先锋/林德勒型加速度对奥尔特云的影响
Impact of a Pioneer/Rindler-type acceleration on the Oort cloud
摘要：
根据最近修正的大距离引力模型，在满足一定条件的情况下，Rindler型的径向常数和均匀附加加速度A_Rin作用于中心质量M的静态场中的测试粒子p。除此之外，它被认为是对先锋号异常的一部分的潜在可行的解释。我们研究了一个像|A_Rin| \sim 10^-10 m s^-2那样大的反常林德勒项对奥尔特云中一个典型天体的轨道动力学的影响，该天体的自能远小于其假定的林德勒能量。假设一颗典型的彗星在奥尔特云的整个扩展范围内（0.02 pc-1 pc）沿着一个高度偏心和倾斜的轨道运动，结果表明，增加一个向外的林德勒式加速度，即A_Rin > 0，不允许轨道束缚。相反，如果A_Rin < 0，则得到的数值积分轨迹在空间上是有限的，但它与标准开普勒椭圆完全不同。特别是，彗星的日心距离明显减少，并经历高频振荡，其速度增加，轨迹的整体模式是相当各向同性的。因此，奥尔特云的标准图像被彻底改变，因为它修改后的轨道对银河潮汐和附近经过的恒星的干扰作用不那么敏感，在标准场景中，这些影响是我们对云本身存在的信心所依据的现象学的原因。目前的分析可能会补充在未来的进一步统计蒙特卡洛型调查随机变化的彗星的初始条件。
英文摘要：
According to a recent modified model of gravity at large distances, a radial constant and uniform extra-acceleration A_Rin of Rindler type acts upon a test particle p in the static field of a central mass M if certain conditions are satisfied. Among other things, it was proposed as a potentially viable explanation of a part of the Pioneer anomaly. We study the impact that an anomalous Rindler-type term as large as |A_Rin| \sim 10^-10 m s^-2 may have on the the orbital dynamics of a typical object of the Oort cloud whose self-energy is quite smaller than its putative Rindler energy. By taking a typical comet moving along a highly eccentric and inclined orbit throughout the expected entire extension of the Oort cloud (0.02 pc-1 pc), it turns out that the addition of an outward Rindler-like acceleration, i.e. for A_Rin > 0, does not allow bound orbits. Instead, if A_Rin < 0, the resulting numerically integrated trajectory is limited in space, but it radically differs from the standard Keplerian ellipse. In particular, the heliocentric distance of the comet gets markedly reduced and experiences high frequency oscillations, its speed is increased, and the overall pattern of the trajectory is quite isotropic. As a consequence, the standard picture of the Oort cloud is radically altered since its modified orbits are much less sensitive to the disturbing actions of the Galactic tide and nearby passing stars whose effects, in the standard scenario, are responsible for the phenomenology on which our confidence in the existence of the cloud itself is based. The present analysis may be supplemented in future by further statistical Monte Carlo-type investigations by randomly varying the initial conditions of the comets.
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