太阳系对引力偶极子的限制
Solar System limits on gravitational dipoles
摘要：
哈久科维奇（Hadjukovic，2010）的引力偶极理论是基于反物质具有负引力质量的假设，因此在地球上向上下落。天体物理学上，该模型类似于修正牛顿动力学（MOND），但比MOND更基本，牛顿重力$g_{_N}$朝向一个孤立的点质量，由因子$ν= 1 + \left( α/x \right) \tanh \left( \sqrt{x}/α\right)$推动，其中$x \equiv g_{_N}/a_{_0}$和$a_{_0} = 1.2 \times 10^{-10}$ m/s $^2$是MOND加速度常数。我们表明，$α$必须位于范围${0.4-1}$，以可接受的适合星系旋转曲线。在太阳系中，这个内插函数意味着${αa_{_0}}$的额外向日加速度。这将导致土星在15年内偏离牛顿的预期${7000 \left( α/0.4 \right)}$公里，从已知的初始位置和速度开始在近圆形轨道上运行。我们证明，这一预测不应显着改变假设的偶极晕的其他行星，由于相当小的区域中，每个行星的重力占主导地位的太阳。土星的轨道应该同样不会受到外太阳系可能存在的第九颗行星的影响，也不会受到银河系引力的影响，银河系引力导致了距离太阳几个kAU的引力偶极子的非球形分布。对环绕土星运行的卡西尼号航天器进行的无线电跟踪表明，${5σ}$的${5σ}$偏离其常规计算轨迹的上限为160米。这些测量值意味着$α$的上限比与旋转曲线数据一致所需的最小值要严格得多。因此，没有$α$的值可以同时匹配所有可用的约束条件，以极高的意义证伪了当前形式的引力偶极子理论。
英文摘要：
The gravitational dipole theory of Hadjukovic (2010) is based on the hypothesis that antimatter has a negative gravitational mass and thus falls upwards on Earth. Astrophysically, the model is similar to but more fundamental than Modified Newtonian Dynamics (MOND), with the Newtonian gravity $g_{_N}$ towards an isolated point mass boosted by the factor $ν= 1 + \left( α/x \right) \tanh \left( \sqrt{x}/α\right)$, where $x \equiv g_{_N}/a_{_0}$ and $a_{_0} = 1.2 \times 10^{-10}$ m/s$^2$ is the MOND acceleration constant. We show that $α$ must lie in the range ${0.4-1}$ to acceptably fit galaxy rotation curves. In the Solar System, this interpolating function implies an extra Sunwards acceleration of ${αa_{_0}}$. This would cause Saturn to deviate from Newtonian expectations by ${7000 \left( α/0.4 \right)}$ km over 15 years, starting from known initial position and velocity on a near-circular orbit. We demonstrate that this prediction should not be significantly altered by the postulated dipole haloes of other planets due to the rather small region in which each planet's gravity dominates over that of the Sun. The orbit of Saturn should similarly be little affected by a possible ninth planet in the outer Solar System and by the Galactic gravity causing a non-spherical distribution of gravitational dipoles several kAU from the Sun. Radio tracking of the Cassini spacecraft orbiting Saturn yields a ${5σ}$ upper limit of 160 metres on deviations from its conventionally calculated trajectory. These measurements imply a much more stringent upper limit on $α$ than the minimum required for consistency with rotation curve data. Therefore, no value of $α$ can simultaneously match all available constraints, falsifying the gravitational dipole theory in its current form at extremely high significance.
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