Satellite orbit perturbations induced by tidal forces
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The restitution of the trajectory of near-Earth orbiting satellites with accuracies to some centimeters by evaluating precise tracking data, is essential in satellite geodesy for applications like station positioning, earth orientation parameter determination, altimetry, SAR interferometry, and gravity field recovery from observed satellite orbit perturbations. Besides the stationary gravitational geopotential and non-gravitational forces, tidal induced temporal variations of the potential have to be considered in the numerical integration of the satellite's equation of motion.
Perturbing orbit accelerations have to be modelled which are induced by direct and indirect tidal effects: (a) the tide generating potential through Moon, Sun and planets, (b) changes in the geopotential caused by deformations of the Earth due to Earth tides, and (c) changes in the geopotential caused by mass redistributions and associated loading deformations due to ocean and atmosphere tides.
The induced accelerations for a satellite in about 1000 km altitude amount to 1 (a), 0.2 (b) and 0.03 (c), respectively, in units of 10−6 m/s2. Even the small accelerations caused by the ocean tides in a height of 1000 km lead to periodic perturbations in the satellite's position with an amplitude of several meters and periods of some days to 100 days due to resonant amplifications.
Whereas the tide generating potential and the Earth tides can be modelled with a sufficiently high level of accuracy, the ocean tides are due to the broader spectrum more difficult to describe. Satellite tracking or altimeter data are therefore exploited to recover the principal constituents of the ocean tidal wave spectrum.
The overall spectrum of orbit perturbations due to tides can be analyzed analytically for a specified set of Keplerian orbit parameters with Lagrange's planetary equations in Kaula's formulation when inserting the disturbing tidal potential expressed e.g. by the coefficients of a spherical harmonic expansion. Such analyses are important in order to judge prior to numerical tracking data processing on the parameters which have to be modelled or to be solved for, or can be omitted due to a lack of sensitivity.
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