  It is shown that orbital period ratios of successive secondaries in the Solar
planetary and giant satellite systems and in exoplanetary systems are
preferentially closer to irreducible fractions formed with Fibonacci numbers
between 1 and 8 than to other fractions, in a ratio of approximately 60% to
40%. Furthermore, if sets of minor planets are chosen with gradually smaller
inclinations and eccentricities, the proximity to Fibonacci fractions of their
period ratios with Jupiter or Mars$'$ period tends to increase. Finally, a
simple model explains why the resonances with ratios of orbital periods $P_{1}$
and $P_{2}$ of successive secondaries being equal to ratio of small integers
$p$ and $(p+q)$, $P_{1}/P_{2}=p/(p+q)$, are stronger and more commonly
observed.
