table 5 Accuracy of Bode’s Law
Object Bode’s Calculation Prediction Actual Distance
Mercury 0.4 + 0·0.3 0.4 0.39
Venus 0.4 + 1·0.3 0.7 0.72
Earth 0.4 + 2·0.3 1.0 1.00
Mars 0.4 + 4·0.3 1.6 1.52
Ceres 0.4 + 8·0.3 2.8 2.77
Jupiter 0.4 + 16·0.3 5.2 5.20
Saturn 0.4 + 32·0.3 10.0 9.54
Uranus 0.4 + 64·0.3 19.6 19.19
Neptune 0.4 + 128·0.3 38.8 30.07
Distances are expressed in astronomical units.
agrees with the law, and its distance was taken as strong evidence of the correctness and reliability of the law. The large asteroid Ceres, discovered 1801, has mean orbital distance 2.77, which seemed to fill the apparent gap between Mars and Jupiter. Some astronomers were so impressed by the apparent success of Bode’s Law that they proposed the name Ophion for a large planet predicted to lie beyond Uranus at a distance of 38.8 AU.
Table 5 gives an indication of the accuracy of Bode’s Law.
Alas, Neptune, discovered in 1846, has a mean orbital distance of 30.07, and Pluto, discovered in 1930, has a mean orbital distance of 39.5; these two planets provide large discrepancies from the predicted values of 38.8 and 77.2, respectively. (Note, however, that 38.8 is close to the actual value of 39.5 for Pluto, as if Bode’s Law skips the location of Neptune.) In 2006, the International Astronomical Union gave Ceres and Pluto the designation of
“dwarf planets.”
Astronomers have wondered why such a simple sequence should seem to explain so much about the Solar System. Some astronomers have even conjectured that the deviation of Neptune and Pluto from their predicted positions means that they are no longer in their original orbits in the Solar System. Today scientists have major reservations about Bode’s Law, and the law is clearly not as universally applicable as other laws in this
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book. The relation may be purely empirical and perhaps represents a coincidence.
Some astronomers hypothesize that a phenomenon of “orbital reso- nances,” which is caused by orbiting bodies that gravitationally interact with other orbiting bodies, can create regions around the Sun that are free of long-term stable orbits and thus, to some degree, can account for the spacing of planets. Orbital resonances can occur when two orbiting bodies have periods of revolution that are in a simple integer ratio such that the bodies exert a regular gravitational influence on each other.
Johann Elert Bode (1747–1826), German astronomer famous for his statement of Bode’s Law expressing the proportionate distances of several planets from the Sun.
CURIOSITYFILE: Bode was responsible for naming the planet Uranus after the ancient Greek god that came every night to mate with the Earth Mother, Gaia. The god Uranus had imprisoned Gaia’s youngest children deep within Earth, fearful of their power. In order to prevent Uranus from fathering any more children, Gaia had their son Cronus ambush Uranus and castrate him, tossing the torn testicles into the ocean.
Professor Bode could not explainwhythe rule worked . . . but anybody who could add and multiply had no doubt that it did work.
—Willy Ley,Watchers of the Skies Bode’s Law is neither Bode’s nor a law.
—Mark Littmann,Planets Beyond
From Mars outward there follows a space . . . in which, up to now, no planet has been seen. Can we believe that the Creator of the world has left this space empty? Certainly not!
—Johann Bode, Instruction for the Knowledge of the Starry Heavens
Johann Elert Bode (pronounced b ¯o’duh) was born in Hamburg, Ger- many. His father was a merchant. Little has been published about Bode’s boyhood. We do know that in 1768, Bode published his popular book, Anleitung zur Kenntnis des gestirnten Himmels(Instruction for the Knowl- edge of the Starry Heavens), in which he popularized the empirical law on 146 | a r c h i m e d e s t o h a w k i n g
planetary distances, originally discovered by German astronomer Johann Titius.
Titius had merely presented the law in a footnote to his 1766 German translation of naturalist Charles Bonnet’s Contemplation de la Nature.
Bode discovered the footnote and inserted it into the new edition of his own astronomy book, without reference to Titius. Mark Littmann writes inPlanets Beyond: Discovering the Outer Solar System:
This exercise by Titius, buried in another author’s book, would probably have attracted no attention had not Bode happened across it. Bode was a young, energetic, self-taught astronomer who, at the age of 21, had published a very popular introduction to the heavens. In 1772, he had just been hired by the Berlin Academy of Sciences to work on its annual astronomical almanac [which was]
selling poorly. Bode quickly transformed it from a money loser to a high-profit item by correcting the publication’s inaccuracies and by [supplementing it with] general science news from around the world.
Bode was also employed by the Berlin Academy of Sciences to perform laborious mathematical calculations, and he was a director of the Berlin Observatory. In 1801, while still at the observatory, he published the Uranographia, a gorgeous celestial atlas showing the positions of stars and other astronomical objects—and also included artistic depictions of the constellations. Many of the diagrams are a wonder to behold, with their drawings of animals and mythic heroes superimposed on the stars.
Bode even introduced new constellations in his Uranographia, such as a set of stars forming the constellation Machina Electrica along with a drawing of an electrostatic generator (not quite as majestic an image as the superhuman gods of yore!). However, Bode’s new constellations never achieved lasting acceptance.
