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The American Kepler

J. Donald Fernie

Planet Kirkwood

The fact is that the statistics were really pretty sparse. Because Mercury has no planet between it and the sun, and Neptune in Kirkwood's time had no known planet beyond it, neither could have a D value calculated for it (although their masses entered into the D values for Venus and Uranus respectively). Moreover, since there is no major planet between Mars and Jupiter, although the asteroids are there and the curious Titius-Bode relation predicts a planet there, one cannot determine D for either Mars or Jupiter. That left Venus, Earth, Saturn and Uranus. The rotational period of Venus (and thus n) was essentially unknown at the time, but vague markings seen telescopically suggested a period near one day, and, Venus being consistently referred to as Earth's "sister" planet, that was the value used by Walker and probably Kirkwood. (It is, in fact, 244.3 days, and the rotation is backwards to boot!)

Figure 4. Using modern dataClick to Enlarge Image

With so little to go on, Walker adopted a two-stage procedure. He ingenuously explained how he first used the data for Venus, Earth and Saturn to determine a preliminary relation between n and D. He then used that relation to work backward and establish that the supposed planet (named "Kirkwood" by Walker), which was thought to have broken up to produce the asteroids, must have been 2.908511 times the earth's distance from the sun, had a mass of 0.262290 earth masses and a rotational period of 2.23904 days. With that established he could then calculate D for Mars, "Kirkwood" and Jupiter, and include them in the n-D relation. Furthermore, this procedure also resulted in Walker's "slight modification" of three other masses, and so, in the end, the marvelous results seen in Figure 3. Surprise! Surprise! No wonder that those like Gould and Peirce, who perhaps never delved into the details, were extreme in their praise of these findings. Figure 4 shows what one gets using today's input numbers and restricting oneself to just Venus, Earth, Saturn and Uranus. Not nearly as exciting! As for the putative planet "Kirkwood," it is now virtually certain that no such planet ever existed. More likely the powerful gravity of proto-Jupiter prevented smaller bodies in that region from coalescing into a full-blown planet in the early stages of the solar system, resulting in only a belt of asteroids.

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