Hi Maat
Yes, there have been a variety of alternatives to Bode's law. the one that you give has a linear sequence rather than geometric for the outer planets, just as I have. It is obviously a much better fit. Of course Bode (and Titus) really cheated with Mercury because as you go back from 1.2 to 0.6 to 0.3, the next one should be 0.15 not 0.0.
There were other suggestions that looked at the discrepancies from the main trend and one has a sine wave in it with something like 2*pi/13 in it. That one gets a good fit with extra parameters. But what is really interesting about it, is that it correctly predicted a whole set of closely spaced extra moons for Neptune (and Uranus maybe) inside the existing ones.
When I examine the large moons of the planets, I find that there are many at close to 0.0012 and 0.0024 AU from their planets. Very suggestive.



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