土星、行星X/涅墨西斯和MOND的近日点进动
The perihelion precession of Saturn, planet X/Nemesis and MOND
摘要：
我们表明，土星逆行近日点进动Δ \dot \varpi，最近由不同的天文学家团队通过处理卡西尼号航天器的测距数据估计，相当于每世纪几毫角秒，可以用一个局部的，遥远的天体X来解释，还没有直接发现。通过确定它的潮汐参数K = GM_X/r_X^3作为它的黄道经度λ_X和纬度β_X的函数，我们计算出X在不同质量值下可能存在的距离，从火星大小到太阳大小不等。最小距离发生在X垂直于黄道的位置，而最大距离发生在X位于黄道的位置。我们发现，火星和地球大小的岩石冰行星，它们将分别在大约80-150 au，而一个木星大小的气态巨星将在大约1 kau。一颗典型的褐矮星的质量约为4 kau，而一颗与太阳质量相当的天体的质量约为10 kau，因此它不可能是涅墨西斯，因为涅墨西斯的太阳质量和日心距离被预测为88 kau。如果X指向一个特定的方向，即银河系中心的方向，它将模仿最近在修正牛顿动力学（MOND）框架内提出的外场效应（EFE）的作用。
英文摘要：
We show that the retrograde perihelion precession of Saturn Δ\dot\varpi, recently estimated by different teams of astronomers by processing ranging data from the Cassini spacecraft and amounting to some milliarcseconds per century, can be explained in terms of a localized, distant body X, not yet directly discovered. From the determination of its tidal parameter K = GM_X/r_X^3 as a function of its ecliptic longitude λ_X and latitude β_X, we calculate the distance at which X may exist for different values of its mass, ranging from the size of Mars to that of the Sun. The minimum distance would occur for X located perpendicularly to the ecliptic, while the maximum distance is for X lying in the ecliptic. We find for rock-ice planets of the size of Mars and the Earth that they would be at about 80-150 au, respectively, while a Jupiter-sized gaseous giant would be at approximately 1 kau. A typical brown dwarf would be located at about 4 kau, while an object with the mass of the Sun would be at approximately 10 kau, so that it could not be Nemesis for which a solar mass and a heliocentric distance of about 88 kau are predicted. If X was directed towards a specific direction, i.e. that of the Galactic Center, it would mimick the action of a recently proposed form of the External Field Effect (EFE) in the framework of the MOdified Newtonian Dynamics (MOND).
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