Dynamical derivation of Bode's law

Details Dynamical derivation of Bode's law Dynamical derivation of Bode's law

2002-09-13

arxiv.org/abs/astro-ph/0209276v1

Int.J.Mod.Phys. D14 (2005) 153-170

Astronomy and Astrophysics

Astrophysics

27 pages

Scientific paper

10.1142/S0218271805006195

In a planetary or satellite system, idealized as n small bodies in initially coplanar, concentric orbits around a large central body, obeying Newtonian point-particle mechanics, resonant perturbations will cause dynamical evolution of the orbital radii except under highly specific mutual relationships, here derived analytically apparently for the first time. In particular, the most stable situation is achieved (in this idealized model) only when each planetary orbit is roughly twice as far from the Sun as the preceding one, as observed empirically already by Titius (1766) and Bode (1778) and used in both the discoveries of Uranus (1781) and the Asteroid Belt (1801). ETC.

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