General relativistic laser interferometric observables of the GRACE-Follow-On mission

Abstract

We develop a high-precision model for laser ranging interferometric (LRI) observables of the GRACE Follow-On (GRACE-FO) mission. For this, we study the propagation of an electromagnetic wave in the gravitational field in the vicinity of an extended body, in the post-Newtonian approximation of the general theory of relativity. We present a general relativistic model for the phase of a plane wave that accounts for contributions of all the multipoles of the gravitating body, its angular momentum, as well as the contribution of tidal fields produced by external sources. We develop a new approach to model a coherent signal transmission in the gravitational field of the solar system that relies on a relativistic treatment of the phase. We use this approach to describe high-precision interferometric measurements on GRACE-FO and formulate the key LRI observables, namely the phase and phase rate of a coherent laser link between the two spacecraft. We develop a relativistic model for the LRI-enabled range between the two GRACE-FO spacecraft, accurate to less than 1 nm, and a high-precision model for the corresponding range rate, accurate to better than 0.1 nm/s. We also formulate high-precision relativistic models for the double one-way range (DOWR) and DOWR-enabled range rate observables originally used on GRACE and now studied for interferometric measurements on GRACE-FO. Our formulation justifies the basic assumptions behind the design of the GRACE-FO mission and highlights the importance of achieving nearly circular and nearly identical orbits for the GRACE-FO spacecraft.

Diffraction of electromagnetic waves in the gravitational field of the Sun

“…These equations determine the direction of light propagation and related relativistic frequency shifts [43,44]. However, geodesic equations provide no information about gravitationally induced changes in the intensity of light.…”

“…If needed, one can account for the contribution of the higher-order multipoles using the tools developed in [42,43]. Limiting our discussion to the monopole given by (B15), we have…”

Influences of dark energy and dark matter on gravitational time advancement

“…The GRACE-FO, which is scheduled for launch in 2017, will be equipped with a laser ranging interferometer and is expected to provide a range with an accuracy of 1 nm. With such a level of accuracy general-relativistic effects may become significant [63]. It is, therefore, important to examine whether the time advancement can have any significant effect on the observables of GRACE-FO.…”

Satellite Remote Sensing of the Greenland Ice Sheet Ablation Zone: A Review

“…GRACE-FO uses the same orbital acceleration measurement technology as the original GRACE mission and will continue the GRACE measurement time series for a planned ten years. In addition to providing gravity time series continuity, GRACE-FO will test a laser ranging interferometer that is expected to improve the satellite-to-satellite distance measurement relative to the GRACE microwave ranging system [42,43]. Following a period of in-orbit checks, GRACE-FO entered the science phase of its mission in January 2019 [249].…”