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 n b an astronomical body of mass M which, in turn, slowly revolves around a distant object of mass M with orbital frequency n b n b is considered. The characteristic frequencies of the non-Keplerian orbital variations of m and of M itself are assumed to be negligible with respect to both n b and n b . General expressions for the resulting Newtonian and post-Newtonian tidal orbital shifts of m are obtained. The future missions BepiColombo and JUICE to Mercury and 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 orbiter of the JUICE mission. Although future improvements in spacecraft tracking and orbit determination might, perhaps, reach the required sensitivity, the systematic bias represented by the other known orbital perturbations of both Newtonian and post-Newtonian origin would be overwhelming. The realization of a dedicated artificial mini-planetary system to be carried onboard and Earth-orbiting spacecraft is considered as well. Post-Newtonian tidal precessions as large as ≈ 1 − 10 2 mas yr −1 could be obtained, but the quite larger Newtonian tidal effects would be a major source of systematic bias because of the present-day percent uncertainty in the product of the Earth's mass times the Newtonian gravitational parameter.

Solar system constraints onf(T) gravity

“…Thus, in the following, it is adequate to consider only the terms and . Lastly, note that the dimensions of the two parameters are The orbital effects of extra potentials having the functional forms of and have been incorporated analytically several times with a variety of different approaches in the framework of Solar system investigations (Islam ; Cardona & Tejeiro ; Kerr, Hauck & Mashhoon ; Kraniotis & Whitehouse ; Iorio , , ; Jetzer & Sereno ; Kagramanova, Kunz & Lammerzahl ; Sereno & Jetzer ; Adkins & McDonnell ; Adkins, McDonnell & Fell ; Sereno & Jetzer ), and they can be straightforwardly handled using, for instance, the standard Lagrange perturbative scheme (Bertotti, Farinella & Vokrouhlický ). From the equations for the variations of the osculating Keplerian orbital elements (Bertotti et al ), we immediately deduce that only the longitude of the pericentre ϖ ≐ Ω + ω (with Ω the longitude of the ascending node and ω the argument of the pericentre) and the mean anomaly undergo secular precessions due to the spherical symmetry of equations and and their time independence.…”

Out-of-Plane Equilibrium Points in the Photogravitational CR3BP with Oblateness and P-R Drag

“…Researchers like Bruno (1994), Gutzwiller (1998), Valtonen & Karttunen (2006) and Chenciner (2007) investigated the complete solution of the general three-body problem. There are also various forms of three-body problems in general relativity (Fokker 1921;Nordvedt 1968;Renzetti 2012;Iorio 2014). The restricted three-body problem describes the motion of a particle of negligible mass in the vicinity of two massive bodies, called primaries, which move in circular orbits around their common center of mass, on account of their mutual gravitational attraction.…”

Triangular Libration Points in the CR3BP with Radiation, Triaxiality and Potential from a Belt

“…The presence of parameters p, σ 1 , σ 2 , M b in the Eq. (10) show that the coordinates are affected by the radiation of the bigger primary, triaxiality of the smaller primary and the gravitational potential from the belt.…”

“…The collinear libration points L 1 , L 2 , L 3 are unstable, while the triangular libration points L 4 , L 5 are stable for the mass ratio of the primaries less than 0.03852 · · · , [38]. The 3BP, under different forms and aspects, has been used for studies in fundamental physics, general relativity and alternative theories of gravity [1,2,5,10,20,24,31,41].…”