[论文解读] A comment on the possibility of testing the Dvali-Gabadadze-Porrati gravity model with the outer planets of the Solar System

Lorenzo Iorio|arXiv (Cornell University)|Oct 25, 2005

Geophysics and Gravity Measurements被引用 4

一句话总结

本文研究了是否可以利用外太阳系行星（特别是卡西尼号数据中的土星）的轨道动力学来检验达瓦利-加布达德泽-波拉蒂（Dvali-Gabadadze-Porrati，简称DGP）膜世界引力模型。尽管该模型预测了与半长轴无关但依赖于轨道偏心率的微小长期近日点和平均近点角摄动，但当前的观测精度已排除了利用卡西尼号和盖亚任务现有或近未来数据进行探测的可能性。

ABSTRACT

The multidimensional braneworld gravity model by Dvali, Gabadadze and Porrati was primarily put forth to explain the observed acceleration of the expansion of the Universe without resorting to dark energy. One of the most intriguing features of such a model is that it also predicts small effects on the orbital motion of test particles which could be tested in such a way that local measurements at Solar System scales would allow to get information on the global properties of the Universe. Lue and Starkman derived a secular extra-perihelion \\omega precession of 5\ imes 10^-4 arcseconds per century, while Iorio showed that the mean longitude \\lambda is affected by a secular precession of about 10^-3 arcseconds per century. Such effects depend only on the eccentricities e of the orbits via second-order terms: they are, instead, independent of their semimajor axes a. Up to now, the observational efforts focused on the dynamics of the inner planets of the Solar System whose orbits are the best known via radar ranging. Since the competing Newtonian and Einsteinian effects like the precessions due to the solar quadrupole mass moment J2, the gravitoelectric and gravitomagnetic part of the equations of motion reduce with increasing distances, it would be possible to argue that an analysis of the orbital dynamics of the outer planets of the Solar System, with particular emphasis on Saturn because of the ongoing Cassini mission with its precision ranging instrumentation, could be helpful in evidencing the predicted new features of motion. In this note we investigate this possibility in view of the latest results in the planetary ephemeris field. Unfortunately, the current level of accuracy rules out this appealing possibility and it appears unlikely that Cassini and GAIA will ameliorate the situation.

研究动机与目标

• 评估外行星（尤其是土星）的轨道动力学是否可作为检验达瓦利-加布达德泽-波拉蒂膜世界引力模型的手段。
• 评估该模型预测的近日点和平均近点角的长期摄动（依赖于轨道偏心率但与半长轴无关）是否能被当前或未来的空间任务探测到。
• 确定卡西尼任务的高精度测距数据和盖亚天体测量任务是否能改善对DGP模型的约束。
• 考察外行星是否因在较大距离上牛顿效应与广义相对论效应的干扰减少，而成为比内行星更优的检验平台。

提出的方法

• 分析DGP模型预测的约5×10⁻⁴角秒/世纪的长期额外近日点摄动。
• 评估该模型预测的平均近点角约10⁻³角秒/世纪的长期摄动，同样依赖于轨道偏心率且与半长轴无关。
• 将这些DGP引起的效应与随距离增大而减弱的标准牛顿效应及后牛顿效应（如太阳J₂项、电致引力与磁致引力项）进行比较。
• 利用最新的行星星历表评估当前观测精度对测量外行星轨道参数的限制。
• 评估卡西尼测距与盖亚天体测量未来可能带来的精度提升潜力。

实验结果

研究问题

• RQ1 外行星（如土星）的轨道运动中能否探测到DGP模型预测的长期近日点摄动？
• RQ2 由于DGP摄动依赖于轨道偏心率而非半长轴，外行星是否比内行星更适合作为检验平台？
• RQ3 当前行星星历表中的观测不确定性在多大程度上限制了对外太阳系天体中DGP效应的探测？
• RQ4 卡西尼任务与盖亚空间任务的未来数据在多大程度上能显著提升对DGP型引力效应的探测灵敏度？

主要发现

• DGP模型预测的长期额外近日点摄动约为5×10⁻⁴角秒/世纪，与半长轴无关但依赖于轨道偏心率。
• 该模型还预测平均近点角存在约10⁻³角秒/世纪的长期摄动，同样与半长轴无关。
• 尽管外行星（如土星）在理论上因远离太阳导致相对论效应干扰减少而具备理论优势，但当前观测精度仍不足以探测这些DGP效应。
• 最新的行星星历表尚不足以通过外行星动力学对DGP模型进行有意义的检验。
• 即使拥有卡西尼任务的高精度数据和盖亚天体测量任务的数据，当前的观测精度仍不足以探测到预测的DGP引起的摄动。