mean distribution of Jupiter satellites

The titius-bode rule gives the distribution of the planets in
astronomical units by

r=0.4+(0.3)2^n
where n=-oo for mercury, and then n=1 for venus, n=2 for earth and so
on.

Since that is a geometric progression, I will throw out one for the
natural sattellites of Jupiter from the first natural sattellite,
adrastea, to the last Galilean, callisto. After callisto it just becomes
impossible. I have made a mean curve where io and europa fall short and
ganymede and callisto long. It is:

r=(2^n)+1 where n starts at ( -2) for adrastea and we define its actual
distance from jupiter to be 1. Thus the predicted distance is r=1.25.
The next is amalthea (n=-1)at an actual distance of 1.4. The predicted
distance is 1.5. Next is thebe (n=0) at an actual distance of 1.7 and a
predicted distance of 2.0. io, the first galilean satellite is at n=1
and has an actual distance of 3.3 and a predicted distance of 3.0.
Europa (n=2) has an actual distance of 5.2 and a predicted distance of
5.0. Ganymede (n=3) has an actual distance of 8.3 and predicted
distance of 9.0. Callisto (n=4) has an actual distance of 14.6 and
predicted distance of 17.
--Ian


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