Abstract. We describe two techniques for fast multiple-precision evaluation of linearly convergent series, including power series and Ramanu-

No abstract

The integration of differential equations is a fundamental tool in the problem of orbit determination. In the present study, we focus on the accuracy assessment of numerical integrators in what refers to the categories of single-step and multistep methods. The investigation is performed in the frame of current satellite gravity missions i.e. Gravity Recovery and Climate Experiment (GRACE) and Gravity Field and steady-state Ocean Circulation Explorer (GOCE). Precise orbit determination is required at the level of a few cm in order to satisfy the primary missions' scope which is the rigorous modelling of the Earth's gravity field. Therefore, the orbit integration errors are critical for these low earth orbiters. As the result of different schemes of numerical integration is strongly affected by the forces acting on the satellites, various validation tests are performed for their accuracy assessment. The performance of the numerical methods is tested in the analysis of Keplerian orbits as well as in real dynamic orbit determination of GRACE and GOCE satellites by taking into account their sophisticated observation techniques and orbit design. Numerical investigation is performed in a wide range of the fundamental integrators' parameters i.e. the integration step and the order of the multistep methods.

<p>Precise orbit determination is a major objective in satellite geodesy and data analysis of several satellite missions observing Earth or another planet. Satellite gravity missions such as the Gravity Recovery And Climate Experiment (GRACE) Follow-On mission, require high level of orbit precision (cm level) in order to capture the gravity field modelling of static and time-variable components. The mission’s on-board accelerometers form a key instrument for the direct measurement of non-gravitational perturbations. The accelerometry data processing is crucial for accelerometers with reduced performance following the launch into space such as the case of one of the GRACE-FO satellites. The current study focuses on the GRACE-FO accelerometer calibration modelling within a scheme of precise orbit determination. In particular, the estimation of accelerometer calibration parameters includes bias, drift and scale factors in combination with a minimum number of empirical forces of cycle-per-revolution terms and bias accelerations. The consideration of such empirical perturbations aims at capturing periodic mismodelling effects and accelerometer data errors. The applied approach leads to orbital residuals varying within a few mm to cm while the inter-satellite LRI and KBR range-rate data residuals vary within a few μm/sec.</p>

The ocean tide is the most energetic water mass redistribution changing the Earth's gravity field periodically once and twice per day. Its significant perturbation on motion of near-Earth orbiting satellites was reported soon after the birth of satellite geodesy (Kaula, 1966; Lambeck et al., 1974). For example, a few μ gal (10 −8 m/ s 2) of gravitational acceleration exerted by ocean tidal mass change on a satellite at 1,000 km altitude may yield several meters of perturbation with periods of several days or longer due to resonant amplification (Schwintzer, 1997). Since that time, accounting for tidal variations in the geopotential has been routine practice in global gravity field analysis and spacecraft orbit determination, a necessary first step to study other geophysical processes causing smaller perturbations (Lambeck, 1988; Petit & Luzum, 2010). Numerous ocean tide models have been developed on global and regional domains and at various spatial scales using hydrodynamic numerical modeling, in situ data, and satellite measurements (Stammer et al., 2014). In addition to satellite altimeter measurements of tidal sea level change (Le Provost et al., 1995), satellite gravity measurements of tidal mass change from Gravity Recovery and Climate Experiment (GRACE)