Uranographia contained eighteen maps and two planispheres (polar projections with an adjustable overlay to show the stars visible at a par- ticular time and place). The book showed almost 17,000 stars and 2,500 nebulae and represented all astronomical objects defined by the cartogra- phers during the previous centuries.Uranographia marked the end of a long history of artistic representations of the constellations, because soon the star atlas would no longer be a single work aimed at both the amateur and professional astronomer. The ideal of one large book that contains all visible objects in the sky, superimposed with artful constellation drawings, slowly lost its popularity, and subsequent atlases showed fewer ornate figures.
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The constellation Virgo, from Johann Bode’sUranographia, published in 1801.
Together with Johann Heinrich Lambert (see “Lambert’s Law of Emis- sion,” above), Bode founded theAstronomisches Jahrbuch(Astronomical Yearbook) and then theBerliner Astronomisches Jahrbuch, which he con- tinued to publish until his death in 1826.
During his life, Bode discovered several nebulae and star clusters. Alas, he also added a large number of nonexistent astronomical objects without verification—more than twenty of his discoveries never actually existed.
He also observed a number of actual comets and calculated cometary orbits.
Bode was fascinated by Uranus, the new planet discovered by German- born British astronomer William Herschel (1738–1822) in 1781. Although Herschel always referred to this planet as “Georgium Sidus” (George’s Star) to honor King George III of England, Bode proposed the name
“Uranus” after the Greek God—a name that was gradually adopted.
French astronomers actually began calling the planet Herschel before Bode proposed the name Uranus, which did not come into common usage until around 1850.
Bode collected the available astronomical observations of Uranus and published many of them in his belovedAstronomisches Jahrbuch. As he compiled the information, Bode realized that Uranus had actually been first observed by German astronomer Tobias Mayer (1723–1762) in 1756 and even earlier in 1690 by English astronomer John Flamsteed (1646–
1719), when it was cataloged as “star” 34 Tauri.
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In 1786, Bode was elected as a member of the Berlin Academy. In 1825, he retired from the post of Director of the Berlin Observatory, and he died a year later while working on theJahrbuchfor 1830. A lunar crater with a diameter of 18 kilometers was named after Bode and approved in 1935 by the International Astronomical Union General Assembly. The asteroid Bodea, discovered in 1923, was also been named after Bode. The galaxy M81 that he discovered is popularly known as “Bode’s Nebula” or “Bode’s Galaxy.”
Author and astronomer David Darling notes that Bode believed that all significant objects in space—the Sun, stars, planets, moons, and comets—are inhabited by intelligent beings. Bode remarked that habit- ability was “the most important goal of creation” and that alien life forms throughout the universe “are ready to recognize the author of their exis- tence and to praise his goodness.”
To address the seeming inhospitality of comets, Bode said, “Who can conceive what special arrangements of the wise Creator in regard to the climate, zones, dwelling places . . . may not be expected for all those on a cometary body?” Bode believed that space was probably infinite in extent, but that the cosmos was finite with God beyond the cosmos.
FURTHER READING
Darling, David, “Bode, Johann Elert (1747–1826),” in Encyclopedia of Astrobiology, Astronomy and Spaceflight; see www.daviddarling.info/
encyclopedia/B/Bode.html.
Frommert, Hartmut, and Christine Kronberg, “Johann Elert Bode (January 19, 1747–November 23, 1826),” SEDS (Students for the Exploration and Development of Space); see www.seds.org/messier/Xtra/Bios/bode.html.
Littmann, Mark, Planets Beyond: Discovering the Outer Solar System(New York: Courier Dover Publications, 2004).
Sticker, Bernhard, “Johann Bode,” in Dictionary of Scientific Biography, Charles Gillispie, editor-in-chief (New York: Charles Scribner’s Sons, 1970).
INTERLUDE: CONVERSATION STARTERS For me, a hypothesis is a statement whosetruthis tem- porarily assumed, but whosemeaningmust be beyond all doubt.
—Albert Einstein to Edward Study, September 25, 1918 I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out
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be simple, like the checker board with all its apparent complexities.
—Richard Feynman,The Character of Physical Law
Scientific principles and laws do not lie on the surface of nature. They are hidden, and must be wrested from nature by an active and elaborate technique of inquiry.
—John Dewey,Reconstruction in Philosophy
If you’re willing to answer yes to a God outside of nature, then there’s nothing inconsistent with God on rare occa- sions choosing to invade the natural world in a way that appears miraculous. If God made the natural laws, why could he not violate them when it was a particularly sig- nificant moment for him to do so?
—Francis Collins, “God vs. Science” (interview),Time, November 13, 2006
The empirical basis of objective science has nothing
“absolute” about it. Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were above a swamp. It is like a building erected on plies. The piles are driven down from above into the swamp, but not down to any natural or “given” base; and if we stop driving the piles deeper, it is not because we have reached firm ground. We simply stop when we are satisfied that the piles are firm enough to carry the structure, at least for the time being.
—Karl Popper,The Logic of Scientific Discovery
If one accepts the premise that all knowledge comes to us through our senses, Hume says, then one must logically conclude that both “Nature” and “Nature’s laws” are creations of our own imagination.
—Robert Pirsig,Zen and the Art of Motorcycle Mainte- nance
The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic under- standing of experience, can reach them. In this method- ological uncertainty, one might suppose that there were 150 | a r c h i m e d e s t o h a w k i n g
any number of possible systems of theoretical physics all equally well justified; and this opinion is no doubt correct, theoretically. But the development of physics has shown that at any given moment, out of all conceivable con- structions, a single one has always proved itself decidedly superior to all the rest.
—Albert Einstein, “Principles of Research”
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