太阳系卫星圆规则轨道的禁区，R3BP
Forbidden zones for circular regular orbits of the Moons in Solar system, R3BP
摘要：
在前面，我们已经考虑了拉格朗日形式的三体问题的运动方程（这意味着考虑了三体之间的相对运动）。分析这样一个方程组，我们考虑了质量可忽略的小天体绕两个巨天体（它们在开普勒轨道上绕着它们共同的质心旋转）中的第二个天体运动的情况，假设第二个天体的质量小于中心天体的质量。在目前的发展中，我们已经导出了一个关键参数，它决定了第三个小天体相对于第二个天体（行星）的准圆周运动的性质。即通过对三体问题的运动方程进行几次近似，将系统归结为关键的Riccati型常微分方程。在R3 BP（限制性三体问题）的假设下，我们还注意到，如果关键的控制（无量纲）参数保持在0.001-0.01的范围内，上述Riccati型常微分方程应该具有不变的形式。这样一个惊人的事实，让我们评估禁区内太阳系的卫星轨道或距离的意义的区域（月球-行星之间），其中的小天体的运动可以预测是不稳定的，根据Riccati型的解决方案的基本特征。
英文摘要：
Previously, we have considered the equations of motion of the three-body problem in a Lagrange form (which means a consideration of relative motions of 3-bodies in regard to each other). Analyzing such a system of equations, we considered the case of small-body motion of negligible mass around the 2-nd of two giant-bodies (which are rotating around their common centre of masses on Kepler trajectories), the mass of which is assumed to be less than the mass of central body. In the current development, we have derived a key parameter that determines the character of quasi-circular motion of the small 3-rd body relative to the 2-nd body (Planet). Namely, by making several approximations in the equations of motion of the three-body problem, such the system could be reduced to the key governing Riccati-type ordinary differential equations. Under assumptions of R3BP (restricted three-body problem), we additionally note that Riccati-type ODEs above should have the invariant form if the key governing (dimensionless) parameter remains in the range 0.001-0.01. Such an amazing fact let us evaluate the forbidden zones for Moons orbits in the inner Solar system or the zones of the meanings of distances (between Moon-Planet) for which the motion of small body could be predicted to be unstable according to basic features of the solutions of Riccati-type.
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