Frontiers in Astronomy and Space Sciences (Aug 2014)
Orbital motions as gradiometers for post-Newtonian tidal effects
Abstract
The direct long-term changes occurring in the orbital dynamics of a local gravitationally bound binary system S due to the post-Newtonian tidal acceleration caused by an external massive source are investigated. A class of systems made of a test particle m rapidly orbiting with orbital frequency nb an astronomical body of mass M which, in turn, slowly revolves around a distantobject of mass M with orbital frequency nb'<< □ nb is considered. The characteristic frequenciesof the non-Keplerian orbital variations of m and of M itself are assumed to be negligible withrespect to both nb and nb'. General expressions for the resulting Newtonian and post-Newtoniantidal orbital shifts of m are obtained. The future missions BepiColombo and JUICE to Mercuryand Ganymede, respectively, are considered in view of a possible detection. The largest effects,of the order of □ 0:1 □□ 0:5 milliarcseconds per year (mas yr□□1), occur for the Ganymede orbiterof the JUICE mission. Although future improvements in spacecraft tracking and orbit determina14tion might, perhaps, reach the required sensitivity, the systematic bias represented by the otherknown orbital perturbations of both Newtonian and post-Newtonian origin would be overwhel16ming. The realization of a dedicated artificial mini-planetary system to be carried onboard andEarth-orbiting spacecraft is considered as well. Post-Newtonian tidal precessions as large as1 □□ 102 mas yr□□1 could be obtained, but the quite larger Newtonian tidal effects would be amajor source of systematic bias because of the present-day percent uncertainty in the product of the Earth’s mass times the Newtonian gravitational parameter.
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