开普勒定律与Titius-Bode定则的密切联系
A Close Correlation between Third Kepler Law and Titius-Bode Rule
摘要：
本文提出了开普勒定律与Titius-Bode经验规则之间的密切关系。具体地说，我们证明了第三开普勒定律，或相应的离心力和牛顿引力之间的平衡条件，意味着行星轨道动量有效地成为一个函数的行星距离作为唯一的变量，反之亦然。然后，行星距离的近似由其一阶泰勒展开行星轨道动量保持一个指数形式对应的提丢斯-波德规则。这样，它是没有必要假设指数形式的行星距离（因为它已经这样做的Scardigli），但只有离散值的论点。从物理上讲，它只是意味着，在线性近似下，“量子化”的行星轨道动量做几何级数。
英文摘要：
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.
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