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R. Neuhaeuser, J. V. Feitzinger. A generalized distance formula for planetary and satellite systems. Astronomy and Astrophysics, 1986, 170(1): 174-178.

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  • 标题: 太阳系行星、规则卫星距离规律的物理意义Physical Significance of the Distance Law of Planets and Reg-ular Satellites

    作者: 李金宝

    关键字: 行星, 规则卫星, 距离规律, 开普勒第三定律, 星云盘Planet; Regular Satellite; Distance Law; Kepler’s Third Law; Nebula Disk

    期刊名称: 《Astronomy and Astrophysics》, Vol.1 No.2, 2013-04-30

    摘要: 太阳系形成演化过程中星云成盘状分布,在星云盘中星云绕太阳做开普勒运动。如果一个绕转体行星胎离中心天体的距离为R,它的公转周期为T,依据开普勒第三定律推导可证明位于1.5874R处的星云绕中心天体的公转周期恰好等于2T,因此:1) R处的行星胎与1.5874R处的星云发生“冲”、“上合”的位置将相对保持恒定;2) 两者之间的夹角180度时,轨道为R处的行星胎对轨道为1.5874R处星云摄动力总是在同一向径出现;3) 在相等的演化时间里,R处的行星胎与1.5874R处的星云在同一向径发生“冲”、“上合”的次数最多。在这三种因素的综合累积作用下,使星云盘在1.5874R处出现空隙并向轨道R处收缩,被行星胎吸积,因此两相邻行星、规则卫星距离比值在1.5874这个常数左右摆动。土星、天王星、海王星的光环缝是由于卫星的摄动形成,当一条光环缝距中心天体的距离为R,那么在1.5874R处存在一个对应的卫星。根据开普勒第三定律的准确表达式推导论证出太阳系行星、规则卫星距离规律由3个因子决定,1) 常数项1.5874;2) 行星、规则卫星轨道的偏心率(偏心率大者,则相邻外侧行星、规则卫星与其距离比值大);3) 行星、规则卫星自身质量(质量大者,则远离内侧行星、卫星,靠近外侧行星、卫星)。 In this paper, the nebula during the solar system formation period is assumed to be distributed in disk form, and the nebula material was rotating around the sun following Kepler’s laws. If the distance of a rotating planetary fetal from the sun is R and its period of revolution is T, the period of revolution of the nebula material at a distance of 1.5874R should be 2T following Kepler’s third law. Therefore, 1) the locations, where the collisions and the superior conjunctions for the planetary fetals at distances 1R and 1.5874R to occur, should keep invariant; 2) when their included angle is 180 degree, the disturbing force on the nebula at distance 1.5874R caused by the planetary fetal at distance R will appear at the same radius vector; 3) during the same evolution period, the number of collisions and superior conjunctions for them will be the most. Due to the integrated combining actions by the three factors mentioned above, the nebula disk at distance 1.5874R will form gaps to contract towards the planetary fetal at distance R, resulting to the fact that the distance ratios of two neighboring planets or satellites are usually around the constant 1.5874. The gaps in the rings of Saturn, Uranus and Neptune were just caused by disturbing forces of satellites based on the rules found, i.e., a ring gap at R usually corresponds to a satellite at distance 1.5874R. According to deduction from Kepler’s third law, the distance law of planets and regular satellites are decided by three factors, i.e., the constant 1.5874, the orbital eccentricity and the mass of the planet or satellite. The larger for the orbital eccentricity, the larger for the distance ratio; the larger mass for a planet or satellite, the larger distance from the planet or satellite inside and therefore closer to the ones outside.