178 research outputs found
A Physical Interpretation of the Titius-Bode Rule and its Connection to the Closed Orbits of Bertrand's Theorem
We consider the geometric Titius-Bode rule for the semimajor axes of
planetary orbits. We derive an equivalent rule for the midpoints of the
segments between consecutive orbits along the radial direction and we interpret
it physically in terms of the work done in the gravitational field of the Sun
by particles whose orbits are perturbed around each planetary orbit. On such
energetic grounds, it is not surprising that some exoplanets in multiple-planet
extrasolar systems obey the same relation. But it is surprising that this
simple interpretation of the Titius-Bode rule also reveals new properties of
the bound closed orbits predicted by Bertrand's theorem and known since 1873.Comment: Final version, issues resolved, submitted to RA
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