2009/03/10 by Vladan Panković, Vladan Pankovic, Pankovic, Vladan +2
Engineering · Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #History and Developments in Astronomy #Relativity and Gravitational Theory #Spacecraft Dynamics and Control #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.0903.1732
4 pages, no figures
arxiv created 2009/03/10 · openalex publication_date 2009/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we present a close correlation between third Kepler law and Titius-Bode empirical rule. Concretely, we demonstrate that third Kepler law, or, corresponding equilibrium condition between centrifugal and Newtonian gravitational force, implies that planet orbital momentum becomes effectively a function of the planet distance as unique variable and vice versa. Then, approximation of the planet distance by its first order Taylor expansion over planet orbital momentum holds an exponential form corresponding to Titius-Bode rule. In this way it is not necessary postulate exponential form of the planet distance (as it has been done by Scardigli) but only discrete values of its argument. Physically, it simply means that, in the linear approximation, "quantized" planets orbital momentums do a geometrical progression.