Erratum: First-order post-Newtonian analysis of the relativistic tidal effects for satellite gradiometry and the Mashhoon-Theiss anomaly [Phys. Rev. D93, 044057 (2016)]

Abstract

We would like to make the following amendments to the paper: 1. In Eqs. (11a), (11b), (11c), and (11d), the indices of the matrix K N , K GE , K GM , and K LT must all be lower indices. The correct expressions should be ðK N Þ μν in Eq. (11a), ðK GE Þ μν in Eq. (11b), ðK GM Þ μν in Eq. (11c), and ðK LT Þ μν in Eq. (11d). 2. In Eq. (11d), the (3, 3) element is 0, which is missed. 3. In Eq. (22b), the (2, 3) and (3, 2) elements must be replaced by − 1 4 sin i½Ψðcos 2Ψ þ 1Þ þ sin 2Ψ: We are grateful to Neil Ashby for pointing out the typos in Eq. (22b).

Secular gravity gradients in non-dynamical Chern–Simons modified gravity for satellite gradiometry measurements

“…here K G R (i)( j) agrees exactly with the former result derived in [37]. Due to the relativistic precessions of the free-falling local frame and the orbit plane, the modulations of Newtonian tidal tensor given in Eq.…”

“…It was firstly noticed by Mashhoon and Theiss [22,[34][35][36] that along orbit motions relativistic secular tidal effects that growing with time may exist (known as the Mashhoon-Theiss anomaly), which would greatly improve the measurement accuracy of relativistic tidal components. Recently, the physical mechanism behind such secular tidal effects had been studied and explained in [37,38]. From the post-Newtonian (PN) point of view, the difference between the relativistic precession of the local free-falling frame (or the parallel transported measurement axes) and the orbit plane with respect to the sidereal frame will produce modulations of Newtonian tidal forces along certain axes and then gives rise to periodic secular tidal signals [37,39].…”

“…Recently, the physical mechanism behind such secular tidal effects had been studied and explained in [37,38]. From the post-Newtonian (PN) point of view, the difference between the relativistic precession of the local free-falling frame (or the parallel transported measurement axes) and the orbit plane with respect to the sidereal frame will produce modulations of Newtonian tidal forces along certain axes and then gives rise to periodic secular tidal signals [37,39]. Back to the tests of the CS modified gravity, in the far field expansion of the non-dynamical theory, the CS gravity will add modifications to the GM sector of GR [12,13], and therefore will give rise to new secular tidal effects that could be read out precisely along certain measurement axes of an orbiting gradiometer.…”

Towards constraining parity-violations in gravity with satellite gradiometry

“…As ζ → 0, these PN tidal tensors K GE (i)( j) and K GM (i)( j) agree exactly with the results from GR that obtained in [23,28]. Due to the relativistic precessions of the free-falling local frame and the orbit plane, the modulations of Newtonian tidal tensor given in eq.…”

“…Relativistic gravitational experiments with satellite gradiometry was first studied in 1980s [22,23,24], and it is noticed by Mashhoon and Theiss [22,26,27,25] that the existence of secular gravity gradients or tidal effects in local free-falling frames along orbit motions (known as the Mashhoon-Theiss anomaly) would greatly improve the measurement accuracy. The physical mechanism behind such secular tidal effects had been clarified in [28,29], which can also be explained in terms of the modulations of Newtonian tidal forces along certain axes due to relativistic differential precessions of local free-falling frames and the orbit planes [28,30]. The GOCE satellite [35], launched in March 2009, carried a high sensitive 3-axis electro-static gravity gradiometer to map out the details of the geopotential of Earth, which had reached the sensitivity level about 10 mE/Hz 1/2 in the frequency band of 5 ∼ 100 mHz.…”