English translation of the Preface of Gauss's book:-
... it seems somewhat strange that the general problem, - "To determine the orbit of a heavenly body, without any hypothetical assumption, from observations not embracing a great period of time, and not allowing a selection with a view to the application of special methods," was almost wholly neglected up to the beginning of the present century; or, at least, not treated by any one in a manner worthy of its importance; since it assuredly commended itself to mathematicians by its difficulty and elegance, even if its great utility in practice were not apparent. An opinion had universally prevailed that a complete determination from observations embracing a short interval of time was impossible, - an ill-founded opinion, - for it is now clearly shown that the orbit of a heavenly body may be determined quite nearly from good observations embracing only a few days; and this without any hypothetical assumption.

Some ideas occurred to me in the month of September of the year 1801, engaged at the time on a very different subject, which seemed to point to the solution of the great problem of which I have spoken. Under such circumstances we not infrequently, for fear of being too much led away by an attractive investigation, suffer the associations of ideas, which, more attentively considered, might have proved most fruitful in results, to be lost from neglect. And the same fate might have befallen these conceptions, had they not happily occurred at the most propitious moment for their preservation and encouragement that could have been selected. For just about this time the report of the new planet, discovered on the first day of January of that year with the telescope at Palermo, was the subject of universal conversation; and soon afterwards the observations made by that distinguished astronomer Piazzi from the above date to the eleventh of February were published. Nowhere in the annals of astronomy do we meet with so great an opportunity, and a greater one could hardly be imagined, for showing most strikingly, the value of this problem, than in this crisis and urgent necessity, when all hope of discovering in the heavens this planetary atom, among innumerable small stars after the lapse of nearly a year, rested solely upon a sufficiently approximate knowledge of its orbit to be based upon these very few observations. Could I ever have found a more seasonable opportunity to test the practical value of my conceptions, than now in employing them for the determination of the orbit of the planet Ceres, which during these forty-one days had described a geocentric arc of only three degrees, and after the lapse of a year must be looked for in a region of the heavens very remote from that in which it was last seen? This first application of the method was made in the month of October, 1801, and the first clear night, when the planet was sought for [by von Zach on 7 December 1801] as directed by the numbers deduced from it, restored the fugitive to observation.

Gauss solved the problem using only elementary mathematics and the article [20] presents an excellent account of the mathematics. Here is a short quote giving an overview of Gauss's method:-
Gauss's first goal, and the most challenging one, was to determine the distance of Ceres from the Earth, for at least one of the three observations. In fact, Gauss chose the second of the unknown distances - the one corresponding to the intermediate of the three selected observations - as the prime target of his efforts. Finding that distance essentially  breaks the back of the problem. Having accomplished that, Gauss would be in a position to successively "mop up" the rest. In fact, Gauss used his calculation of that value to determine the distances for the first and third observations; from that, in turn, he determined the corresponding spatial positions of Ceres, and from the two spatial conditions and the corresponding time, he calculated a first approximation of the orbital elements. Using the coherence provided by that approximate orbital calculation, he could revise the initial calculation of the distances, and obtain a second, more precise orbit, and so on, until all values in the calculation became coherent with each other and the three selected observations.
The least squares method was developed by Gauss as a direct consequence of the method he had used to solve the problem of Ceres's orbit.

On 28 March 1802, Olbers discovered another small "planet" roughly the same distance from the Sun as Ceres. He named it Pallas. Soon after this discovery William Herschel began to argue that a new name was needed for these bodies. He wrote in a letter to his friend William Watson in April 1802:-
Now as we already have Planets, Comets, Satellites, pray help me to another dignified name as soon as possible. If I could in any way express the condition of a nimble, small, interloper going obliquely through the majestic orbits of the great bodies of the Solar System it would be just what is required.
Of a number of suggestions that came back to William Herschel, although he did not greatly like any of them, he thought "asteroid" was the best. On 22 May 1802 he wrote to Gauss, Méchain, Lalande, Laplace, Bode, von Zach, Olbers, Karl Seyffer, Johann Schroeter and Piazzi telling them he favoured calling these bodies 'asteroids'. For example, to Gauss he wrote:-
These new stars are mixed with the small fixed stars of the heavens and resemble them so much that even with a good telescope they cannot be distinguished from them. From this their asteroidal or starlike appearance I take my name, and call these new celestial bodies Asteroids.
William Herschel ended his letter to Piazzi as follows:-
Moreover, if we were to call Ceres a planet, it would not fill the intermediate space between Mars and Jupiter with the proper dignity required for that station. Whereas, in the rank of Asteroids it stands first, and on account of the novelty of the discovery reflects double honour on the present age as well as on Mr Piazzi who discovered it. I hope you will see the above classification in its proper light, as so far from undervaluing your eminent discovery it places it, in my opinion, in a more exalted station. To be the first who made us acquainted with a new species of primary heavenly bodies is certainly more meritorious than merely to add what, if it were called planet, must stand in a very inferior situation of smallness.
Piazzi wrote back to William Herschel suggesting that "planetoid" would be a better name but Herschel continued to argue for "asteroid". Had Herschel been prepared to go with Piazzi's suggestion, it would almost certainly have gained fairly rapid acceptance. With his persistence with asteroid, there was quite a strong opposition but eventually it was eventually accepted by most. It is interesting, however, that William Herschel's son John Herschel did not accept 'asteroid' and, writing in 1833, he calls Ceres, Pallas, Vesta and Juno planets.

The International Astronomical Union was founded in 1919 and it never used the name asteroid, calling Ceres and similar bodies "minor planets". At the 26th General Assembly of the International Astronomical Union held in Prague in August 2006, it was decided to call Ceres and similar bodies "dwarf planets".

In 2007 NASA's Dawn mission launched from Cape Canaveral in Florida on a journey to orbit Vesta and Ceres. On 6 March 2015 Dawn was captured by Ceres and began to orbit it:-
Dawn discovered that the inner solar system's only dwarf planet was an ocean world where water and ammonia reacted with silicate rocks. As the ocean froze, salts and other tell-tale minerals concentrated into deposits that are now exposed in many locations across the surface. Dawn also found organics in several locations on Ceres' surface.

### References (show)

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https://www.jpl.nasa.gov/news/ceres-keeping-well-guarded-secrets-for-215-years
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